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

An insulated cylinder of volume $60\,cm^{3}$ is filled with a gas at $27^{\circ}C$ and $2$ atmospheric pressure. Then the gas is compressed making the final volume $20\,cm^{3}$ while allowing the temperature to rise to $77^{\circ}C$. The final pressure is . . . . . . atmospheric pressure.

$A$ balloon contains $1500 \ m^3$ of $He$ at $27^{\circ} C$ and $4 \ atm$ pressure. The volume of $He$ at $-3^{\circ} C$ temperature and $2 \ atm$ pressure will be: (in $m^3$)

The tyre of a bicycle has a volume of $2 \times 10^{-3} \ m^3$. Initially,the tube is filled to $75 \%$ of its volume with air at an atmospheric pressure of $10^5 \ N \ m^{-2}$. When a rider is on the bicycle,the area of contact of the tyre with the road is $24 \times 10^{-4} \ m^2$. The mass of the rider with the bicycle is $120 \ kg$. If a pump delivers a volume of $500 \ cm^3$ of air in each stroke,then the number of strokes required to inflate the tyre is $(g = 10 \ m \ s^{-2})$.

Two different isotherms representing the relationship between pressure $p$ and volume $V$ at a given temperature for the same ideal gas are shown for masses $m_1$ and $m_2$ of the gas respectively in the figure given. Then:

The figure shows the isotherms of a fixed mass of an ideal gas at three temperatures $T_A, T_B$ and $T_C$. Then: