$A$ vessel contains $3$ moles of $He$,$1$ mole of $Ar$,$5$ moles of $N_2$,and $3$ moles of $H_2$. If the vibrational modes are ignored,the total internal energy of the system of gases is (in $RT$)

$A$ gas mixture consists of equal masses of Helium and Oxygen. What is the ratio of $C_P$ to $C_V$ for the mixture?

When $16 \, g$ of $O_2$ at $37^\circ C$ is added to $22 \, g$ of $CO_2$ at $27^\circ C$,what will be the final temperature in $^\circ C$?

Two ideal gases $A$ and $B$ having the same temperature $T$,same pressure $P$,and same volume $V$,are mixed together. If the temperature of the mixture is kept constant and the volume occupied by the mixture is reduced to $\frac{V}{2}$,then the pressure of the mixture will become:

Find $\gamma$ for the mixture of $11 \, g$ of $CO_{2}$ and $14 \, g$ of $N_{2}$.

$A$ container has two chambers of volumes $V_1=2 \ L$ and $V_2=3 \ L$ separated by a partition made of a thermal insulator. The chambers contain $n_1=5$ and $n_2=4$ moles of an ideal gas at pressures $p_1=1 \ atm$ and $p_2=2 \ atm$,respectively. When the partition is removed,the mixture attains an equilibrium pressure of: (in $atm$)