Question

If for $H_2$ gas, $c_p-c_v=a$ and for $O_2$ gas $c_p-c_v=b$, where $c_p$ and $c_v$ are specific heats in $\text{cal/g.K}$ at constant pressure and constant volume respectively, then select the correct relation between $a\&b$.

• A. $b=8b$
• B. $a=b$
• C. $a=16b$
• D. $a=4b$

Answer 1

The correct option is C $a=16b$

From Mayer's formula,
$C_p-C_V=R...\left(i\right)$
where $C_p$ and $C_V$ are the molar heat capacity in $\text{cal/mol.K}$
$\Rightarrow$From relation between specific heat capacity and molar capacity,
$C_p=M{c}_p$
$C_V=M{c}_v$
Where $M$ is molar mass in $\text{g/mol}$,
putting in Eq $\left(i\right)$,
$\Rightarrow M(c_p-c_v)=R$
$\Rightarrow c_p-c_v=\frac{R}{M}...\left(ii\right)$
For $H_2$ gas, $M=2$
$\Rightarrow c_p-c_v=\frac{R}{2}$
$\therefore a=\frac{R}{2}$
For $O_2$ gas, $M=32$
$\Rightarrow c_p-c_v=\frac{R}{32}$
$\therefore b=\frac{R}{32}$
From values of $a\&b$,
$a=16b$