$A$ vessel of volume $0.02 \, m^3$ contains a mixture of hydrogen and helium at $20 \, ^oC$ and $2$ atmospheric pressure. The mass of the mixture is $5 \, g$. Find the ratio of the mass of hydrogen to that of helium in the mixture.

$A$ container is divided into two chambers by a partition. The volume of the first chamber is $4.5 \, L$ and the second chamber is $5.5 \, L$. The first chamber contains $3.0 \, \text{moles}$ of gas at a pressure of $2.0 \, \text{atm}$, and the second chamber contains $4.0 \, \text{moles}$ of gas at a pressure of $3.0 \, \text{atm}$. After the partition is removed and the mixture attains equilibrium, the common equilibrium pressure existing in the mixture is $x \times 10^{-1} \, \text{atm}$. The value of $x$ is......... (in $.5$)

The molar heat capacity of a mixture of two gases at constant volume is $13R/6$. The ratio of the number of moles of the first gas to the second is $1:2$. The respective gases may be:

$A$ mixture of hydrogen and oxygen has a volume of $2000 \; cm^{3}$,a temperature of $300 \; K$,a pressure of $100 \; kPa$,and a mass of $0.76 \; g$. The ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture is:

Two rigid boxes placed on a table contain different ideal gases. Box $A$ contains $1 \text{ mole}$ of nitrogen at temperature $T_0$. Box $B$ contains $1 \text{ mole}$ of helium at temperature $(7/3) T_0$. Both boxes are brought into thermal contact,and heat flows until they reach a common final temperature $T_f$. (Neglect the heat capacity of the boxes). Express the final temperature $T_f$ in terms of $T_0$.

$A$ container has two chambers of volumes $V_1=2 \ L$ and $V_2=3 \ L$ separated by a partition made of a thermal insulator. The chambers contain $n_1=5$ and $n_2=4$ moles of an ideal gas at pressures $p_1=1 \ atm$ and $p_2=2 \ atm$,respectively. When the partition is removed,the mixture attains an equilibrium pressure of: (in $atm$)