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The pressure P , volume V and temperature T of a certain material are related by the equation P = α T 2 / V . The work done by the material at constant pressure, when the temperature changes from T 0 to 2 T 0 , is

Options

  1. A3 α T 0 2
  2. B5 α T 0 2
  3. C2 3 α T 0 2
  4. D7 α T 0 2

Correct answer

A. 3 α T 0 2

Step-by-step solution

The given relation is P = α T 2 V ∴ V = α T 2 P As pressure is kept constant, dV = 2 α T P dT W = ∫ P · dV = ∫ T 0 2T 0 P 2 α T P dT = 2 α T 2 2 T 0 2T 0 = 3 α T 0 2

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