AIIMS2019Physics-Thermodynamics

AIIMS 2019 Physics Specific Heat Capacities MCQ Question

Type: MCQ-conceptual-Medium-Class 11

Assertion: The ratio CvCp\frac{\text{C}_\text{v}}{\text{C}_\text{p}} for a monoatomic gas is less than for a diatomic gas.

Reason: The molecules of a monoatomic gas have more degrees of freedom than those of a diatomic gas.

A

If both assertion and reason are true and reason is the correct explanation of assertion.

B

If both assertion and reason are true but reason is not the correct explanation of assertion.

C

If assertion is true but reason is false.

D

If both assertion and reason are false.

Correct Answer

Option C

Detailed Explanation

In the context of specific heat capacities for ideal gases, the ratio CvCp\frac{C_v}{C_p} is derived from the degrees of freedom of the gas molecules. For a diatomic gas, which has 5 degrees of freedom, the specific heat capacities are Cv=5R2C_v = \frac{5R}{2} and Cp=7R2C_p = \frac{7R}{2}, leading to CvCp=57\frac{C_v}{C_p} = \frac{5}{7}. This indicates that option B is correct for diatomic gases. However, the question specifically asks for the ratio of CvC_v to CpC_p for a monoatomic gas, which is 35\frac{3}{5}, corresponding to option A. Therefore, option C (7/5) is incorrect as it does not represent the ratio for either gas type.

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