Thermodynamics, Statistical Physics, and Quantum Mechanics

115

Therefore,

Substituting(S.4.24.8) and(S.4.24.2) into(S.4.24.3), we obtain

and

The temperatureindeed has decreased. As for thepressure, we have for
the initial state

Now so

and

4.25 Isothermal Compression and Adiabatic

Expansion of Ideal Gas (Michigan)

a)We can calculate the work as anintegral,using the ideal gas law:

where is, as usual, the absolutetemperature. Graphically, it is simply
the areaunder the curve(see Figure S.4.25).Alternatively, we can say that
the work done is equal to the change of free energy F of the system (see
Problem4.38):

THERMODYNAMICS AND STATISTICAL PHYSICS