Heat and Thermodynamics 1 Question 8
8. $C _p$ 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 $C _p-C _V=b$ for nitrogen gas. The correct relation between $a$ and $b$ is
(2017 Main)
(a) $a=b$
(b) $a=14 b$
(c) $a=28 b$
(d) $a=\frac{1}{14} b$
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Solution:
- By Mayor’s relation, for $1 g$ mole of a gas,
$$ C _p-C _V=R $$
So, when $n$ gram moles are given,
$$ C _p-C _V=\frac{R}{n} $$
As per given question,
$$ \begin{aligned} & a=C _p-C _V=\frac{R}{2} ; \text { for } H _2 \\ & b=C _p-C _V=\frac{R}{28} ; \text { for } N _2 \\ & a=14 b \end{aligned} $$
