How Does Phonon Contribution Affect Heat Capacity in Liquid Helium Below 0.6K?

In summary, the conversation discusses the heat capacity of liquid Helium at temperatures below 0.6K. It is represented by the equation Cv=(9.819 x 10^-3 K^-3)NkT^3, where N is the number of molecules, k is Boltzmann's constant, and T is temperature in Kelvin. There is a prediction for the contribution of phonons to the heat capacity based on the data of the speed of sound in liquid He (238 m/s) and the density of liquid He (0.145 g cm^-3). However, there is some confusion regarding the specific heat having a T^3 dependence at low temperatures for a system of massless bosons.
  • #1
precondition
57
0
Below 0.6K the heat capacity of liquid He is well represented by the equation
Cv=(9.819 x 10^-3 K^-3)NkT^3
Given that transverse shear waves cannot propagate in a liquid, predict the phonon contribution to the heat capacity of He from the data
c=238 m/s (speed of sound in liquid He)
p=0.145 g cm^-3 (density of liquid He)

......difficult...T_T
 
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  • #2
x is supposed to be multiplication
N number of molecules
k Boltzmann's constant
T temperature in kelvin
Cv heat capacity
 
  • #3
I find this rather hard to follow since I'm not getting that the specific heat has a T^3 dependence at low temperatures for a system of massless bosons (read: the phonons). I'm getting that U ~ T^3 and, then C_v ~ T^2, so I'm a little confused. I also haven't slept much the past two weeks so I could be doing something silly here.
 

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