Calculate the variation of cp with pressure at constant temperature for a substance for which
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The Specific Heat at Constant Volume
Remember that if we specify any two properties of the system, then
the state of the system is fully specified. In other words we can
write
,
or
. [VW, S & B: 5.7]
Consider the form
, and use the chain rule to write how
changes with respect to
and
:
(2..5)
For a constant volume process, the second term is zero since there is no change in volume, . Now if we write the First Law for a quasi-static process, with , (2..6)
we see that again the second term is zero if the process is also constant volume. Equating (2.5) and (2.6) with canceled in each,
and rearranging
In this case, any energy increase is due only to energy transfer as heat. We can therefore use our definition of specific heat from Equation (2.4) to define the specific heat for a constant volume process,
For a constant volume process, the second term is zero since there is no change in volume, . Now if we write the First Law for a quasi-static process, with , (2..6)
we see that again the second term is zero if the process is also constant volume. Equating (2.5) and (2.6) with canceled in each,
and rearranging
In this case, any energy increase is due only to energy transfer as heat. We can therefore use our definition of specific heat from Equation (2.4) to define the specific heat for a constant volume process,
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