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Physics Question 48 – JEE-MAIN 2025

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γA is the specific heat ratio of monatomic gas A having 3 translational degrees of freedom. γB is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If γAγB=(1+1n), then the value of n is _______.

Understand how degrees of freedom contribute to the internal energy of a gas, which in turn affects its specific heat capacities.

● Video Walkthrough
Step 1: Determine degrees of freedom for each gas✦ Active

For monatomic gas A, the degrees of freedom are purely translational.

fA=3

For polyatomic gas B, there are translational, rotational, and vibrational degrees of freedom. Each vibrational mode contributes 2 degrees of freedom.

fB=ftranslational+frotational+fvibrational=3+3+(1×2)=8
Step 2: Calculate the specific heat ratio (γ) for each gas○ Expand

The specific heat ratio γ is given by the formula γ=1+2f.

γA=1+2fA=1+23=53
γB=1+2fB=1+28=1+14=54
Step 3: Solve for 'n' using the given relation○ Expand

Substitute the calculated values of γA and γB into the given equation γAγB=(1+1n).

5/35/4=1+1n
43=1+1n
1n=43−1=13
n=3
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