$A$ gas mixture contains $2$ moles of $O_2$ and $4$ moles of $Ar$. Neglecting vibrational modes,what is the total internal energy of the system at temperature $T$ (in $, RT$)?

One litre of oxygen at a pressure of $1 \,atm$ and two litres of nitrogen at a pressure of $0.5 \,atm$ are introduced into a vessel of volume $1 \,L$. If there is no change in temperature, the final pressure of the mixture of gas (in $atm$) is

$A$ gas mixture consists of $3 \, moles$ of oxygen and $5 \, moles$ of argon at temperature $T$. Considering only translational and rotational modes,the total internal energy of the system is: (in $, RT$)

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?

$2 \text{ mole}$ of $N_2$ gas at $27 \, ^oC$ is mixed with $1 \text{ mole}$ of $He$ gas at $-73 \, ^oC$. Find the final temperature $T_{\text{mix}}$ of the mixture.

$A$ 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?