If U is considered a function of T and P, the natural heat capacity is neither C
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If U is considered a function of T and P, the “natural” heat capacity is neither CV nor CP, but rather the derivative (∂U/∂T)P . Develop the following connections between (∂U/∂T)P , CP, and CV:
To what do these equations reduce for an ideal gas? For an incompressible liquid?
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Related Book For 
Introduction To Chemical Engineering Thermodynamics
ISBN: 9781260597684
9th International Edition
Authors: J.M. Smith, Mark Swihart Hendrick C. Van Ness, Michael Abbott
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