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 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 quasistatic 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
 Consider the infinitesimal quantity
Is this an exact differential? If not, find the integrating factor that converts it into an exact differential.
 A system undergoes a quasistatic 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
20160125