JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Heat & Thermodynamics

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γ_{A}

is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom.

γ_{B}

is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If

\frac{γ _{A}}{γ _{B}} = (1 + \frac{1}{n})

, then the value of

n

is _______.

Answer: 3

Solution

For

f

active degrees of freedom

γ = \frac{f + 2}{f}

. Gas A is monoatomic with

f_{A} = 3

, so

γ_{A} = \frac{5}{3}

. Gas B has 3 translational, 3 rotational and one vibrational mode, the vibration counting as two, so

f_{B} = 3 + 3 + 2 = 8

and

γ_{B} = \frac{10}{8} = \frac{5}{4}

. Then

\frac{γ _{A}}{γ _{B}} = \frac{5/3}{5/4} = \frac{4}{3} = 1 + \frac{1}{3}

, so

n = 3

JEE Main · 2025 · 02 Apr 2025 · Shift 1 · Integer answer

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