The pressure of a given mass of gas at $20^{\circ}C$ is $P$. At constant volume,at what temperature in $^{\circ}C$ will the pressure of the gas become $2P$?

If the pressure of a gas increases by $2 \%$ at constant volume,then its temperature

Find the value of the universal gas constant $R$ in $J \ mol^{-1} K^{-1}$.

The following graph represents the $T-V$ curves of an ideal gas (where $T$ is the temperature and $V$ is the volume) at three pressures $P_1, P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines. Then the correct relation is:

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P = P_0 \left[ 1 - \frac{1}{2} \left( \frac{V_0}{V} \right)^2 \right]$. Here $P_0$ and $V_0$ are constants. Calculate the change in the temperature of the gas if its volume changes from $V_0$ to $2V_0$.

$A$ long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the piston,it moves down. If the air in the enclosure is cooled from temperature $T$ to $T-\Delta T$,the piston moves back to its original position. Then $\Delta T / T$ is close to (Assuming air to be an ideal gas,$g=10 \,m/s^2$,atmospheric pressure is $10^5 \,Pa$)