Question

A mixture of one mole of monoatomic gas and one mole of diatomic gas (rigid) are kept at room temperature (\( 27^\circ \text{C} \)). The ratio of specific heat of gases at constant volume respectively is:

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

Hint:

The specific heat of a gas increases with the number of degrees of freedom. Monoatomic gases have only translational motion, while diatomic gases have translational and rotational motion, resulting in a higher specific heat.

Answer 1

The Correct Option is C

The specific heat capacity at constant volume (\( C_V \)) is determined by a gas's degrees of freedom:

- For a monoatomic gas:
\[
C_V = \frac{3}{2}R,
\]
where \( R \) is the universal gas constant.

- For a rigid diatomic gas (excluding vibrational degrees of freedom):
\[
C_V' = \frac{5}{2}R.
\]

Step 1: Determine the Ratio of Specific Heats
The ratio of specific heat capacities between the monoatomic and diatomic gases is calculated as:
\[
\frac{C_V}{C_V'} = \frac{\frac{3}{2}R}{\frac{5}{2}R}.
\]
Simplifying this yields:
\[
\frac{C_V}{C_V'} = \frac{3}{5}.
\]



Final Answer:
\[
\boxed{\frac{3}{5}}
\]