Question

For an isothermal expansion of a perfect gas, the value of \( \frac{\Delta P}{P} \) is equal to:

• A. \( -\gamma^{1/2} \frac{\Delta V}{V} \)
• B. \( -\gamma \frac{\Delta V}{V} \)
• C. \( \gamma \frac{\Delta V}{V} \)
• D. \( -\gamma^{1/2} \frac{\Delta V}{V} \)

Hint:

For an isothermal process, the change in pressure is inversely proportional to the change in volume.

Answer 1

The Correct Option is B

Step 1: Isothermal expansion definition.
In an isothermal process, the temperature of the gas remains constant. The relationship between pressure and volume during an isothermal expansion is governed by \( P \propto \frac{1}{V} \).

Step 2: Deriving the expression.
The differential change in pressure \( \Delta P \) is related to the change in volume by: \[ \frac{\Delta P}{P} = -\gamma \frac{\Delta V}{V} \] Thus, the correct answer is (2).