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An ideal gas is expanded from p 1 , V 1 , T 1 to ( p 2 , V 2 , T 2 ) under different conditions. The incorrect statement among the following is?

Options

  1. AThe word done by the gas is less when it is expanded reversibly from V 1 to V 2 under adiabatic conditions as
  2. BThe change in internal energy of the gas is (i) zero, if it is expanded reversibly with T 1 = T 2 and (ii) pos
  3. CIf the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
  4. DThe work done on the gas is maximum when it is compressed irreversibly from p 2 , V 2 to p 1 , V 1 against con

Correct answer

B. The change in internal energy of the gas is (i) zero, if it is expanded reversibly with T 1 = T 2 and (ii) pos

Step-by-step solution

Area under curve in reversible isothermal is more. So, more work will be done by gas. T 1 = T 2 Δ U = n C V Δ T = 0 In reversible adiabatic expansion, T 2 < T 1 So Δ T = - v e , Δ U = - v e In free expansion, P e x t = 0 So W = 0 If carried out isothermally Δ U = 0 q = 0 (adiabatic); from I law If carried out adiabatically q = 0 Δ U = 0 (isothermal); From I law During irreversible compression, maximum work is done on the gas (corresponding to shaded area).

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