Q66 / 90 · JEE Main 2017 (02 Apr) · Physics

$C_{p} - C_{v} = \frac{R}{M}$ and $C_{v}$ are specific heats at constant pressure and constant volume respectively. It is observed that, $C_{p} - C_{v} = a$ for hydrogen gas and $C_{p} - C_{v} = b$ for nitrogen gas. The correct relation between $a$ and $b$ is:

A
$a = 28 b$
B
$a = \frac{1}{14} b$
C
$a = b$
Correct answer
D
$a = 14 b$

Solution

C_{p} - C_{v} = \frac{R}{M}

For hydrogen

C_{p} - C_{v} = \frac{R}{2} = a

For nitrogen

C_{p} - C_{v} = \frac{R}{28} = b

\frac{a}{b} = 14

a = 14 b

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

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