Question

For hydrogen gas, $C_p-C_v$ = a and for nitrogen gas $C_p-C_v$ = b, then the relation between a and b is:
(where $C_p$ and $C_v$ are specific heats defined per gram)

• A. $a=16b$
• B. $b=16a$
• C. $a=b$
• D. $a=14b$

Answer 1

The correct option is D $a=14b$

We know relation between specific heats per unit mass:
$C_p-C_v$ = $\frac{R}{M}$
where R = Gas constant and $M$ = Molar mass of the gas
For Hydrogen,
$C_p-C_v$ = a = $\frac{R}{M}$ = $\frac{R}{2}$
Similarly, for nitrogen
$C_p-C_v$ = b = $\frac{R}{M}$ = $\frac{R}{28}$
So, ratio of $a$ and $b$
$\frac{a}{b}$ = $\frac{\frac{R}{2}}{\frac{R}{28}}$
$\frac{a}{b}$ = 14
$a=14b$