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:

$A$ gas mixture consists of molecules of type $1, 2$ and $3$,with molar masses $m_1 > m_2 > m_3$. $v_{rms}$ and $\bar K$ are the $r.m.s.$ speed and average kinetic energy of the gases. Which of the following is true?

$A$ vessel of volume $V$ contains a mixture of ideal gases at temperature $T$. The gas mixture contains $n_1, n_2$ and $n_3$ moles of three gases. Assuming an ideal gas system,the pressure of the mixture is

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:

$A$ gaseous mixture consists of $4 \ g$ oxygen and $4 \ g$ of helium. The ratio $\frac{C_p}{C_V}$ of the mixture is ($C_p$ and $C_V$ are molar specific heats of the mixture at constant pressure and at constant volume respectively).

$A$ gas mixture consists of $2$ moles of oxygen and $4$ moles of neon at temperature $T$. Neglecting all vibrational modes,the total internal energy of the system will be $...........\,RT$.