Question

For hydrogen gas $C_P-C_V=a$ and for oxygen gas
$C_P-C_V=b,$ where $C_p$ and $C_v$ are molar specific heats. Then relation between $a$ and $b$ is

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

Answer 1

Answer: (A)

Relation between specific heats per unit mass:
$<br/>C_P-C_V=r=\frac{R}{M}<br/>$
Hence, $r=\frac{R}{M}$
Here, $M$ is molecular weight
Hydrogen:
$<br/>\begin{array}{l}<br/>C_P-C_V=a\\ <br/>⟹a=\frac{R}{M}=\frac{R}{2}<br/>\end{array}<br/>$
Oxygen:
$<br/>C_P-C_V=b<br/>$
$<br/>⟹b=\frac{R}{M}=\frac{R}{32}<br/>$
Ratio of $a$ and $b$ :
$<br/>\frac{a}{b}=\frac{R/2}{R/32}=16<br/>$
Hence, $a=16b$