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

Three samples A , B and C of the same gas ( = 1.5 ) initially have equal volumes and temperatures. Each sample's volume is doubled, with the process being isothermal for A , adiabatic for B , and isobaric for C . If the final pressures are equal for all three samples, determine the ratio of their initial pressures.

Options

  1. A1 : 2 : 2 2
  2. B2 : 2 2 : 1
  3. C2 2 : 2 : 1
  4. D2 : 3 : 1

Correct answer

B. 2 : 2 2 : 1

Step-by-step solution

Let the initial volume of each sample be V₀ and the final pressure of each sample be P_f . For sample A (isothermal process): P_A V₀ = P_f (2V₀) P_A = 2P_f For sample B (adiabatic process): P_B V₀^ = P_f (2V₀)^ Given = 1.5 = 3 2 , P_B = P_f (2)^ 3/2 = 2 2 P_f For sample C (isobaric process): Pressure remains constant, so P_C = P_f The ratio of their initial pressures is: P_A : P_B : P_C = 2P_f : 2 2 P_f : P_f = 2 : 2 2 : 1

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