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If for a gas, R/(C_V)=0.67, this gas is made up of molecules which are

Asked in NEET 1992 · Ratio of specific heats

(1) diatomic
(2) mixture of diatomic and polyatomic molecules
(3) monoatomic
(4) polyatomic

Answer: (3) monoatomic

Step-by-step solution

Idea: Mayer's relation turns the given ratio straight into γ.

C_P-C_V=R, so R/(C_V)=(C_P-C_V)/(C_V)=γ-1.

γ-1=0.67.

γ=1.67=5/3.

γ=5/3 corresponds to f=3, which is a monoatomic gas.

Why the other options are wrong

(1) A rigid diatomic has γ=1.4, which makes R/(C_V)=0.40.
(2) Such a mixture has γ between 4/3 and 7/5, so R/(C_V) falls between 0.33 and 0.40.
(4) A polyatomic gas has γ=4/3, so R/(C_V)=0.33.

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