For hydrogen gas $(H_2)$,$C_P - C_V = a$,and for oxygen gas $(O_2)$,$C_P - C_V = b$. What is the relationship between $a$ and $b$?

For a gas,the value of $\frac{R}{C_v} = 0.4$. What is the nature of the gas? ($R$ is the universal gas constant)

The value of the gas constant $(R)$ calculated from the perfect gas equation is $8.32 \ J/mol \cdot K$,whereas its value calculated from the knowledge of $C_P$ and $C_V$ of the gas is $1.98 \ cal/mol \cdot K$. From this data,the value of $J$ is ......... $J/cal$.

The specific heat of argon at constant pressure and constant volume are $C_p$ and $C_v$ respectively. Its density $\rho$ at $N.T.P.$ will be: [Where $P$ and $T$ are pressure and temperature respectively at $N.T.P.$]

What is the relationship between the internal energy $U$ of an ideal gas and its pressure $P$ and volume $V$?

For an ideal non-rigid diatomic gas,the value of $\frac{R}{C_V}$ is nearly,given that $\gamma = \frac{C_P}{C_V} = \frac{9}{7}$.