For an ideal gas, a cyclic process $ABCA$ as shown in the $P-T$ diagram, when presented in a $P-V$ plot, would be:

Given below are two statements:
Statement $I:$ If heat is added to a system,its temperature must increase.
Statement $II:$ If positive work is done by a system in a thermodynamic process,its volume must increase.
In the light of the above statements,choose the correct answer from the options given below.

One mole of a gas expands obeying the relation as shown in the $P-V$ diagram. The maximum temperature in this process is equal to

$A$ gas is expanded from an initial state to a final state along a path on a $P-V$ diagram. The path consists of $(i)$ an isothermal expansion of work $50 J$,$(ii)$ an adiabatic expansion,and $(iii)$ an isothermal expansion of work $20 J$. If the internal energy of the gas is changed by $-30 J$,then the work done by the gas during the adiabatic expansion is: (in $J$)

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is