A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (Cp and Cv are the specific heats at constant pressure and constant volume, respectively).
- \(\frac{5}{3}\)
- \(\frac{7}{5}\)
- \(\frac{4}{3}\)
- \(\frac{3}{2}\)
The Correct Option is C
Solution and Explanation
The degrees of freedom, \( f \), for a gas particle with 3 translational and 3 rotational degrees of freedom is:
\[ f = 3 \, (\text{translational}) + 3 \, (\text{rotational}) = 6. \]
Step 1: Formula for Specific Heat Ratio
The specific heat ratio \( \gamma \) is given by:
\[ \gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}. \]
Step 2: Substituting \( f = 6 \)
Substitute \( f = 6 \) into the formula:
\[ \gamma = 1 + \frac{2}{6} = 1 + \frac{1}{3} = \frac{4}{3}. \]
Conclusion:
Thus, the ratio \( \frac{C_P}{C_V} \) for the gas is \( \frac{4}{3} \).
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