$A$ 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:

$1 \text{ mole}$ 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:

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 $R$)

$A$ closed container of volume $0.02 \ m^3$ contains a mixture of neon and argon gases at a temperature of $27^{\circ}C$ and a pressure of $1 \times 10^5 \ N/m^2$. The total mass of the mixture is $28 \ g$. If the atomic weights of neon and argon are $20$ and $40$ respectively,find the mass of each gas in the container in $g$,assuming they behave as ideal gases. $(R = 8.314 \ J/mol \cdot K)$

$A$ mixture of two non-reactive ideal gases is enclosed in a vessel consisting of one mole of a monatomic gas '$A$' and 'n' moles of a diatomic gas '$B$' at a temperature '$T$'. If the adiabatic constant of the gaseous mixture is $\frac{13}{9}$,then the value of 'n' is:

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy,the final temperature of the mixture is