If one mole of an ideal monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with one mole of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$,the value of $\gamma$ for the mixture is:

In a container,there is a mixture of two different gases. Will both gases have the same kinetic energy?

Sound travels in a mixture of $2$ moles of helium and $n$ moles of hydrogen. If the root-mean-square (rms) speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound,then the value of $n$ will be:

Three ideal gases at absolute temperatures $T_1, T_2$,and $T_3$ are mixed. Their number of molecules are $n_1, n_2$,and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture will be .....

$A$ gas mixture consists of molecules of $A, B$ and $C$ with masses $m_A > m_B > m_C$. Rank the three types of molecules in decreasing order of $(a)$ average $K.E.$,$(b)$ $rms$ speeds.

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be: