$A$ 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 $, RT$)

$A$ mixture of two moles of hydrogen and one mole of argon gas is taken in a closed container at room temperature. Consider the following two statements:
$(i)$ The average kinetic energy of each molecule of $H_2$ and $Ar$ are the same.
$(ii)$ The partial pressure due to argon gas is more than that due to hydrogen gas.

Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium $M_1 = 4 \ g/mol$ and that of hydrogen $M_2 = 2 \ g/mol$. The equivalent molar mass of the mixture is:

$1 \, g$ of $H_2$ at $27 \, ^oC$ is mixed with $16 \, g$ of $O_2$ at $37 \, ^oC$. The temperature of the mixture is about ....... $^oC$.

$A$ gas mixture consists of $8$ moles of argon and $6$ moles of oxygen at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system is (in $RT$)

If three moles of monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$,the value of adiabatic exponent $\gamma$ for the mixture is: