By definition, the constant-pressure heat capacity is given by
Cp = d(U + PV)/dT
However, for liquids the molar volume V changes very little upon heating. Therefore, at constant pressure, we can neglect the second term to good approximation in liquids:
Cp ~ dU/dT
Rearranging, we arrive at an equation we can integrate to get a relation between U and T:
Cp dT = dU
-MSS
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