The equation of state for a gas is given by PV = nRT + α V , where n is the number of moles and α…

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 T0 and P0 respectively. The work done by the gas when its temperature doubles isobarically will be :
  1. P 0 T 0 ln⁡ 2
  2. P 0 T 0 R P 0 + α
  3. P 0 T 0 R P 0 - α
  4. P 0 T 0 R

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

Asked in: JEE Main 2014 (09 Apr Online)

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