In a gas of N diatomic molecules, two possible models for a classical description of a diatomic molecule are:
Which of the following statements about this gas is true?
A. Model I has a specific heat cv = ³⁄₂Nk
B. Model II has a smaller specific heat than Model I
C. Model I is always correct
D. Model II is always correct
E. The choice between Models I and II depends on the temperature
Equipartition of Energy: E = ½ fNkT
Specific heat: cv = ∂E/∂t = ½ fNk
(A) FALSE
Model I is diatomic molecules in low temperature
→ 5 DoF (3 translational + 2 rotational)
→ cv = ⁵⁄₂Nk
(B) FALSE
Model II is diatomic molecules in high temperature
→ 7 DoF (3 translational + 2 rotational + 2 vibrational)
→ cv = ⁷⁄₂Nk
(C) and (D) are vague answers.
Answer: E
Which of the following statements about this gas is true?
A. Model I has a specific heat cv = ³⁄₂Nk
B. Model II has a smaller specific heat than Model I
C. Model I is always correct
D. Model II is always correct
E. The choice between Models I and II depends on the temperature
(GR8677 #87)
Solution:Equipartition of Energy: E = ½ fNkT
Specific heat: cv = ∂E/∂t = ½ fNk
f = Degree of Freedom (DoF)
(A) FALSE
Model I is diatomic molecules in low temperature
→ 5 DoF (3 translational + 2 rotational)
→ cv = ⁵⁄₂Nk
(B) FALSE
Model II is diatomic molecules in high temperature
→ 7 DoF (3 translational + 2 rotational + 2 vibrational)
→ cv = ⁷⁄₂Nk
(C) and (D) are vague answers.
Answer: E
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