Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R) : In isothermal process, PV = constant, while in adiabatic process $$PV^{\gamma}$$ = constant. Here $$\gamma$$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below :

Assertion (A): With increase in pressure, volume falls off more rapidly in an isothermal process compared to an adiabatic process.

For isothermal: $$PV = C$$, so $$\frac{dV}{dP} = -\frac{V}{P}$$

For adiabatic: $$PV^\gamma = C$$, so $$\frac{dV}{dP} = -\frac{V}{\gamma P}$$

Since $$\gamma > 1$$: $$\left|\frac{dV}{dP}\right|_{isothermal} = \frac{V}{P} > \frac{V}{\gamma P} = \left|\frac{dV}{dP}\right|_{adiabatic}$$

So the volume decreases more rapidly (larger magnitude of dV/dP) in the isothermal process. Assertion A is true.

Reason (R): States the equations PV = constant (isothermal) and $$PV^\gamma$$ = constant (adiabatic). This is true and directly explains why the assertion holds (the extra factor of $$\gamma$$ in the adiabatic case makes the volume change slower).

Both A and R are true, and R is the correct explanation of A.

The correct answer is Option 1.