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NEETChemistryThermodynamics (C)

One mole of an ideal gas undergoes a 3-step cyclic process as follows: (i) Isochoric heating from temperature T₁ to T₂ at volume V₁ . (ii) Isothermal expansion at temperature T₂ from volume V₁ to V₂ . (iii) Isobaric compression from volume V₂ back to V₁ at pressure P₁ (returning the gas to temperature T₁ ). Which of the following expressions represents the net thermodynamic work ( w ) for the complete cycle? (Assume

Options

  1. A-RT₂ ( V₂ V₁ )
  2. B-RT₂ ( V₂ V₁ ) - R(T₂ - T₁)
  3. C-RT₂ ( V₂ V₁ ) + R(T₂ - T₁)
  4. D-RT₁ ( V₂ V₁ ) + R(T₂ - T₁)

Correct answer

C. -RT₂ ( V₂ V₁ ) + R(T₂ - T₁)

Step-by-step solution

According to the IUPAC sign convention, work done is given by w = - P dV . Step (i) Isochoric heating: Since volume is constant ( V₁ ), V = 0 . Work done, w₁ = 0 Step (ii) Isothermal expansion: The gas expands from V₁ to V₂ at constant temperature T₂ . Work done, w₂ = -nRT₂ ( V₂ V₁ ) = -RT₂ ( V₂ V₁ ) (since n = 1 ) Step (iii) Isobaric compression: The gas is compressed from V₂ to V₁ at constant pressure P₁ . Work done, w₃ = -P₁(V₁ - V₂) = -P₁ V₁ + P₁ V₂ Using the ideal gas equation for states 1 and 3: P₁ V₁ = RT₁ a

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