Question

The ratio of the molar specific heat capacities of monatomic and diatomic gases at constant pressure is:

• A. \( 1:7 \)
• B. \( 5:7 \)
• C. \( 3:7 \)
• D. \( 2:7 \)

Hint:

Monatomic gases have fewer degrees of freedom, leading to a lower specific heat compared to diatomic gases, which have rotational modes contributing to energy storage.

Answer 1

The Correct Option is B

Step 1: Define Molar Specific Heat Capacity For a monatomic gas, the specific heat at constant pressure is: \[ C_p = \frac{5}{2} R \] For a diatomic gas, the specific heat at constant pressure is: \[ C_p = \frac{7}{2} R \]
Step 2: Compute the Ratio The ratio of the specific heats: \[ \frac{C_{p,\text{monatomic}}}{C_{p,\text{diatomic}}} = \frac{5}{7} \] Thus, the correct answer is \( 5:7 \).