A dry gas of volume V (litres) at temperature T has its pressure doubled from 1 kgf/cm^2 to 2 kgf/cm^2 at constant temperature. What will be the new gas volume?

Introduction / Context:Isothermal compression or expansion of gases is governed by Boyle’s law for ideal behavior. This relationship is used routinely in sizing compressors, storage vessels, and performing quick back-of-the-envelope checks.

Given Data / Assumptions:

• Initial pressure P1 = 1 kgf/cm^2; final pressure P2 = 2 kgf/cm^2.
• Temperature constant (isothermal process).
• Gas assumed ideal and dry.

Concept / Approach:Boyle’s law states P * V = constant for a given mass of ideal gas at constant temperature. Therefore, P1 V1 = P2 V2, so V2 = (P1/P2) * V1. Doubling the pressure halves the volume.

Step-by-Step Solution:

Verification / Alternative check:A pressure–volume hyperbola confirms inverse proportionality: doubling P halves V.

Why Other Options Are Wrong:

• 2V or V^2: contradict inverse relationship.
• V/4: would correspond to quadrupling the pressure, not doubling.
• Unchanged: only true if pressure remained constant.

Common Pitfalls:Mixing absolute and gauge units; ensure consistent pressure basis when applying gas laws.

Final Answer:V/2