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The molar specific heat at constant pressure of an ideal gas is (7/2)R. The ratio of specific heat at constant pressure to that at constant volume is

Asked in NEET 2006 · Ratio of specific heats

(1) 9/7
(2) 7/5
(3) 8/7
(4) 5/7

Answer: (2) 7/5

Step-by-step solution

Given: C_P=7/2R.

Idea: Mayer's relation, C_P-C_V=R, supplies C_V.

C_V=C_P-R=7/2R-R=5/2R.

γ=(C_P)/(C_V)=(7R/2)/(5R/2).

γ=7/5.

Why the other options are wrong

(1) Comes from reading the given 7/2R as C_V and then adding R to get C_P=9/2R.
(3) Comes from the same misreading with R halved: C_V=7/2R and C_P=4R.
(4) Is the reciprocal of the right answer, C_V/C_P; γ is always greater than 1 because C_P exceeds C_V.

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