The equation of state for $n$ moles of an ideal gas is $PV = nRT$,where $R$ is a constant. The $SI$ unit for $R$ is

The figure shows graphs of pressure $(P)$ versus density $( ho)$ for an ideal gas at two temperatures $T_1$ and $T_2$.

The pressure and temperature of an ideal gas in a closed vessel are $720 \, kPa$ and $40^\circ C$ respectively. If $\frac{1}{4}^{th}$ of the gas is released from the vessel and the temperature of the remaining gas is raised to $353^\circ C$,the final pressure of the gas is ....... $kPa$.

$A$ gas is filled in a cylinder. If its temperature is increased by $20\%$ and its volume decreases by $10\%$, what percentage of the gas will have leaked out?

$A$ 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 ..... $^{\circ}C$

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$, the piston moves through a length of $5 \, cm$. The length of the cylindrical vessel in $cm$ is: