Thermal Physics - Heat Capacity

For an ideal diatomic gas in thermal equilibrium, the ratio of the molar heat capacity at constant volume at very high temperatures to that at very low temperatures is equal to

A. 1
B. 5/3
C. 2
D. 7/3
E. 3

(GR9677 #79)

Solution:

C_V  for diatomic gas: C_V  = C_Vtrans + C_Vrot  + C_Vvib

For very low T, only translational component contributes
→ C_V(T≪) = ³/₂ Nk

For very high T, all 3 components (translational, vibrational, rotational) contribute
→ C_V(T≫) = (³/₂ + 1 + 1) R = ⁷/₂ Nk

Ratio C_V(T≪) / C_V(T≫)  = 7/3

Answer: D