Question

For hydrogen gas $C_P-C_V=a$ and for oxygen gas $C_P-C_V=b$ then the relation between $a$ and $b$ is (where $C_P$ and $C_V$ are gram specific heats).

• A. $a=16b$
• B. $b=16a$
• C. $a=b$
• D. None of these

Answer 1

The correct option is A $a=16b$

Relation between specific heats per unit mass:

$C_P-C_V=r=\frac{R}{M}$

Hence, $r=\frac{R}{M}$

Here, M is molecular weight

Hydrogen:

$C_P-C_V=a⟹a=\frac{R}{M}=\frac{R}{2}$

Oxygen:

$C_P-C_V=b⟹b=\frac{R}{M}=\frac{R}{32}$

Ratio of a and b:

$\frac{a}{b}=\frac{R/2}{R/32}=16$

Hence, $a=16b$