When the pressure of the gas contained in a closed vessel is increased by $2.5 \%$,the temperature of the gas increases by $4 \ K$. The initial temperature of the gas is (in $K$)

An open and wide glass tube is immersed vertically in mercury in such a way that a length of $0.05 \, m$ extends above the mercury level. The open end of the tube is closed and the tube is raised further by $0.43 \, m$. The length of the air column above the mercury level in the tube will be ...... $m$. Take $P_{atm} = 76 \, cm$ of mercury.

An oxygen cylinder of volume $30 \; L$ has 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 After some oxygen is withdrawn from the cylinder,the gauge pressure drops to $11 \; atm$ and its temperature drops to $17 \; ^{\circ}C$. Estimate the mass (in $kg$) of oxygen taken out of the cylinder ($R = 8.31 \; J \; mol^{-1} K^{-1}$,molecular mass of $O_{2} = 32 \; u$).

If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%,$ the increase in temperature is $2 \, K.$ The initial temperature of the gas is ...... $^\circ C$

$A$ sample of oxygen gas is compressed from a volume of $500 \, cc$ to $400 \, cc$ at a pressure of $2 \, atm$. If the temperature is kept constant,what pressure in $atm$ is required?

$A$ closed vessel contains $8\,g$ of oxygen and $7\,g$ of nitrogen. The total pressure is $10\,atm$ at a given temperature. If oxygen is now absorbed by introducing a suitable absorbent,the pressure of the remaining gas in $atm$ will be: