An ideal gas can be expanded from an initial state to a certain volume, through two different processes: $\left(\mathrm{i}\right) P{V}^2=$constant and $\left(\mathrm{ii}\right) P=K{V}^2$, where $K$ is a positive constant. Then,

A cyclic process $\mathrm{ABCD}$ is shown in the P–V diagram. ($\mathrm{BC}$ and $\mathrm{DA}$ are isothermal)

Which of the following curves represent the same process?

When a system is taken from state $\mathrm{i}$ to state $\mathrm{f}$ along the path $\mathrm{iaf}$, it is found that $Q=50 \mathrm{cal}$ and $W=20 \mathrm{cal}$. Along the path $\mathrm{ibf}$ $Q=36 \mathrm{cal}$, then work (in $\mathrm{cal}$) along the path $\mathrm{ibf}$ is-