Question

If $c_p$ and $c_v$ denotes the specific heat of nitrogen at constant pressure and constant volume respectively, then

• A. $c_p-c_v=28R$
• B. $c_p-c_v=\frac{R}{28}$
• C. $c_p-c_v=\frac{R}{14}$
• D. $c_p-c_v=R$

Answer 1

The correct option is B $c_p-c_v=\frac{R}{28}$

$\text{Molar heat capacity}=\text{Molar mass}\times \text{specific heat capacity}$
$\Rightarrow C_P=M{c}_p\&C_V=M{c}_v...\left(i\right)$
$C_P-C_V=R...\left(ii\right)$
From Eq $\left(i\right)\&\left(ii\right)$,
$M{c}_p-M{c}_v=R$
$28c_p-28c_v=R$
$\therefore c_p-c_v=\frac{R}{28}$