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

$A$ gas mixture contains $n_1$ moles of a monoatomic gas and $n_2$ moles of a gas of rigid diatomic molecules. Each molecule in the monoatomic and diatomic gas has $3$ and $5$ degrees of freedom respectively. If the adiabatic exponent $\left(\frac{C_p}{C_V}\right)$ for this gas mixture is $1.5$, then the ratio $\frac{n_1}{n_2}$ will be

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_1$ and contains ideal gas at pressure $P_1$ and temperature $T_1$. The other chamber has volume $V_2$ and contains ideal gas at pressure $P_2$ and temperature $T_2$. If the partition is removed without doing any work on the gas,the final equilibrium temperature of the gas in the container will be

$A$ 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 $, RT$)

The capacity of a vessel is $3 \, L$. It contains a mixture of $6 \, g$ oxygen,$8 \, g$ nitrogen,and $5 \, g$ $CO_2$ at $27^{\circ}C$. If $R = 8.31 \, J/(mol \cdot K)$,then the pressure in the vessel in $N/m^2$ will be (approx.)

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: