Thermal Equilibrium Experiment

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This laboratory focused on the thermodynamic processes involved when two incompressible substances are mixed together. 12 experiments were performed, 10 involving the combination of a measured amount of hot and cold water and 2 involving the combination of ice and liquid water, the majority of these experiments were performed three times. The average variance in final temperature for each experiment was less than 10 percent providing proof of repeatability. Equipment used during the experiment included a gram scale, thermocouple, Styrofoam cup, glass beakers, microwave, an ice bath and ice. The first half of the experiment was dedicated to the mixing of two containers of water at different temperatures. The mass of the water in each container was measured and the containers were then heated or cooled to achieve the temperature desired for the experiment. The temperature was measured with a thermocouple before and after mixing. The data was recorded and is included in tables. The second half of the experiment involves the mixing of ice and liquid water. Water was weighed and cooled then mixed with an amount of ice that was also weighed. The temperature before and after mixing was recorded and included in tables. When the experiments were completed analysis was performed using the laws of thermodynamics. The data collected was used in equations to find theoretical values for final equilibrium temperature. The theoretical values were compared with those measured during the experiment. The total average percent difference between the measured final temperature and the theoretical final temperature is less than 5.0%. This low deflection between measurement and theory lends credibility to the experiment and proof of the concepts provided within the experiment.


When two incompressible substances of different temperatures are combined, there will be a resultant equilibrium temperature that lies between the temperatures of the substances that were combined. The mass of the substances greatly affects the resulting final temperature. An incompressible substance is one whose volume can be considered constant no matter the change in pressure. In this laboratory, the incompressible substance water was used in its liquid and solid states. The First Law of Thermodynamics is essentially an energy balance equation and is state below.

Q – W = ΔU (Eq. 1)

Q represents the amount of heat transferred into or out of the system. W represents the amount of work done by or on a system.
ΔU represents the change in the internal energy of the system.

The units for Q, W and U are kilojoules. When analyzing a thermodynamic process, a system boundary must be established. Establishing the boundary will determine how complicated or simple the first law analysis is. The boundary for this experiment was established in such a way that there was no heat transferred into or out of the system. There was also no work being done on or by the system. A value for work would be required if a device such as a compressor or turbine was included in the system. Since there is no heat transfer across the boundary or work done, the Q and W values are considered to be zero. The equation now becomes.

0 = ΔU = Ut2 – Ut1(Eq. 2)

In order to use equation 2, the mass and specific heat of the incompressible material was determined. Specific heat refers to the amount of energy, measured in kilojoules, required to raise one kilogram of the incompressible substance by one degree Kelvin or Celsius. The specific heat value for water at 1 atmosphere of pressure varies according to temperature, but the average is 4.18 KJ / KG* ºK Using mass and specific heat values, the following equation for the change in internal energy was used to calculate final equilibrium temperature.

0 = [ M * C * ( T2 – T1 ) ]substance 1 + [ M * C * ( T2 – T1 ) ]substance 2(Eq. 3)

M represents the...
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