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

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Question: Answered & Verified by Expert

A polyatomic ideal gas has

24

vibrational modes. What is the value of

γ ?

PhysicsKinetic Theory of GasesJEE MainJEE Main 2021 (17 Mar Shift 1)

Options:

A $1.03$
B $1.30$
C $1.37$
D $10.3$

Solution:

2066 Upvotes Verified Answer

The correct answer is:

1.03

Since each vibrational mode has $2$ degrees of freedom hence total vibrational degrees of freedom $= 48$

$f = 3 + 3 + 48 = 54$

$γ = 1 + \frac{2}{f} = \frac{28}{27} = 1.03$

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