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The equation of state for a gas is given by PV = nRT + α V , where n is the number of moles and α is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are T 0 and P 0 respectively. The work done by the gas when its temperature doubles isobarically will be :

Options

  1. AP 0 T 0 ln ⁡ 2
  2. BP 0 T 0 R P 0 + α
  3. CP 0 T 0 R P 0 - α
  4. DP 0 T 0 R

Correct answer

C. P 0 T 0 R P 0 - α

Step-by-step solution

PV = nRT + α V P 0 dV dT = R + α dV dT P 0 - α dV dT = R ∴ dV = RdT P 0 - α ∴ W = ∫ P 0 dV = ∫ T 0 2 T 0 P 0 R P 0 - α dT = P 0 T 0 R P 0 - α

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