$A$ steel cylinder contains helium gas at $250 \, kPa$ pressure and $300 \, K$ temperature. The cylinder can withstand a maximum pressure of $1 \times 10^6 \, Pa$. The room in which the cylinder is placed catches fire. Predict whether the cylinder will burst before it melts. (Melting point of the cylinder = $1800 \, K$)

Under what conditions will a pure sample of an ideal gas not only exhibit a pressure of $1 \, atm$ but also a concentration of $1 \, mol \, L^{-1}$ $(R = 0.082 \, L \, atm \, mol^{-1} \, K^{-1})$?

$A$ container is filled with nitrogen gas at a certain temperature and pressure. The mass of the gas is $0.6 \ g$. Now,the container is filled with another gas at the same temperature and pressure. If the mass of the second gas under the given conditions is $0.73 \ g$,identify the gas.

The volume versus temperature graph of $1 \ mole$ of an ideal gas is given below. The pressure of the gas (in $atm$) at $X, Y$ and $Z$,respectively,are

At $27\,^oC$ temperature in a $2\, L$ closed vessel,$10\, g$ of $H_2$ and $22\, g$ of $CO_2$ gases are filled. Find the partial pressure of each gas and the total pressure of the mixture. (Use $R = 0.08314\, L \cdot bar \cdot K^{-1} \cdot mol^{-1}$ and formula $pV = nRT$)

$A$ closed tank has two compartments $A$ and $B$,both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $1$). If the old partition is replaced by a new partition which can slide and conduct heat but does $NOT$ allow the gas to leak across (Figure $2$),the volume (in $m^3$) of the compartment $A$ after the system attains equilibrium is. . . . . . . .