When the temperature of a gas in a closed container is increased by $1 ^\circ C$,its pressure increases by $0.4 \%$. What is the initial temperature of the gas?

$A$ vessel of volume $8\, L$ contains an ideal gas at $300\, K$ and $2\, atm$ pressure. The gas is allowed to leak until the pressure becomes $125\, kPa$. Calculate the number of moles that leaked out if the temperature remains constant.

$A$ $20 \,cm$ long tube is closed at one end. It is held vertically,and its open end is dipped in water until only half of it is outside the water surface. Consequently,water rises in it by height $h$ as shown in the figure. The value of $h$ is closest to (assume that the temperature remains constant,$P_{\text{atm}} = 10^5 \,N/m^2$,density of water $\rho = 10^3 \,kg/m^3$,and acceleration due to gravity $g = 10 \,m/s^2$): (in $,cm$)

$A$ cylinder of $5 \ L$ capacity,filled with air at $N.T.P.$,is connected to another evacuated cylinder of $30 \ L$ capacity. The resultant air pressure in both the cylinders will be ...... $cm$ of $Hg$. (in $.85$)

The pressure versus temperature graph of an ideal gas at constant volume $V$ and mass $m$ is shown by the straight line $A$. If the mass of the gas is doubled and the volume is halved,then the corresponding pressure versus temperature graph will be shown by the line:

An ideal gas undergoes a process maintaining the relation between pressure $(P)$ and volume $(V)$ as $P = P_o(1 + (\frac{V_o}{V})^2)^{-1}$, where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo the above-mentioned process, calculate the difference in the temperatures of these samples, $T_B - T_A$, assuming the process is evaluated at their initial states. ($R$ = gas constant)