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So I have a question regarding the specific heat capacities in thermodynamics. In general the specific heat capacities for a gas (or gas mixture in thermo-chemical equilibrium) can be expressed as,

## c_p = \left(\frac{\partial h}{\partial T}\right)_p \qquad \text{and} \qquad c_v= \left(\frac{\partial e}{\partial T}\right)_v ##

.

Additionally, from the state postulate of thermodynamics one can write state relationships as,

## h = h\left(p,v\right) \qquad \text{and} \qquad e = e\left(p,v\right) \qquad \text{and} \qquad T=T\left(p,v\right) ##

Now I know that the specific heats are a defined thermodynamic property and not a state variable, however, would the above relationships imply,

## c_p =c_p\left(p,v\right) \qquad \text{and} \qquad c_v= c_v\left(p,v\right) ##

?? I have never come across such a relationship (obviously not explicit) in a textbook, or even seen a surface plot to indicate this relationship. Any help would be greatly appreciated.

Note: I am aware of the reciprocity relations and Maxwell relations, but I am trying to reduce the specific heats to functional relationships of density and pressure without the temperature appearing. These relationships will be formed numerically with Cantera, but I wan't to make sure my thought process is on the right track.

Thanks,

-Mr. Cosmos

## c_p = \left(\frac{\partial h}{\partial T}\right)_p \qquad \text{and} \qquad c_v= \left(\frac{\partial e}{\partial T}\right)_v ##

.

Additionally, from the state postulate of thermodynamics one can write state relationships as,

## h = h\left(p,v\right) \qquad \text{and} \qquad e = e\left(p,v\right) \qquad \text{and} \qquad T=T\left(p,v\right) ##

Now I know that the specific heats are a defined thermodynamic property and not a state variable, however, would the above relationships imply,

## c_p =c_p\left(p,v\right) \qquad \text{and} \qquad c_v= c_v\left(p,v\right) ##

?? I have never come across such a relationship (obviously not explicit) in a textbook, or even seen a surface plot to indicate this relationship. Any help would be greatly appreciated.

Note: I am aware of the reciprocity relations and Maxwell relations, but I am trying to reduce the specific heats to functional relationships of density and pressure without the temperature appearing. These relationships will be formed numerically with Cantera, but I wan't to make sure my thought process is on the right track.

Thanks,

-Mr. Cosmos

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