An air bubble of volume $2.9 \ cm^3$ rises from the bottom of a swimming pool $5 \ m$ deep. At the bottom of the pool,the water temperature is $17^{\circ} C$. The volume of the bubble when it reaches the surface,where the water temperature is $27^{\circ} C$,is . . . . . . $cm^3$. ($g = 10 \ m/s^2$,density of water $\rho = 10^3 \ kg/m^3$,and $1 \ atm = 10^5 \ Pa$)

The product of the pressure and volume of an ideal gas is

The pressure $P$,volume $V$,and temperature $T$ of a gas in jar $A$ are given. The gas in another jar $B$ is at pressure $2P$,volume $V/4$,and temperature $T/4$. What is the ratio of the number of molecules in jar $A$ to jar $B$?

$A$ cylinder of volume $30 \, L$ contains oxygen at an initial gauge pressure of $15 \, atm$ and a temperature of $27^{\circ}C$. After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \, atm$ and its temperature drops to $17^{\circ}C$. The mass of oxygen taken out of the cylinder is approximately ........ $kg$. (Given: $R = 8.31 \, J \, mol^{-1} K^{-1}$,molar mass of $O_2 = 32 \, g/mol$ or $32 \times 10^{-3} \, kg/mol$)

$A$ gas is contained in a closed vessel. The initial temperature of the gas is $100^{\circ} C$. If the pressure of the gas is increased by $4 \%$,what is the increase in the temperature of the gas (in $^{\circ} C$)?

$A$ 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 $\,K$)