Q125 / 150 · MHT CET 2017 · Physics

For a rigid diatomic molecule, the universal gas constant $R = n C_{P}$ , where, $C_{P}$ is the molar specific heat at constant pressure and $n$ is a number. Hence, $n$ is equal to

A
$0.2257$
B
$0.4$
Correct answer
C
$0.2857$
D
$0.3557$

Solution

For rigid diatomic molecule

\frac{C_{P}}{C_{V}} = \frac{7}{5}

∴ C_{V} = \frac{5}{7} C_{P}

Also

C_{P} - C_{V} = R

C_{P} - \frac{5}{7} C_{P} = R

\frac{2}{7} C_{P} = R

∴ n = \frac{2}{7} = 0.2857

Hence, the correct answer is option: 'C'.

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