If for hydrogen $C_{P} - C_{V} = m$ and for nitrogen $C_{P} - C_{V} = n$ , where $C_{P}$ and $C_{V}$ refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between m and n is (molecular weight of hydrogen $= 2$ and molecular weight of nitrogen $= 28$ )

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n = 14 m

n = 7 m

m = 7 n

m = 14 n

answer is D.

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Detailed Solution

$C_{P} - C_{V} = r = \frac{R}{M}$

As the molecular mass of nitrogen is 28, $n = \frac{R}{28}$

As the molecular mass of hydrogen is 2, $m = \frac{R}{2}$

$\Rightarrow m = 14 n$

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