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Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases

Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 10^5 Pa and a temperature of 300 K . It is adiabatically compressed to half its original volume. Determine the final pressure of the gas. Take = 1.5 .

Options

  1. A5.0 10^5 Pa
  2. B3.5 10^5 Pa
  3. C7.1 10^5 Pa
  4. D8.8 10^4 Pa

Correct answer

C. 7.1 10^5 Pa

Step-by-step solution

For an adiabatic process, the relation between pressure and volume is given by P₁ V₁^ = P₂ V₂^ . Rearranging for the final pressure P₂ : P₂ = P₁ ( V₁ V₂ )^ Given P₁ = 2.5 10^5 Pa , V₁ = 100 cc , V₂ = 50 cc , and = 1.5 : P₂ = 2.5 10^5 ( 100 50 )^ 1.5 P₂ = 2.5 10^5 (2)^ 1.5 P₂ = 2.5 10^5 2 2 Using 2 1.414 : P₂ = 2.5 10^5 2.828 P₂ 7.07 10^5 Pa 7.1 10^5 Pa

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