$A$ vessel with an open mouth contains air at $60^{\circ}C$. When the vessel is heated up to temperature $T$,one-fourth of the air goes out. The value of $T$ is ..... $^{\circ}C$

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

$A$ thin tube sealed at both ends is $100 \ cm$ long. It lies horizontally, the middle $20 \ cm$ containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced? (Given: cross-section of the tube can be assumed to be uniform) ........ $cm$

The adjoining figure shows graphs of pressure and volume of a gas at two temperatures $T_1$ and $T_2$. Which of the following is correct?

The change in the magnitude of the volume of an ideal gas when a small additional pressure $\Delta P$ is applied at a constant temperature is the same as the change when the temperature is reduced by a small quantity $\Delta T$ at constant pressure. The initial temperature and pressure of the gas were $300 \ K$ and $2 \ atm$ respectively. If $|\Delta T| = C|\Delta P|$,then the value of $C$ in $(K/atm)$ is......

An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?