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:
$
C_{P}-C_{V}=r=\frac{R}{M}
$
Hence, $r=\frac{R}{M}$
Here, $M$ is molecular weight
Hydrogen:
$
\begin{array}{l}
C_{P}-C_{V}=a \\
\Longrightarrow a=\frac{R}{M}=\frac{R}{2}
\end{array}
$
Oxygen:
$
C_{P}-C_{V}=b
$
$
\Longrightarrow b =\frac{ R }{ M }=\frac{ R }{32}
$
Ratio of $a$ and $b$ :
$
\frac{ a }{ b }=\frac{ R / 2}{ R / 32}=16
$
Hence, $a=16 b$