Thermal Physics Questions

The specific latent heat of vaporization of a substance is the quantity of energy required to A. raise the temperature of a unit mass of a substance by one degree Celsius. B. convert a unit mass of liquid to vapour at constant temperature and pressure. C. convert a unit mass of solid to vapour at constant temperature and pressure. D. convert a unit mass of liquid to vapour at a temperature of 100°C and a pressure of one atmosphere. Thermal energy is transferred through the glass windows of a house mainly by A. conduction. B. radiation. C. conduction and convection. D. radiation and convection. Thermal energy is transferred through the glass windows of a house mainly by A. conduction. B. radiation. C. conduction and convection. D. radiation and convection. Some students were asked to design and carry out an experiment to determine the specific latent heat of vaporization of water. They set up the apparatus shown below. The current was switched on and maintained constant using the variable resistor. The readings of the voltmeter and the ammeter were noted. When the water was boiling steadily, the reading of the top-pan balance was taken and, simultaneously, a stopwatch was started. The reading of the top-pan balance was taken again after 200 seconds and then after a further 200 seconds. The change in reading of the top-pan balance during each 200 second interval was calculated and an average found. The power of the heater was calculated by multiplying together the readings of the voltmeter and the ammeter. (a) Suggest how the students would know when the water was boiling steadily. ..................................................................................................................................... ..................................................................................................................................... (1) (b) Explain why a reading of the mass lost in the first 200 seconds and then a reading of the mass lost in the next 200 second interval were taken, rather than one single reading of the mass lost in 400 seconds. (2) ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... The students repeated the experiment for different powers supplied to the heater. A graph of the power of the heater against the mass of water lost (the change in balance reading) in 200 seconds was plotted. The results are shown below. (Error bars showing the uncertainties in the measurements are not shown.) (c) (i) On the graph above, draw the best-fit straight line for the data points. (1) (ii) Determine the gradient of the line you have drawn. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) In order to find a value for the specific latent heat of vaporization L, the students used the equation P = mL, where P is the power of the heater and m is the mass of water evaporated per second. (d) Use your answer for the gradient of the graph to determine a value for the specific latent heat of vaporization of water. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (e) The theory of the experiment would suggest that the graph line should pass through the origin. Explain briefly why the graph does not pass through the origin. ..................................................................................................................................... ..................................................................................................................................... (2) (Total 12 marks)

Two different objects are in thermal contact with one another. The objects are at different temperatures. The temperatures of the two objects determine A. the process by which thermal energy is transferred. B. the heat capacity of each object. C. the direction of transfer of thermal energy between the objects. D. the amount of internal energy in each object.

The specific heat capacity of a metal block of mass m is determined by placing a heating coil in its centre, as shown in the diagram above. The block is heated for time t and the maximum temperature change recorded is Δθ. The ammeter and voltmeter readings during the heating are I and V respectively. The specific heat capacity is best calculated using which one of the following expressions? A. c = B. c = C. c = D. c =

The specific heat capacity of a metal block of mass m is determined by placing a heating coil in its centre, as shown in the diagram above. The block is heated for time t and the maximum temperature change recorded is Δθ. The ammeter and voltmeter readings during the heating are I and V respectively. Which one of the following is not a source of error in the experiment? A. Some thermal energy is retained in the heater. B. The thermometer records the temperature at one point in the block. C. Some thermal energy is lost from the variable resistor in the circuit. D. The block is heated at its centre, rather than throughout its whole volume. (1)

A container holds 20 g of neon (mass number 20) and also 8 g of helium (mass number 4). What is the ratio ? A. 0.4 B. 0.5 C. 2.0 D. 2.5 This question is about modelling the thermal processes involved when a person is running. When running, a person generates thermal energy but maintains approximately constant temperature. (a) Explain what thermal energy and temperature mean. Distinguish between the two concepts. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) The following simple model may be used to estimate the rise in temperature of a runner assuming no thermal energy is lost. A closed container holds 70 kg of water, representing the mass of the runner. The water is heated at a rate of 1200 W for 30 minutes. This represents the energy generation in the runner. (b) (i) Show that the thermal energy generated by the heater is 2.2 × 106 J. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) Calculate the temperature rise of the water, assuming no energy losses from the water. The specific heat capacity of water is 4200 J kg−1 K−1. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (c) The temperature rise calculated in (b) would be dangerous for the runner. Outline three mechanisms, other than evaporation, by which the container in the model would transfer energy to its surroundings. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (6) A further process by which energy is lost from the runner is the evaporation of sweat. (d) (i) Describe, in terms of molecular behaviour, why evaporation causes cooling. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (ii) Percentage of generated energy lost by sweating: 50%
Specific latent heat of vaporization of sweat: 2.26 × 106 J kg−1 Using the information above, and your answer to (b) (i), estimate the mass of sweat evaporated from the runner. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (iii) State and explain two factors that affect the rate of evaporation of sweat from the skin of the runner. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 25 marks)

This question is about estimating the area of solar panels and the diameter of a wind turbine. It is suggested that a combination of solar power and wind power be used to provide the hot water system in a house. An active solar heater is to provide the energy to heat the water. A wind turbine is to provide the energy to pump the water. Solar heater The following data are available: volume of hot water tank = 1.2 m3 density of water = 1.0 ×103 kg m−3 initial temperature of the water = 10°C final temperature of the water = 40°C specific heat capacity of water = 4.2 × 103 J kg−1K−1 average power per unit area from the Sun = 0.80 kW m−2 time required to heat the water = 2.0 hours (a) Using the above data, (i) deduce that 1.5 × 108 J of energy is required to heat the volume of water in the tank from 10°C to 40°C. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) estimate the minimum area of the solar panel needed to provide 1.5 × 108 J of energy in 2.0 hours. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (iii) discuss whether, in this situation, using a solar panel to heat the water is a sensible method. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) Wind turbine The following data are available: power of solar heater pump = 0.4 kW average local wind speed = 6.0 m s−1 average density of air = 1.0 kg m−3 (b) (i) Using the above data, estimate the minimum radius of the wind turbine needed to provide the power required to drive the solar heater pump. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (ii) Discuss whether, in this situation, using a wind turbine to pump the water is a sensible method. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (1) (Total 10 marks)

Which two values of temperature are equivalent to the nearest degree when measured on the Kelvin and on the Celsius scales of temperature? | Kelvin scale | Celsius scale | A. | 40 | 313 | B. | 273 | 100 | C. | 313 | 40 | D. | 373 | 0 | A sample of an ideal gas is held in an insulated container and it undergoes an adiabatic change. The graph below shows the change in pressure p with change in volume V as the gas changes from X to Y. Which of the following describes correctly the work done and the change in the internal energy of the gas? | Work done | Internal energy | A. | on the gas | increases | B. | on the gas | decreases | C. | by the gas | decreases | D. | by the gas | increases | A substance changes from solid to liquid at its normal melting temperature. What change, if any, occurs in the average kinetic energy and the average potential energy of its molecules? | Average kinetic energy | Average potential energy | A. | constant | constant | B. | increases | constant | C. | increases | decreases | D. | constant | increases | (1)

The specific latent heat of vaporization of a substance is greater than its specific latent heat of fusion because A. boiling takes place at a higher temperature than melting. B. thermal energy is required to raise the temperature from the melting point to the boiling point. C. the volume of the substance decreases on freezing but increases when boiling. D. the increase in potential energy of the molecules is greater on boiling than on melting. (1)

The kelvin temperature of an object is a measure of A. the total energy of the molecules of the object. B. the total kinetic energy of the molecules of the object. C. the maximum energy of the molecules of the object. D. the average kinetic energy of the molecules of the object. The specific latent heat of fusion of a substance is defined as the amount of thermal energy required to change the phase of A. the substance at constant temperature. B. unit mass of the substance to liquid at constant temperature. C. unit mass of the substance at constant temperature. D. the substance to gas at constant temperature. (1)

A small lump of ice (a hailstone) at 0°C falls to the Earth’s surface. When the hailstone hits the surface, all of the kinetic energy of the hailstone is transferred to thermal energy in the ice. Calculate the minimum speed of the hailstone so that it just melts when it hits the surface. The specific latent heat of fusion of ice is 340 kJ kg–1. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (b) By reference to your answer in (a), suggest whether hailstones are likely to melt on hitting the Earth’s surface. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 5 m This question is about wind turbines. (a) State two factors that affect the maximum theoretical power output of a wind turbine. ..................................................................................................................................... ..................................................................................................................................... (2) A wind farm is to be built to supply electrical energy to a small town. The following data is available. Energy consumption for the town for 1 year = 5.0 × 107 kWh
Length of turbine blade = 20.0 m
Average wind speed = 8.0 ms–1
Density of air = 1.1 kg m–3
1 year = 3.2 × 107 s (b) Deduce from this data that approximately 16 wind turbines are required. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (5) (c) State three reasons why in fact more than 16 turbines will be needed. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 10 marks)

This question is about gases and specific heat capacity. (a) State what is meant by an ideal gas. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) An ideal gas occupies a volume of 1.2 m3 at a temperature of 27°C and a pressure of 1.0 × 105 Pa. The density of the gas is 1.6 kg m–3. It is found that 1.5 × 104 J of energy is required to raise the temperature of the gas to 52°C when the gas is held at constant volume. (b) Determine the specific heat capacity at constant volume of the gas. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (c) A second sample of the same gas as above is heated from 27°C to 52°C at constant pressure. (i) Show that the volume of the gas at 52°C is 1.3 m3. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) Calculate the work done by the gas during the heating process. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (d) The specific heat capacity for the gas kept at constant volume is different to that when the gas is kept at constant pressure. State and explain whether the specific heat capacity for an ideal gas at constant pressure is greater or less than the specific heat capacity of the gas at constant volume. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 12 marks)

The distance between the 0°C and 100°C marks on a mercury-in-glass thermometer is 20 cm. When the thermometer bulb is placed in a mixture of ice and salt, the mercury level is 4 cm below the 0°C mark. The temperature of the mixture is A. +20°C. B. +5°C. C. –5°C. D. –20°C. Some liquid is contained in a shallow dish that is open to the atmosphere. The rate of evaporation of the liquid does not depend on A. the temperature of the liquid. B. the temperature of the atmosphere. C. the depth of the liquid. D. the pressure of the atmosphere. (1)

The equation of state for an ideal gas, pV = nRT, describes the behaviour of real gases A. only at low pressures and large volumes. B. only at high temperatures. C. only at large volumes and large pressures. D. at all pressures and volumes. The temperature of an ideal gas is reduced. Which one of the following statements is true? A. The molecules collide with the walls of the container less frequently. B. The molecules collide with each other more frequently. C. The time of contact between the molecules and the wall is reduced. D. The time of contact between molecules is increased. This question is about the change of phase (state) of ice. A quantity of crushed ice is removed from a freezer and placed in a calorimeter. Thermal energy is supplied to the ice at a constant rate. To ensure that all the ice is at the same temperature, it is continually stirred. The temperature of the contents of the calorimeter is recorded every 15 seconds. The graph below shows the variation with time t of the temperature θ of the contents of the calorimeter. (Uncertainties in the measured quantities are not shown.) (a) On the graph above, mark with an X, the data point on the graph at which all the ice has just melted. (1) (b) Explain, with reference to the energy of the molecules, the constant temperature region of the graph. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) The mass of the ice is 0.25 kg and the specific heat capacity of water is 4200 J kg–1 K–1. (c) Use these data and data from the graph to (i) deduce that energy is supplied to the ice at the rate of about 530 W. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (ii) determine the specific heat capacity of ice. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (iii) determine the specific latent heat of fusion of ice. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (Total 12 marks)

This question is about p–V diagrams. The graph below shows the variation with volume of the pressure of a fixed mass of gas when it is compressed adiabatically and also when the same sample of gas is compressed isothermally. (a) State and explain which line AB or AC represents the isothermal compression. ..................................................................................................................................... ..................................................................................................................................... (2) (b) On the graph, shade the area that represents the difference in work done in the adiabatic change and in the isothermal change. (1) (c) Determine the difference in work done, as identified in (b). ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (d) Use the first law of thermodynamics to explain the change in temperature during the adiabatic compression. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 9 marks)

A temperature scale is to be constructed using the property X of a substance. Which of the following must be a characteristic of the property X? A. The value of the property must be zero at zero kelvin. B. The property must increase with increase of temperature. C. The property must have a different value at each temperature to be measured. D. The value of the property must vary linearly with kelvin temperature. (1)

Which of the following is not an assumption on which the kinetic model of an ideal gas is based? A. All molecules behave as if they are perfectly elastic spheres. B. The mean-square speed of the molecules is proportional to the kelvin temperature. C. Unless in contact, the forces between molecules are negligible. D. The molecules are in continuous random motion. As part of an experiment to determine the latent heat of vaporisation of water, a student boils some water in a beaker using an electric heater as shown below. The student notes two sources of error. Error 1: thermal energy is lost from the sides of the beaker
Error 2: as the water is boiling, water splashes out of the beaker Which of the following gives the correct effect of these two errors on the calculated value for the specific latent heat? | Error 1 | Error 2 | A. | Increase | Decrease | B. | Increase | No change | C. | Decrease | Increase | D. | Decrease | No change | (1)

This question is about specific heat capacity and specific latent heat. (a) Define specific heat capacity. ..................................................................................................................................... ..................................................................................................................................... (1) (b) Explain briefly why the specific heat capacity of different substances such as aluminium and water are not equal in value. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) A quantity of water at temperature θ is placed in a pan and heated at a constant rate until some of the water has turned into steam. The boiling point of the water is 100°C. (c) (i) Using the axes below, draw a sketch-graph to show the variation with time t of the temperature θ of the water. (Note: this is a sketch-graph; you do not need to add any values to the axes.) (1) (ii) Describe in terms of energy changes, the molecular behaviour of water and steam during the heating process. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) Thermal energy is supplied to the water in the pan for 10 minutes at a constant rate of 400 W. The thermal capacity of the pan is negligible. (d) (i) Deduce that the total energy supplied in 10 minutes is 2.4 × 105 J. ........................................................................................................................... (1) (ii) Using the data below, estimate the mass of water turned into steam as a result of this heating process. initial mass of water = 0.30 kg initial temperature of the water θ = 20°C specific heat capacity of water = 4.2 × 103 J kg–1 K–1 specific latent heat of vaporization of water = 2.3 × 106 Jkg–1 ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (iii) Suggest one reason why this mass is an estimate. ........................................................................................................................... ........................................................................................................................... (1) (Total 14 marks)

Which of the following is the internal energy of a system? A. The total thermal energy gained by the system during melting and boiling. B. The sum of the potential and the kinetic energies of the particles of the system. C. The total external work done on the system during melting and boiling. D. The change in the potential energy of the system that occurs during melting and boiling. (1)

During an experiment, a solid is heated from 285 K to 298 K. Which one of the following gives the rise in temperature, in deg C, and the final temperature, in °C, of the solid? | Rise in temperature in deg C | Final temperature in °C | A. | 13 | 571 | B. | 13 | 25 | C. | 286 | 571 | D. | 286 | 25 | (1)

A liquid is contained in a dish open to the atmosphere. Which one of the following contains three factors that affect rate of evaporation of the liquid? A. | Temperature of the liquid | Surface area | Specific latent heat of vaporization | B. | Temperature of the liquid | Mass of liquid | Specific latent heat of vaporization | C. | Surface area | Mass of liquid | Temperature of the liquid | D. | Mass of liquid | Surface area | Specific latent heat of vaporization | (1)

The equation of state of an ideal gas is pV = nRT. In this equation, the constant n is the number of A. atoms in the gas. B. molecules in the gas. C. particles in the gas. D. moles of the gas. (1)

This question is about an experiment to measure the temperature of a flame. (a) Define heat (thermal) capacity. ..................................................................................................................................... ..................................................................................................................................... (1) A piece of metal is held in the flame of a Bunsen burner for several minutes. The metal is then quickly transferred to a known mass of water contained in a calorimeter. The water into which the metal has been placed is stirred until it reaches a steady temperature. (b) Explain why (i) the metal is transferred as quickly as possible from the flame to the water; ........................................................................................................................... ........................................................................................................................... (1) (ii) the water is stirred. ........................................................................................................................... ........................................................................................................................... (1) The following data are available: heat capacity of metal = 82.7 J K–1 heat capacity of the water in the calorimeter = 5.46 × 102 J K–1 heat capacity of the calorimeter = 54.6 J K–1 initial temperature of the water = 288 K final temperature of the water = 353 K (c) Assuming negligible energy losses in the processes involved, use the data to calculate the temperature T of the Bunsen flame. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 7 marks)

A liquid is evaporating, causing the liquid to cool.
The temperature of the liquid decreases because A. the number of liquid molecules is decreasing. B. the mean kinetic energy of the liquid molecules is decreasing. C. the pressure above the liquid surface is increasing. D. the rate of evaporation is increasing. Data analysis question At high pressures, a real gas does not behave as an ideal gas. For a certain range of pressures, it is suggested that the relation between the pressure P and volume V of one mole of the gas at constant temperature is given by the equation PV = A + BP where A and B are constants. In an experiment to measure the deviation of nitrogen gas from ideal gas behaviour, 1 mole of nitrogen gas was compressed at a constant temperature of 150 K. The volume V of the gas was measured for different values of the pressure P. A graph of the product PV of pressure and volume was plotted against the pressure P and is shown below. (Error bars showing the uncertainties in measurements are not shown). (a) Draw a line of best fit for the data points. (1) (b) Use the graph to determine the values of the constants A and B in the equation PV = A + BP. Constant A ………………………………................................................................. ………………………………................................................................. ………………………………................................................................. Constant B ………………………………................................................................. ………………………………................................................................. ………………………………................................................................. ………………………………................................................................. ………………………………................................................................. (5) (c) State the value of the constant B for an ideal gas. ..................................................................................................................................... (1) (d) The equation PV = A + BP is valid for pressures up to 6.0 × 107 Pa. (i) Determine the value of PV for nitrogen gas at a pressure of 6.0 × 107 Pa. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) Calculate the difference between the value of PV for an ideal gas and nitrogen gas when both are at a pressure of 6.0 × 107 Pa. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (e) In the original experiment, the pressure P was measured to an accuracy of 5% and the volume V was measured to an accuracy of 2%. Determine the absolute error in the value of the constant A. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 14 marks)

he specific latent heat of vaporization of a substance is defined as the amount of thermal energy required to A. change a liquid to vapour at constant pressure. B. change a liquid to vapour at constant temperature. C. change unit mass of liquid to vapour at constant pressure. D. change unit mass of liquid to vapour at constant temperature. (1)

A gas is contained in a cylinder fitted with a piston as shown below. When the gas is compressed rapidly by the piston its temperature rises because the molecules of the gas A. are squeezed closer together. B. collide with each other more frequently. C. collide with the walls of the container more frequently. D. gain energy from the moving piston. (1)

This question is about thermal physics. (a) Explain why, when a liquid evaporates, the liquid cools unless thermal energy is supplied to it. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (b) State two factors that cause an increase in the rate of evaporation of a liquid. 1. ................................................................................................................................. 2. ................................................................................................................................. (2) (c) Some data for ice and for water are given below. Specific heat capacity of ice = 2.1 × 103 J kg–1 K–1
Specific heat capacity of water = 4.2 × 103 J kg–1 K–1
Specific latent heat of fusion of ice = 3.3 × 105 J kg–1 A mass of 350 g of water at a temperature of 25°C is placed in a refrigerator that extracts thermal energy from the water at a rate of 86 W. Calculate the time taken for the water to become ice at –5.0°C. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 9 marks)

This question is about ideal gases and specific heat capacity. (a) (i) State, in terms of kinetic theory, what is meant by an ideal gas. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (ii) Explain why the internal energy of an ideal gas is kinetic energy only. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) A fixed mass of an ideal gas has a volume of 870 cm3 at a pressure of 1.00 × 105 Pa and a temperature of 20.0°C. The gas is heated at constant pressure to a temperature of 21.0°C. (b) (i) Calculate the change in volume of the gas. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (ii) Determine the external work done during this process. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (c) (i) Define specific heat capacity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) Explain what happens to the molecules of an ideal gas when the temperature of the gas is increased at constant volume. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (iii) Apply the first law of thermodynamics to show that, if the temperature of a gas is raised at constant pressure, the specific heat capacity of the gas is different from that when the temperature is raised at constant volume. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 17 marks)

Temperature is the only property that determines A. the total internal energy of a substance. B. the phase (state) of a substance. C. the direction of thermal energy transfer between two bodies in thermal contact. D. the process by which a body loses thermal energy to the surroundings. (1)

A substance is heated at a constant rate. The sketch graph shows the variation with time t of the temperature  of the substance. In which region or regions of the graph must there be more than one phase of the substance present? A. WX and YZ B. WX only C. WX, XY and YZ D. XY only (1)

Two ideal gases X and Y, are contained in a cylinder at constant temperature. The mass of the atoms of X is m and of Y is 4m. Which one of the following is the correct value of the ratio A. 1 B. 2 C. 4 D. 16 Container X below has volume V and holds n moles of an ideal gas at kelvin temperature T. Container Y has volume 2V and holds 3n moles of an ideal gas also at kelvin temperature T. The pressure of the gas in X is PX and in Y is PY. The ratio is A. B. C. 5. D. 6. The physics of cooling (a) Explain what is meant by the temperature of a substance. ................................................................................................................................... ................................................................................................................................... (2) A thermometer is placed in a liquid contained in an open beaker. The reading of the thermometer is recorded at regular intervals. The variation with time t of the temperature  is shown below. (b) The temperature of the surroundings is 20C. On the graph continue the line to show the variation with time of the temperature for the next 3000 s. (2) (c) By reference to the graph, state and explain the rate of loss of thermal energy from the substance between (i) 0 and 600 s; ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (ii) 600 and 1800 s. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) The mass of the liquid is 0.11 kg and the specific heat capacity of the liquid is 1300 J kg–1 K–1. (d) (i) Use the graph to deduce that the rate of loss of thermal energy at time t = 600 s is approximately 4 W. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (ii) Calculate the specific latent heat of fusion of the liquid. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (Total 16 marks)

his question is about an ideal gas. An ideal gas is contained in a cylinder fitted with a frictionless piston, as shown below. The piston has surface area A. A constant external pressure p acts on the piston. (a) Deduce that, for an increase in volume V of the gas, the external work done W is given by W = pV. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3) (b) The energy supplied to the gas for this increase in volume is found to be greater than pV. State and explain any change in the gas. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (Total 5 marks)

For a system that undergoes a small change of state, Q = U + W where +Q = thermal energy transferred to the system +U = increase in internal energy of the system +W = the work done by the system. In an adiabatic compression of an ideal gas, which one of the following is true in respect of Q, U and W? Q | U | W | A. | Zero | Positive | Negative | B. | Zero | Negative | Negative | C. | Positive | Positive | Positive | D. | Negative | Zero | Positive | (1)

The specific heat capacity c of a solid block of mass m is determined by heating the block and measuring its temperature. The graph below shows the variation of the temperature T of the block with the thermal energy Q transferred to the block. The gradient of the line is equal to A. B. C. mc. D. Which of the following correctly shows the changes, if any, in the potential energy and in the kinetic energy of the molecules of a solid as it melts? Potential energy | Kinetic energy | A. | Decreases | Increases | B. | Increases | Stays the same | C. | Stays the same | Decreases | D. | Stays the same | Stays the same | (1)

This question is about specific heat capacity and a domestic shower. (a) Define the term specific heat capacity. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (1) (b) Equal masses of two different solid substances A and B are at the same temperature. The specific heat capacity of substance A is greater than the specific heat capacity of substance B. The two substances now have their temperatures raised by the same amount. Explain which substance will have the greater increase in internal energy assuming both remain in the solid phase. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (c) In an experiment to measure the specific heat capacity of a metal, a piece of the metal is immersed in boiling water and left there for several minutes. It is then transferred quickly into some cold water in a calorimeter. The water is stirred and the maximum temperature of the water is recorded. (i) State why the metal is left in the boiling water for several minutes. ......................................................................................................................... ......................................................................................................................... (1) (ii) Write down a word equation for the thermal energy QM lost by the metal to the water. ......................................................................................................................... ......................................................................................................................... (1) (iii) Write down a word equation for the thermal energy QW gained by the water in the calorimeter. ......................................................................................................................... ......................................................................................................................... (1) (iv) A value of the specific heat capacity of the metal may be calculated from (ii) and (iii) by assuming that QM = QW. State why in practice, this assumption leads to an error in the calculated value of the specific heat capacity. ......................................................................................................................... ......................................................................................................................... (1) (d) The diagram below shows part of the heating circuit of a domestic shower. Cold water enters the shower unit and flows over an insulated heating element. The heating element is rated at 7.2 kW, 240 V. The water enters at a temperature of 14C and leaves at a temperature of 40C. The specific heat capacity of water is 4.2  103 J kg−1 K−1. (i) Describe how thermal energy is transferred from the heating element to the water. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (ii) Estimate the flow rate in kg s−1 of the water. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (iii) Suggest two reasons why your answer to (b) is only an estimate. 1. ............................................................................................................... ............................................................................................................... 2. ............................................................................................................... ............................................................................................................... (2) (iv) Calculate the current in the heating element when the element is operating at 7.2 kW. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (v) Explain why, when the shower unit is switched on, the initial current in the heating element is greater than the current calculated in (iv). ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (e) In some countries, shower units are operated from a 110 V supply. A heating element operating with a 240 V supply has resistance R240 and an element operating from a 110 V supply has resistance R110. (i) Deduce, that for heating elements to have identical power outputs ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (ii) Using the ratio in (i), describe and explain one disadvantage of using a 110 V supply for domestic purposes. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (Total 25 marks)

A lump of metal is initially at a temperature of 100C. The metal is heated so that its temperature rises by  degrees, as measured on the Celsius scale. The rise in temperature, as measured on the Kelvin scale is A.  − 273. B.  . C.  + 273. D.  + 373. A large mass M of ice of specific latent heat L is at its melting point (0C). A small mass m of water at  C is poured on to the block of ice. The specific heat capacity of water is S. Which one of the following is a correct expression for the mass of ice melted? A. B. C. D. This question is about thermodynamic processes. (a) State what is meant by the concept of internal energy of an ideal gas. ................................................................................................................................... ................................................................................................................................... (1) (b) The diagram below shows the variation with volume of the pressure of a fixed mass of an ideal gas. The change from B to C is an isothermal change at 546 K. At point A, the pressure of the gas is 1.01  105 Pa, the volume of the gas is 22.0 m3 and the temperature of the gas is 273 K. (i) State the temperature of the gas at point C; ......................................................................................................................... (1) (ii) Calculate the volume of the gas at point C. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (c) For the change from B to C, 31.5  105 J of thermal energy is transferred to the gas. (i) State the work done in the change from A to B. ......................................................................................................................... (1) (ii) Determine the work done during the change C to A. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (iii) Explain whether the work in (ii) is done by the gas or on the gas. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (iv) Determine the work done by the gas during one cycle ABCA. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (Total 11 marks)

The first law of thermodynamics may be expressed in terms of the quantities below. U, the increase in the internal energy of the system Q, the energy transferred to the system by heating W, the work done on the system Which one of the following is a correct statement of the law? A. W = U + Q B. W = −U − Q C. W = U − Q D. W = −U + Q The diagram below shows energy transfers in a heat pump operating between two reservoirs at temperatures TH and TC (TH  TC). Which of the following gives the correct relationship between W, QC and QH? A. W  QH − QC B. W  QH − QC C. W = QH − QC D. W = QH + QC This question is about an ideal gas. (a) The pressure P of a fixed mass of an ideal gas is directly proportional to the kelvin temperature T of the gas. That is, P  T. State (i) the relation between the pressure P and the volume V for a change at constant temperature; ......................................................................................................................... ......................................................................................................................... (1) (ii) the relation between the volume V and kelvin temperature T for a change at a constant pressure. ......................................................................................................................... ......................................................................................................................... (1) (b) The ideal gas is held in a cylinder by a moveable piston. The pressure of the gas is P1, its volume is V1 and its kelvin temperature is T1. The pressure, volume and temperature are changed to P2, V2 and T2 respectively. The change is brought about as illustrated below. State the relation between (i) P1, P2, T1 and T . ......................................................................................................................... ......................................................................................................................... (1) (ii) V1, V2, T  and T2. ......................................................................................................................... ......................................................................................................................... (1) (c) Use your answers to (b) to deduce, that for an ideal gas PV = KT where K is a constant. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (4) (Total 8 marks)

This question is about mechanical power and heat engines. Mechanical power (a) Define power. ................................................................................................................................... ................................................................................................................................... (1) (b) A car is travelling with constant speed v along a horizontal straight road. There is a total resistive force F acting on the car. Deduce that the power P to overcome the force F is P = Fv. ................................................................................................................................... ................................................................................................................................... (2) (c) A car drives up a straight incline that is 4.80 km long. The total height of the incline is 0.30 km. The car moves up the incline at a steady speed of 16 m s−1. During the climb, the average resistive force acting on the car is 5.0  102 N. The total weight of the car and the driver is 1.2  104 N. (i) Determine the time it takes the car to travel from the bottom to the top of the incline. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (ii) Determine the work done against the gravitational force in travelling from the bottom to the top of the incline. ......................................................................................................................... (1) (iii) Using your answers to (i) and (ii), calculate a value for the minimum power output of the car engine needed to move the car from the bottom to the top of the incline. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (d) From the top of the incline, the road continues downwards in a straight-line. At the point where the incline starts to go downwards, the driver of the car in (c) stops the car to look at the view. In continuing his journey, the driver decides to save fuel. He switches off the engine and allows the car to move freely down the incline. The car descends a height of 0.30 km in a distance of 6.40 km before levelling out. The average resistive force acting on the car is 5.0  102 N. Estimate (i) the acceleration of the car down the incline; ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (5) (ii) the speed of the car at the bottom of the incline. ......................................................................................................................... ......................................................................................................................... (2) (e) In fact, for the last few hundred metres of its journey down the incline, the car travels at constant speed. State the value of the frictional force acting on the car whilst it is moving at constant speed. ................................................................................................................................... (1) The heat engine (f) The diagram below shows the idealised pressure-volume (P-V) diagram for one cycle of the gases in an engine similar to that used in the car. The changes A  B and C  D are adiabatic changes. (i) Explain what is meant by an adiabatic change. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (ii) State the name given to the change B  C. ......................................................................................................................... (1) - (g) The useful power output of the engine is 20 kW and the overall efficiency of the engine is 32. The car engine completes 50 cycles every second. Deduce that QH = 1.3 kJ. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3) (Total 24 marks)

The heat capacity of a solid body is defined as A. the thermal energy required to increase the body’s temperature by one degree. B. the maximum thermal energy that must be supplied to melt the solid. C. the total kinetic energy of the solid’s molecules. D. the average kinetic energy of the solid’s molecules. (1)

A fixed quantity of an ideal gas is compressed at constant temperature. The best explanation for the increase in pressure is that the molecules A. are moving faster. B. are colliding more frequently with the container walls. C. exert greater forces on each other. D. are colliding more frequently with each other. (1)

This question is about temperature and internal energy. Two solid copper spheres, having different radii, undergo the same temperature change. A student states that the change in internal energy of the two objects would be the same. Briefly discuss this statement. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. .............................................................................................................................................. This question is about the first law of thermodynamics and about a steam engine. (a) State the first law of thermodynamics. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (b) An ideal gas in a cylinder is compressed by a piston. The work done on the gas is 250 J and the change in internal energy of the gas is 150 J. Explain how these energy changes are consistent with the first law of thermodynamics. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3) (c) In one cycle of a steam engine, water is heated at high pressure until changed into steam at a very high temperature. This steam expands and is then compressed such that it turns back to water. The graph below shows the idealised relationship between the pressure P and volume V of the water and steam for one cycle of this steam engine. (i) Use the graph above to deduce that the work done by the engine in one cycle is approximately 4  104 J. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (ii) As a result of compressing the steam, the energy transferred to the surroundings is approximately 1  105 J. Estimate the efficiency of the steam engine. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3) (Total 10 marks)

Which one of the following correctly describes the changes, if any, of the kinetic energy and the potential energy of the molecules of a liquid as it is boiling? Kinetic energy | Potential energy | A. | increases | increases | B. | increases | stays constant | C. | stays constant | increases | D. | stays constant | stays constant | (1)

A metal ball at a temperature of 200C is suspended in an evacuated container. The walls of the container are kept at a constant temperature of 100C. Which one of the following statements about the temperature of the ball is correct? A. It will eventually reach absolute zero. B. It will remain constant at 200C. C. It will eventually become 100C. D. It will eventually reach a constant temperature between 200C and 100C. (1)

An ideal gas expands isothermally, doing 2500 J of external work in the process. The thermal energy absorbed by the gas in this process is A. zero. B. less than 2500 J. C. equal to 2500 J. D. more than 2500 J. Two objects X and Y are made of the same material. Object X is more massive than object Y. Both objects are at the same temperature. Which of the following correctly compares the average kinetic energy and also the total energy of the molecules in the objects? average kinetic energy of the molecules in X and Y | total energy of the molecules in
X and Y | A. | same | greater in X than in Y | B. | same | less in X than in Y | C. | greater in X than in Y | same | D. | less in X than in Y | same | (1)

Which of the following correctly describes the changes in the kinetic energy of the molecules and the potential energy of the molecules as a liquid changes phase to a gas? kinetic energy of the molecules | potential energy of the molecules | A. | no change | increases | B. | no change | no change | C. | increases | increases | D. | increases | no change | (1)

The specific heat capacity of an object is defined as the thermal energy required to raise the temperature of A. the volume of the object by 1 K. B. unit volume of the object by 1 K. C. the mass of the object by 1 K. D. unit mass of the object by 1 K. Specific latent heat (a) Define specific latent heat of fusion. ................................................................................................................................... ................................................................................................................................... (1) (b) Solar radiation is incident on a pond of area 12 m2. The pond is covered by a layer of ice of thickness 3.0 cm. The temperature of the ice is 0.0C. (i) The density of ice is 900 kg m–3. Deduce that the mass of ice on the pond is approximately 320 kg. ......................................................................................................................... ......................................................................................................................... (2) (ii) The average power per unit area incident on the ice over a period of 6.0 hours is 340 W m–2. Deduce that the energy incident on the pond in this time is 8.8  107 J. ......................................................................................................................... ......................................................................................................................... (1) (iii) The specific latent heat of fusion of ice is 330 kJ kg–1. Determine whether all the ice on the pond will melt in the 6.0 hour time period. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2) (iv) State one assumption you made in reaching your answer to (b)(iii). ......................................................................................................................... ......................................................................................................................... (1) (c) During the night, the air temperature drops to –5C. The ice that melted during the day freezes again. Outline one mechanism by which thermal energy is lost by the ice. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (Total 9 marks)

This question is about the first law of thermodynamics. (a) Describe what is meant by the internal energy of an ideal gas. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (b) The internal energy of an ideal gas increases by an amount U. During this process, an amount q of thermal energy is transferred to the gas and the gas does an amount w of external work. (i) Use the first law of thermodynamics to state a relation between U, q and w. ......................................................................................................................... (1) (ii) Suggest how the state of an ideal gas may be changed such that each of the following conditions is met separately. U = 0 ....................................................................................................... w = 0 ....................................................................................................... q = 0 ....................................................................................................... (3) (T When the volume of a fixed mass of an ideal gas is reduced at constant temperature, the pressure of the gas increases. This pressure increase occurs because the atoms of the gas A. collide more frequently with each other. B. collide more frequently with the walls of the containing vessel. C. are spending more time in contact with the walls of the containing vessel. D. are moving with a higher mean speed. (1)

Gases and liquids (a) Describe two differences, in terms of molecular structure, between a gas and a liquid. 1. ......................................................................................................................... ......................................................................................................................... 2. ......................................................................................................................... ......................................................................................................................... (2) (b) The temperture of an ideal gas is a measure of the average kinetic energy of the molecules of the gas. Explain why the average kinetic energy is specified. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2) (c) Define heat (thermal) capacity. ................................................................................................................................... ................................................................................................................................... (1) (d) Water is heated at a constant rate in a container that has negligible heat capacity. The container is thermally insulated from the surroundings. The sketch-graph below shows the variation with time of the temperature of the water. The following data are available: initial mass of water = 0.40 kg initial temp of water = 20C rate at which water is heated = 300 W specific heat capacity of water = 4.2  103 J kg–1C−1 (i) State the reason why the temperature is constant in the region AB. ......................................................................................................................... ......................................................................................................................... (1) (ii) Calculate the temperature  at which the water starts to boil. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (5) (e) All the water is boiled away 3.0  103 s after it first starts to boil. Determine a value for the specific latent heat L of vaporization of water. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (2)

A solid is at an initial temperature of 500 K. The solid is heated so that its temperature rises by 50 K. What are the initial temperature and the temperature rise of the solid, as measured on the Celsius scale of temperature? | initial temperature | temperature rise | A. | 227°C | 50°C | B. | 227°C | 323°C | C. | 773°C | 50°C | D. | 773°C | 323°C | A copper block and a steel block each have the same mass. The copper block is at a higher temperature than the steel block. The blocks are placed in thermal contact and they then reach thermal equlibrium. There is no energy exchange with the surroundings. How do the magnitude of the change in temperature ∆T and the magnitude of the change in internal energy ∆U of the two blocks compare? | ∆T | ∆U | A. | same | Same | B. | same | Different | C. | different | same | D. | different | different | The specific latent heat of fusion of a substance is the quantity of thermal energy required to convert, at constant temperature, A. a solid to a liquid. B. unit mass of solid to liquid. C. a liquid to a solid. D. unit mass of liquid to solid. A sample of an ideal gas is contained in a cylinder. The volume of the gas is suddenly decreased. A student makes the following statements to explain the change in pressure of the gas. I. The average kinetic energy of the gas atoms increases. II. The atoms of the gas hit the walls of the cylinder more frequently. III. There are more atoms that are able to collide with the walls of the cylinder. Which of these statements is true? A. I and II only B. I and III only C. II and III only D. I, II and III (1)

hich of the following will not affect the rate of evaporation of a liquid? A. The temperature of the liquid B. The surface area of the liquid C. The mass of the liquid D. Convection currents of air above the liquid surface Gas leaks slowly out of a cylinder of constant volume. The temperature of the gas in the cylinder does not change. Which of the following is constant for the gas molecules in the cylinder? A. The number striking unit area of surface in unit time B. The number of the collisions between molecules per unit time C. The number per unit volume D. The average speed A block of metal at a temperature of 90C is placed in a beaker of water at a temperature of 0°C. The mass of the metal block and the mass of the water are equal. The final temperature of the water and the metal block is 9°C. Which of the following is the best estimate of the ratio ? A. B. C. 9 D. 10 (1)