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?
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AV/2
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B2V
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CV/4
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DV^2
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Eunchanged at V
Answer
Correct Answer: V/2
Explanation
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:
Write law: P1 V1 = P2 V2.Insert values: (1) * V = (2) * V2.Solve: V2 = V / 2.Conclude the new volume equals one-half of the original.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