Heat, Work & First Law of Thermodynamics question from JEE Main 2021 (17 Mar, Shift 2)

Answer: (b)

1. (a) On a $P$-$V$ graph a vertical line means constant $V$ (isochoric), not adiabatic. Wrong.
2. (b) Isothermal means constant $T$, which is a vertical line on a $P$-$T$ graph, not horizontal. Wrong.
3. (c) $V$-$T$: isothermal is vertical ($T$ constant); adiabatic $TV^{\gamma-1} =$ constant, so $V$ falls as $T$ rises. Correct.
4. (d) $P$-$T$: isothermal is vertical; adiabatic $P^{1-\gamma}T^{\gamma} =$ constant gives $P \propto T^{\gamma/(\gamma-1)}$, rising curve. Correct.
5. So the answer is (b) (c) and (d).