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Pressure dependence of the Heat Capacity

  1. Oct 17, 2011 #1
    I am trying to understand the nature of the dependence of heat capacity/specific heat on pressure.

    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!
  2. jcsd
  3. Oct 18, 2011 #2
    specific heat or heat capacity are the properties of the substance . the shall remain same under any condition for the same substance.
  4. Oct 19, 2011 #3
    That explanation isn't compatible with the fact that specific heat is strongly temperature dependent. Why is specific heat temperature dependent and not pressure dependent?
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