$2 \text{ mole}$ 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.

One mole of a gas mixture is heated under constant pressure,and the heat supplied $Q$ is plotted against the temperature difference $\Delta T$ acquired. Find the approximate value of $\gamma$ for the mixture.

$A$ box contains a mixture of ${H_2}$ and $He$ gases. Which of the following statements are correct?

$A$ closed vessel contains $0.1$ mole of a monoatomic ideal gas at $200\, K$. If $0.05$ mole of the same gas at $400\, K$ is added to it,the final equilibrium temperature (in $K$) of the gas in the vessel will be closest to:

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

The molar specific heat of a mixture at constant volume,if one mole of $He$ gas is mixed with three moles of $O_2$ gas,is: (in $R$)