There are two samples $A$ and $B$ of a certain gas,which are initially at the same temperature and pressure. Both are compressed from volume $V$ to $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is

$A$ gas is governed by an equation $V = \frac{aT^3}{P}$,where $P, V$,and $T$ are pressure,volume,and temperature of the gas respectively,and $a$ is a constant. If the temperature of the gas is doubled at constant pressure,then the work done by the gas is: (in $aT^3$)

$A$ cyclic process on an ideal monatomic gas is shown in the figure. The correct statement is:

Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600\, K,$ $T_B = 800\, K,$ $T_C = 2200\, K,$ and $T_D = 1200\, K,$ then the work done per cycle is approximately ...... $kJ$.

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to $4$ times its initial volume $(V_0)$, then isobarically compressed to its original volume. Finally, the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

If one mole of an ideal gas at $(P_{1}, V_{1})$ is allowed to expand reversibly and isothermally ($A$ to $B$),its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B \rightarrow C)$. Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net work done by the gas is equal to ...... .