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.

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.

$A$ certain amount of gas has a volume of $12 \, L$ at a pressure of $3 \, atm$. If the temperature remains constant,what pressure in $atm$ must be applied to reduce its volume to $9 \, L$?

The $PV$ versus $T$ graph for equal masses of $H_2, He$,and $O_2$ is shown in the figure. Choose the correct alternative:

The average force applied on the wall of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

If the pressure of an ideal gas contained in a closed vessel is increased by $0.5\%,$ the increase in temperature is $2 \, K.$ The initial temperature of the gas is ...... $^\circ C$