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The correct relation between γ=C_P/C_V and temperature T is

Asked in JEE Main 31st Jan 1st Shift 2023 · Ratio of specific heats

(1) γ ∝ T⁰
(2) γ ∝ 1/T
(3) γ ∝ T
(4) γ ∝ 1/(√T)

Answer: (1) γ ∝ T⁰

Step-by-step solution

γ=1+2/f is fixed entirely by the number of active modes.

For a given gas over an ordinary temperature range that count does not change.

So γ does not depend on T, i.e. γ∝ T⁰.

Why the other options are wrong

(2) Would make γ fall without limit on heating; it stays between 1 and 5/3.
(3) Would make γ grow without limit, which the mode count forbids.
(4) Again gives γ a temperature dependence it does not have.

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