A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

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by and the number ofmoles on the left and right sides of thecylinder,
respectively, andusing we obtain the total work and, hence,
heat given by theintegral

4.29 Heat Extraction (MIT, Wisconsin-Madison)

a)For a mass of fixedvolume we have

So, by the definition ofC,

SinceCis independent ofT,we may rewrite (S.4.29.2) andintegrate:

The change in entropy isthen

b) The maximum heat may be extracted when the entropy remainscon-

stant. Equating theinitial and finalentropies yields thefinaltemperature

of the two bodies:

SOLUTIONS