temperature and the ideal gas
1.The development of standard temperature scales requires use of the zeroth law of thermodynamics. This law tells us that if a thermometer is in thermodynamic equilibrium with both a test object and an object used to define a standard, then the test and standard objects must be in thermodynamic equilibrium with each other. If this law did not hold, the temperature scale on a thermometer would have no relation to the actual temperature of the test object, and therefore, no standard could be defined.
2.Absolute zero is the temperature at which the motion of atoms in a substance is a minimum and the temperature can decrease no further. There is no fundamental significance to the zero degree point of the Celsius and Fahrenheit temperature scales—they are simply of historical origin.
3.A temperature difference of 1 K is the same as a temperature change of 1(C. Thus, either scale may be used in applications dealing only with temperature differences.
4.Imagine a circle drawn on the plate instead of a hole cut into it. The drawn circle must expand in the same manner as the cut hole. Thus, the center of the plate expands outward whether or not a hole exists and the hole must therefore grow larger.
5.The thermal expansion coefficients of silver and brass only differ by about 5%. Thus, a bimetallic strip made from these materials would bend only slightly during expansion, contrary to its intended purpose.
6.Metals have thermal expansion coefficients several orders of magnitude larger than glass. Running the jar under hot water therefore facilitates its opening since the lid expands more than the jar as its temperature increases.
7.According to the ideal gas law, if the temperature of an ideal gas is negative, then either the pressure or the volume must likewise have a negative value. This requirement is nonsensical since absolute pressure and volume must be positive quantities. Unlike the Celsius and Fahrenheit temperature scales, temperatures in the Kelvin scale are always positive and therefore avoid the aforementioned problem.
8.Conversion of the price per cubic foot of natural gas into the price per mole requires knowledge of the number of moles contained within the given volume. From the macroscopic ideal gas law, the number of moles in a sample is proportional to the volume, pressure, and temperature of the gas. Using the known volume and the additional quantities of pressure and temperature, the number of moles may be calculated and the price may be converted. The conversion could also be made if either the number density or the mass density and the mass per molecule were known. The latter method works whether or not the gas is ideal.
9.The SI units of mass density and number density are kg/m3 and m(3, respectively. An equal number density does not imply an equal mass density because the mass of an individual atom may be different in each gas.
10.From the ideal gas law, two gases at equal temperature and pressure must have identical number densities. The mass of a nitrogen atom is greater than the mass of a helium atom—the mass density of nitrogen is therefore greater.
11.One mole of aluminum atoms has a mass of 27.0 g.
12.The pressure of the air inside the ball increases as it is heated, pushing outward on the dents.
13.The pressure of the air outside the balloon decreases as its distance above the Earth increases. The balloon expands until the pressures inside and outside are equal.
14.Hydrogen and helium molecules in the high-energy tail of the Maxwell-Boltzman distribution have enough kinetic energy to escape from Earth’s atmosphere. Other molecules are gradually boosted into the vacated high-energy region and eventually escape themselves. Only a negligible number of hydrogen and helium molecules have enough kinetic energy to...