Question

$C _{ P }$ and $C _{ V }$ are specific heats at constant pressure and constant volume respectively. It is observed that
$C _{ P }- C _{ V }= a$ for helium gas
$C _{ P }- C _{ V }= b$ for oxygen gas
Such that, $b$ is $n$ times the $a$. Find out value of $n$.

Answer 1

Let molar heat capacity at constant pressure $= SP$ and molar heat capacity at constant volume $=s_{V}$
$\therefore S _{ P }- S _{ V }= R$
Now, principal specific heat, $C =\frac{ s }{ M }$
$\therefore C _{ P }- C _{ V }=\frac{ R }{ M }$
$\therefore $ For $He , a =\frac{ R }{4} ;$ for $O _{2}, b =\frac{ R }{32}$
$\therefore \frac{ b }{ a }=\frac{ R }{32} \times \frac{4}{ R }=\frac{1}{8}$
$\Rightarrow b =0.125\, a =0.13 a$ ...(Rounding off to two digits)