Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures, $T_1$ and $T_2$ respectively. The vessels are joined and  the gas reaches a common pressure $P$ and a common temperature $T$. Then

The ratio $C_P /C_V$ for a gas mixture consisting of $8\,g$ of helium and $16\,g$ of oxygen is

The amount of heat energy required to raise the temperature of $1\, g$ of helium from $T_1\,K$ to $T_2K$ is

One mole of ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of diatomic gas $(\gamma = 7/5)$ . What is $\gamma $ for the mixture ? $\gamma $ denotes the ratio of specific heat at constant pressure, to that at constant volume

The equation of state for $5\,g$ of oxygen at a pressure $P$ and temperature $T$, when occupying a volume $V$, will be where $R$ is the gas constant