Pressure, volume and temperature in thermodynamics

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It seems there are 3 variables that are important for a particular state in thermodynamics, pressure, volume and temperture. For a state function like energy U, I can choose any two variables of the three above and do partial differentiations with it? So the two I choose is arbitary in order to work out quantities like heat capcity and the like.
 

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AlephZero
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Yes - that's why two different specific heats (Cp and Cv) are defined and used. Of course Cp and Cv are related to each other, because, as you said, they are both consistent with the same equations of state of the material.

For example in a situation where the pressure is constant, it is obviously easier to write equations use Cp, rather than to use Cv and have extra terms in the equations because the volume is not constant.
 

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