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JEE Advanced levelSingle correct optionDifficulty 3 of 3td162

Two moles of an ideal gas at expand freely (into vacuum, adiabatic walls) from to . The gas is then compressed reversibly and isothermally at , with heat exchanged with the surroundings, back to . Using , the values of and for the complete two-step process are

  1. A and
  2. B and
  3. C and
  4. D and

Answer: D

The gas returns to its initial state, so over the cycle. In the free expansion , so . In the reversible isothermal compression the gas rejects to the surroundings, so . The total is positive, consistent with the irreversible free expansion.
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