Joule Expansion - Description

Description

We consider n moles of an ideal gas at pressure Pi and temperature Ti, confined to the left-hand side (as drawn) of a thermally-isolated container, that occupies a volume Vi = V0. The right-hand side of the container, also with volume V0, is evacuated. The tap (solid line) between the two halves of the container is then suddenly opened and the gas fills the entire container of volume Vf = 2V0. We propose that both the previous and new temperature and pressure (Tf, Pf) follow the Ideal Gas Law, so that initially we have PiVi = nRTi and then, when the tap is opened, we have PfVf = nRTf, where R is the molar ideal gas constant.

As the system is thermally isolated, it cannot exchange heat with its surroundings. Also, since the system's volume is kept constant, the system does not do work on its surroundings. As a result, the change in internal energy ΔU = 0, and because U is a function of temperature only for the ideal gas, we know that Ti = Tf. This implies that PiV0 = Pf(2V0), and thus the pressure halves; i.e. Pf = ½Pi.

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