The Carnot cycle (reversible) of a gas represented by a Pressure-Volume $(P-V)$ curve is shown in the diagram. Consider the following statements:
$I.$ Area $ABCD =$ Work done by the gas
$II.$ Area $ABCD =$ Net heat absorbed
$III.$ Change in the internal energy in the cycle $= 0$
Which of these are correct?

What is a Carnot cycle?

One mole of an ideal monoatomic gas undergoes the following four reversible processes:
Step $1$: It is first compressed adiabatically from volume $V_{1}$ to $1 \; m^{3}$.
Step $2$: Then expanded isothermally to volume $10 \; m^{3}$.
Step $3$: Then expanded adiabatically to volume $V_{3}$.
Step $4$: Then compressed isothermally to volume $V_{1}$.
If the efficiency of the above cycle is $3/4$, then $V_{1}$ is ............ $m^{3}$.

In a Carnot engine,the temperature of the reservoir is $927\ ^oC$ and that of the sink is $27\ ^oC.$ If the work done by the engine is $12.6 \times 10^6 \ J,$ the quantity of heat absorbed by the engine from the reservoir is:

$A$ diatomic ideal gas is used as the working substance in a Carnot engine. During the adiabatic expansion process,if the volume of the gas increases from $V$ to $32V$,what is the efficiency of the engine?

$A$ Carnot engine uses diatomic gas as a working substance. During the adiabatic expansion part of the cycle,if the volume of the gas becomes $32$ times its initial volume,then the efficiency of the engine is (in $\%$)