$A$ gas of certain mass filled in a closed cylinder at a pressure of $3.23 \ kPa$ has a temperature of $50^{\circ} C$. The gas is now heated until its absolute temperature is doubled. The modified pressure is . . . . . . $Pa$.

The floor area of a room is $20 \, m^2$ and its walls are $3 \, m$ high. If the pressure of air in the room is $1 \, atm$ and the temperature is $27 \, ^\circ C$,find the mass of the air in the room. (Take the molar mass of air as $29 \, g/mol$). Given: $1 \, atm = 1.01 \times 10^5 \, N \, m^{-2}$,$R = 8.31 \, J \, mol^{-1} K^{-1}$.

For an ideal gas undergoing a constant temperature process (isothermal process),what is the nature of the graph between pressure $(P)$ and $\frac{1}{V}$ (where $V$ is volume)?

An open glass tube is immersed in mercury such that a length of $8 \ cm$ extends above the mercury level. The open end of the tube is then closed and sealed,and the tube is raised vertically by an additional $46 \ cm$. What will be the length of the air column above the mercury in the tube now? (Atmospheric pressure = $76 \ cm$ of $Hg$)

The value of $PV/T$ for one mole of an ideal gas is nearly equal to . . . . . . $J$ $mol^{-1}K^{-1}$.

$A$ vessel that can withstand a pressure of $100 \,atm$ is filled with hydrogen at $27^{\circ} C$ up to a pressure of $20 \,atm$. If the vessel is heated, then the temperature at which it explodes is (in $\,K$)