$A$ mixture of $4$ moles of hydrogen,$1$ mole of helium,and $1$ mole of water vapor is treated as an ideal gas mixture. What is the molar specific heat of the mixture at constant pressure?

$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture is

If $22 \, g$ of $CO_2$ gas at $27 \, ^\circ C$ and $16 \, g$ of $O_2$ gas at $37 \, ^\circ C$ are mixed,the final temperature of the mixture will be ...... $^\circ C$.

Two vessels of equal volume contain the same gas. Their pressures and temperatures are $P_1, T_1$ and $P_2, T_2$ respectively. When they are connected,the common pressure and temperature are $P$ and $T$. Then $P/T$ is equal to:

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a 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.

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be: