Previous Year NEET Question- Kinetic Theory L-7

For hydrogen gas $C_p-C_v=R$ and for oxygen gas $C_p-C_v=R$, so the relation between $a$ and $b$ is given by [CBSE AIPMT 1991]#

A) $a=16b$

B) $16 b = a$

C) $a=4b$

D) $a=b$

Answer: $a=b$#

Solution:#

Both hydrogen and oxygen are diatomic gases and $C_p-C_V=R$ is same for all ideal gases, hence $a=b$, provided $C_p$ and $C_V$ are molar specific heats. If it was the case of specific heat of $1 \mathrm{~g}$ $C_p-C_V=R\frac{m}{M}$ $$ \begin{array}{rlr} \therefore \quad C_p-C_V & \left.=\frac{R}{2} \quad \text { (for } \mathrm{H}_2, \frac{R}{2}=a\right) C_p-C_V & \left.=\frac{R}{2} \quad \text { for } \mathrm{O}_2, \frac{R}{2}=b\right) \ R & =2 a=32 b & \ a & =16 b & \end{array} $$