Heat is applied to a rigid diatomic gas at constant pressure. The ratio $\Delta Q : \Delta U : \Delta W$ is

Initial pressure and volume of a gas are $P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $,P$)

$A$ thermodynamic cycle of an ideal gas is shown in the figure. Choose the correct option which represents the same cycle.

In a certain thermodynamical process,the pressure of a gas depends on its volume as $P = kV^{3}$. The work done when the temperature changes from $100^{\circ}C$ to $300^{\circ}C$ will be .......... $nR$,where $n$ denotes the number of moles of a gas.

Air in a cylinder is suddenly compressed by a piston,which is then maintained at the same position. With the passage of time,

Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. The piston of cylinder $A$ is free to move and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)