Question

A gas expands isothermally and reversibly from a volume V to 2V. If the initial pressure is P, what is the final pressure?

• A. \( \frac{P}{2} \)
• B. \( \frac{P}{4} \)
• C. \( 2P \)
• D. \( P \)

Hint:

In isothermal expansions, remember that \( PV = \text{constant} \). Use this to find the relationship between initial and final pressures and volumes.

Answer 1

The Correct Option is A

For an isothermal, reversible expansion of an ideal gas, the product of pressure and volume remains constant: \[ P_1 V_1 = P_2 V_2. \] Given \( V_1 = V \) and \( V_2 = 2V \), we have: \[ P V = P_2 \cdot 2V. \] Solving for \( P_2 \): \[ P_2 = \frac{P}{2}. \] Thus, the final pressure is: \[ \boxed{\frac{P}{2}}. \]