Question 969: Thermodynamics & KTG

Question

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $$\gamma=\frac{C_p}{C_v}$$ is ($$C_P$$ where $$C_V$$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

Accepted Answer

A polygamic gas has 3 translational, 3 rotational and $$f$$ vibration modes
$$\begin{aligned}
& U=\frac{3}{2} k_B T+\frac{3}{2} k_B T+f k_B T \
& U=(3+f) k_B T \
& C_V=(3+f) R \
& C_p=(4+f) R \
& \frac{C_p}{C_v}=\frac{4+f}{3+f}=\gamma \
& 4+f=3 \gamma+f \gamma \
& 4-3 \gamma=f(\gamma-1) \Rightarrow f=\frac{4-3 \gamma}{\gamma-1}
\end{aligned}$$

Answer

$$\frac{4+3 \gamma}{\gamma-1}$$

Answer

$$\frac{3+4 \gamma}{\gamma-1}$$

Answer

$$\frac{4-3 \gamma}{\gamma-1}$$

Answer

$$\frac{3-4 \gamma}{\gamma-1}$$

Thermodynamics & KTG

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant $\gamma=\frac{C_p}{C_v} is (C_P where C_V$ are the specific heat capacities of the gas at constant pressure and constant volume, respectively):

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