An experiment to measure the dependence of the internal energy of a gas on volume was first conducted in 1807 by Joseph-Louis Gay-Lussac (1778– 1850) and later reproduced by Joule. The experimental apparatus is shown in Fig. 2.7. A glass vessel with two parts separated by a stopcock was immersed in a water bath. One part of the vessel contains the gas of interest and the other is initially evacuated. In the experiment the stopcock was opened and the gas flowed freely into the evacuated part of the vessel. A thermometer in the water bath measures the change in the water temperature resulting from the free expansion of the gas.
Analyze the experiment based on the first law and relate the temperature measurement to (∂U/∂V)T . Do you make any assumptions about the apparatus?
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