- #1

- 151

- 1

I understand that one may give the the following relations:

[itex]\frac{C_p}{C_v}=1+\alpha\gamma T[/itex]

where [itex]C_p,C_v,\alpha,\gamma, and T[/itex] are isoberic specific heat, isochoric specific heat, thermal expansivity, Anderson-Gruneisen parameter, and Temperature, respectively.

[itex]C_v=\frac{\alpha V K_T}{\gamma}[/itex]

where V is volume and K_T is the isothermal bulk modulus.

What I do not think I fully grasp from these relationships is how the specific heat is related to the pressure. Is appears as though the heat capacity of a material depends on the pressure only because the density depends on the pressure.

In other words, and more specifically related to my own challenges; If I wanted to model heat transport with both the density and specific heat depending on pressure and temperature in a thermodynamically consistent way (lets ignore conductivity, with which I have no problems), I could use temperature-dependent data for [itex]C_p[/itex] and temperature-pressure dependent data for the density and the model would be fully consistent (lets also ignore phase changes)?

If so, am I correct to say that it must be true that the specific heat, having the dimensions of J kg

^{-1}K

^{-1}actually does NOT have a dependence on pressure? And also, that the volumetric specific heat having dimensions J m

^{-3}K

^{-1}is actually just [itex]\rho C_p[/itex].

Thank you!