JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Heat & Thermodynamics

A polyatomic ideal gas has 24 vibrational modes. What is the value of

γ

(A)1.30
(B)1.03✓ Correct
(C)10.3
(D)1.37

Answer: (B)

Solution

A non-linear polyatomic molecule has

3

translational and

3

rotational degrees of freedom, and each vibrational mode contributes two, one for kinetic and one for potential energy. With

24

vibrational modes,

f = 3 + 3 + 2 (24) = 54

For an ideal gas

γ = 1 + \frac{2}{f}

, so

γ = 1 + \frac{2}{54} = \frac{28}{27}

The ratio of the specific heats is slightly above

1.03

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Single correct option

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