Question

A gas consists of particles, each having three translational and three rotational degrees of freedom. The ratio of specific heats, Cp/Cv, is: (C_p and C_v are the specific heats at constant pressure and constant volume, respectively).

• A. \(\frac{5}{3}\)
• B. \(\frac{7}{5}\)
• C. \(\frac{4}{3}\)
• D. \(\frac{3}{2}\)

Answer 1

The Correct Option is C

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 \( \frac{4}{3} \).