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 (\( C_V \)) depends on the degrees of freedom of a gas: - For a monoatomic gas: \[ C_V = \frac{3}{2}R, \] where \( R \) is the universal gas constant. - For a rigid diatomic gas (no vibrational degrees of freedom): \[ C_V' = \frac{5}{2}R. \] Step 1: Calculate the Ratio of Specific Heats The ratio of specific heat capacities for the monoatomic and diatomic gases is: \[ \frac{C_V}{C_V'} = \frac{\frac{3}{2}R}{\frac{5}{2}R}. \] Simplify: \[ \frac{C_V}{C_V'} = \frac{3}{5}. \] Final Answer: \[ \boxed{\frac{3}{5}} \]