The figure shows a $P$-$V$ diagram with three isotherms at $700$ K, $500$ K and $300$ K. Four processes I, II, III and IV start from a common initial state. Match each process with its type:\\ List-I (Process): I, II, III, IV\\ List-II (Type): (a) Adiabatic, (b) Isobaric, (c) Isochoric, (d) Isothermal.\\ Which of the following is the correct matching?

Solution & Explanation

\textbf{Answer:} (b) I$\to$c, II$\to$a, III$\to$d, IV$\to$b \textbf{Solution:} Starting from the common state, identify each process by its geometry on the $P$-$V$ diagram: $\bullet$ Process I is a vertical line (constant volume) $\Rightarrow$ \textbf{isochoric} (c). $\bullet$ Process II is a steep falling curve, steeper than the isotherm, crossing to a lower-temperature isotherm $\Rightarrow$ \textbf{adiabatic} (a), since an adiabat is steeper than an isotherm and lowers the temperature on expansion. $\bullet$ Process III follows along an isotherm (same temperature curve) $\Rightarrow$ \textbf{isothermal} (d). $\bullet$ Process IV is a horizontal line (constant pressure) $\Rightarrow$ \textbf{isobaric} (b). Hence I$\to$c, II$\to$a, III$\to$d, IV$\to$b, which is option (b).