Here we show that the experimental arrangement results in expansion at constant
enthalpy. Because all changes to the gas occur adiabatically, q = 0 implies that ΔU= w.
Next, consider the work done as the gas passes through the barrier. We focus on
the passage of a fixed amount of gas from the high pressure side, where the pressure
is pi, the temperature Ti, and the gas occupies a volume Vi (Fig. 2.27). The gas
emerges on the low pressure side, where the same amount of gas has a pressure pf ,
a temperature Tf, and occupies a volume Vf. The gas on the left is compressed isothermally by the upstream gas acting as a piston. The relevant pressure is pi and
the volume changes from Vi to 0; therefore, the work done on the gas is