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 heat capacity in cal/g-K, then select the correct reaction.

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

Answer 1

The correct option is C $a=16b$

Solution:- (C) $a=16b$

Given:-

For $H_2$ gas,

$C_p-C_v=a$

For $H_2$ gas,

$C_p-C_v=b$

Solution:-

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,

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

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

$\Rightarrow R=21.....\left(1\right)$

For $O_2$ gas,

$C_p-C_v=\frac{R}{32}$

$\therefore b=\frac{R}{32}$

$\Rightarrow R=32b.....\left(2\right)$

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

$2a=32b$

$\Rightarrow a=16b$

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