Question

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, \( PV = \text{constant} \), while in an adiabatic process \( PV^\gamma = \text{constant} \). 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:

• A. Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
• B. (A) is true but (R) is false
• C. Both (A) and (R) are true and (R) is the correct explanation of (A)
• D. (A) is false but (R) is true

Hint:

In an isothermal process, \( P \) and \( V \) are inversely proportional, while in an adiabatic process, the relationship between \( P \) and \( V \) follows \( PV^\gamma = \text{constant} \), and the decrease in volume is more rapid.

Answer 1

The Correct Option is D

- In an isothermal process, temperature is constant, described by \( PV = \text{constant} \). An increase in pressure results in a proportional decrease in volume, maintaining a constant product.
- In an adiabatic process, \( PV^\gamma = \text{constant} \), where \( \gamma \) represents the ratio of specific heats. The volume reduction in this process is more rapid than in an isothermal one.
Therefore, the assertion (A) is incorrect. The volume decreases more slowly in an isothermal process compared to an adiabatic process. The reason (R) accurately defines both isothermal and adiabatic processes.