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

Two samples A and B of the same gas have equal volumes and pressures. The gas in sample A is expanded isothermally to double its volume, whereas the gas in sample B is expanded adiabatically to double its volume. If the work done by the gas is identical for the two cases, which of the following equations does satisfy?

Options

  1. A1 - 2^ 1- = 2
  2. B1 - 2^ 1- = ( - 1) 2
  3. C1 - 2^ = ( - 1) 2
  4. D1 - 2^ -1 = ( - 1) 2

Correct answer

B. 1 - 2^ 1- = ( - 1) 2

Step-by-step solution

Let the initial pressure and volume of both samples be P₀ and V₀ . For sample A, the gas undergoes isothermal expansion to double its volume. The work done is given by: W_A = nRT₀ ( V_f V_i ) = P₀ V₀ ( 2V₀ V₀ ) = P₀ V₀ 2 For sample B, the gas undergoes adiabatic expansion to double its volume. The work done is given by: W_B = P_i V_i - P_f V_f - 1 Using the adiabatic equation P_i V_i^ = P_f V_f^ , we find the final pressure P_f : P_f = P₀ ( V₀ 2V₀ )^ = P₀ 2^ - Substituting P_f and V_f = 2V₀ into the work equation:

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