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MHT CET202523 Apr 2025Morning ShiftPhysicsKinetic Theory of GasesActual

How much should the pressure be increased in order to reduce the volume of a given mass of gas by 5 % at the constant temperature?

Options

  1. A5 %
  2. B10 %
  3. C5.26 %
  4. D4 %

Correct answer

C. 5.26 %

Step-by-step solution

Boyle's Law states that for a fixed mass of gas at constant temperature, PV = constant . When volume decreases by 5%, the new volume becomes V₂ = 0.95V₁ . Applying Boyle's Law: P₁V₁ = P₂V₂ implies P₁V₁ = P₂(0.95V₁) , so P₂ = P₁ 0.95 . The percentage increase in pressure is given by: P₂ - P₁ P₁ 100 % = ( 1 0.95 - 1 ) 100 % Simplifying: 0.05 0.95 100 % = 1 19 100 % 5.26 % The answer corresponds to option C .

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