cp/cv for monatomic

Question

Ratio γ = Cp/Cv for monatomic ideal gas equals?

RankGuru · Accepted Answer

1. **Degrees of Freedom ($f$)**: A monatomic gas atom (like He, Ne) has **3** degrees of freedom ($f=3$, all translational).
2. **Specific Heats**:
   - $C_v = \frac{f}{2} R = \frac{3}{2} R$.
   - $C_p = C_v + R = \frac{3}{2} R + R = \frac{5}{2} R$.
3. **Ratio ($\gamma$)**:
   - $\gamma = \frac{C_p}{C_v} = \frac{5/2 R}{3/2 R} = \frac{5}{3}$.
4. **Decimal form**: $\approx 1.67$. Note that diatomic gases (like $O_2$) have $\gamma = 7/5 = 1.4$.

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cp/cv for monatomic

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