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 hydrogen gas
$C_p-C_v=b$ for nitrogen gas

The correct relation between a and b is :

• A. $a=\frac{1}{14}b$
• B. $a=b$
• C. $a=14b$
• D. $a=28b$

Answer 1

The correct option is C $a=14b$

Given:-

For $H_2$ gas,

$C_p-C_v=a$

For $N_2$ gas,

$C_p-C_v=b$

As we know that

$C_{p,m}-C_{v,m}=R$

whereas,

$C_{p,m}$ and $C_{v,m}$ are the heat capacity in $cal/mol.K$.

As

$C_{p,m}=M{C}_p$; and

$C_{v,m}=M{C}_v$

Where as $C_p$ and $C_v$ heat capacity in $cal/g-K$

$M{C}_p-M{C}_v=R$

$(C_p-C_v)=\frac{R}{M}$

For $H_2$ gas,

$C_p-C_v=\frac{R}{2}$

$\therefore a=\frac{R}{2}$

$\Rightarrow R=2a---------\left(1\right)$

For $N_2$ gas,

$C_p-C_v=\frac{R}{28}$

$\therefore b=\frac{R}{28}$

$\Rightarrow R=28b---------------\left(2\right)$

Now, from ${eq}^n\left(1\right)\&\left(2\right)$, we have

$2a=28b$

$\Rightarrow a=14b$

Hence $\left(C\right)$ is the correct answer.