Question

If the pressure of an ideal gas is decreased by 10% isothermally, then its volume will

• A. decrease by 9%
• B. increase by 11.11%
• C. increase by 10%
• D. decrease by 11.11%

Hint:

Use the fractional inverse shortcut! A decrease of 10% means the pressure becomes $\frac{9}{10}$ of its original value. Since volume is inversely proportional to pressure ($V \propto \frac{1}{P}$), the volume must become the flipped fraction $\frac{10}{9}$ of its original value. An increase from 1 to $\frac{10}{9}$ is a gain of $\frac{1}{9}$, which equals 11.11% instantly!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
In an isothermal process, pressure decreases by 10%; find the percentage increase in volume.

Step 2: Key Formula or Approach:
Boyle's Law: P₁V₁ = P₂V₂. Percentage change = (ΔV/V₁)×100%.

Step 3: Detailed Explanation:
P₂ = 0.90P₁. P₁V₁ = 0.90P₁·V₂ → V₂ = V₁/0.90 = (10/9)V₁. ΔV = V₁/9. % increase = (100/9)% ≈ 11.11%.

Step 4: Final Answer:
Volume increases by 11.11%, matching option (B).