A Classical model of a diatomic molecule is a springy dumbbell, as shown above, where the dumbbell is free to rotate about axes perpendicular to the spring. In the limit of high temperature, what is the specific heat per mole at constant volume?
B. 5/2 R
C. 7/2 R
D. 9/2 R
E. 11/2 R
(GR9277 #15)
Solution:
CV for diatomic gas: CV = CVtrans + CVrot + CVvib
At high T, all components contribute and each degree of freedom (DoF) contributes ½R to CV .
DoF trans = 3 (since it's 3 dimension)
DoF rot = 2 (diatomic atom)
DoF vib = 2 (1 for kinetic energy + 1 potential energy)
→ 3 + 2 + 2 = 7 → 7 DoF contributes ⁷/₂R
Answer: C
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