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 an isothermal process, $PV$ = constant, while in an 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:
Answer: (A) Both (A) and (R) are true and (R) is the correct explanation of (A)
Differentiate the two laws:
- Isothermal, $PV = $ const: $\dfrac{dV}{dP} = -\dfrac{V}{P}$
- Adiabatic, $PV^\gamma = $ const: $\dfrac{dV}{dP} = -\dfrac{V}{\gamma P}$
Since $\gamma > 1$, the volume falls faster with pressure in the isothermal process. (A) is true, (R) is true, and the two laws in (R) are exactly what give (A).
Solution by Sreeraj P, M.Sc Physics