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A gas has n degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be

Asked in JEE Main 26th July 2nd Shift 2022 · Ratio of specific heats

(1) n/(n + 2)
(2) (n + 2)/n
(3) n/(2n + 2)
(4) n/(n - 2)

Answer: (1) n/(n + 2)

Step-by-step solution

C_V=n/2R and C_P=C_V+R=(n+2)/2R.

The question asks for (C_V)/(C_P), which is 1/γ.

(C_V)/(C_P)=(n/2)/((n+2)/2).

=n/(n+2).

Why the other options are wrong

(2) That is γ=(C_P)/(C_V), the ratio the other way round.
(3) n/(2n+2) matches neither ratio; the denominator of C_P is n+2, not 2n+2.
(4) A minus sign would make C_P smaller than C_V, which is impossible.

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