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Recall the Gibbs equation: Tds = du + Pdv .
This equation can be rearranged into the form:
Solids and Liquids can be estimated as incompressible as their volume does not change significantly under a process. therefore dv can be assumed to equal 0.
The equation then becomes:
as du = cdT,the equation then becomes:
If we integrate both sides between 2 states(state 1 and 2):
we get:
where c is the average specific heat across the 2 states:
is an appropriate estimate.
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