Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2: 3$. The ratio of their partial pressures,when enclosed in a vessel kept at a constant temperature,is $4: 3$. The ratio of their densities is:

$A$ 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 $RT$)

Two ideal gases at absolute temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. The masses of the molecules are $m_1$ and $m_2$ and the number of molecules in the gases are $n_1$ and $n_2$ respectively. The temperature of the mixture will be:

$1 \text{ mole}$ of a gas with $\gamma = 7/5$ is mixed with $1 \text{ mole}$ of a gas with $\gamma = 5/3$. The value of $\gamma$ for the resulting 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 ....... $^oC$.

$2 \text{ mole}$ 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.