For an ideal gas, a cyclic process $ABCA$ is shown in the $P-T$ diagram. Which of the following represents the corresponding $P-V$ plot?

For a monoatomic gas, the work done at constant pressure is $W$. The heat supplied at constant volume for the same rise in temperature of the gas is

The $P-V$ diagram of a certain process (Carnot cycle) is as shown. The process is also represented as:

An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:

Column $I$	Column $II$
$(p)$ isobaric	$(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$
$(q)$ isothermal	$(y)$ $PV$
$(r)$ adiabatic	$(z)$ $PV \ln 2$

The correct matching of column $I$ and column $II$ is given by:

$A$ heat engine is involved with an exchange of heat of $1915\, J,$ $-40\, J,$ $+125\, J,$ and $-Q\, J$ during one cycle,achieving an efficiency of $50.0 \%$. The value of $Q$ is ....... $J$.

An engine operates by taking $n$ moles of an ideal gas through the cycle $ABCDA$ shown in the figure. The thermal efficiency of the engine is: (Take $C_v = 1.5 R$,where $R$ is the gas constant)