   Next: Statistical Thermodynamics Up: Heat and Work Previous: Exact and Inexact Differentials

# Exercises

1. The mean pressure, , of a thermally insulated gas varies with volume according to the relation where and are positive constants. Show that the work done by this gas in a quasi-static process in which the state of the gas evolves from an initial macrostate with pressure and volume to a final macrostate with pressure and volume is 2. Consider the infinitesimal quantity Is this an exact differential? If not, find the integrating factor that converts it into an exact differential.

3. A system undergoes a quasi-static process that appears as a closed curve in a diagram of mean pressure, , versus volume, . Such a process is termed cyclic, because the system ends up in a final macrostate that is identical to its initial macrostate. Show that the work done by the system is given by the area contained within the closed curve in the - plane.   Next: Statistical Thermodynamics Up: Heat and Work Previous: Exact and Inexact Differentials
Richard Fitzpatrick 2016-01-25