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A gas expands adiabatically from (P<sub>1</sub>, V<sub>1</sub>) to (P<sub>2</sub>, V<sub>2</sub>). Work done by gas:

Answer: Both B and C.

  • A P<sub>1</sub>V<sub>1</sub> - P<sub>2</sub>V<sub>2</sub>
  • B (P<sub>1</sub>V<sub>1</sub> - P<sub>2</sub>V<sub>2</sub>)/(gamma-1)
  • C nCv(T<sub>1</sub>-T<sub>2</sub>)
  • D Both B and C

Correct answer: D. Both B and C

Explanation: W = -delta U = nCv(T<sub>1</sub>-T<sub>2</sub>) = (P<sub>1</sub>V<sub>1</sub>-P<sub>2</sub>V<sub>2</sub>)/(gamma-1). These are equivalent. Both B and C are correct.

Carnot Cycle (P-V Diagram)VP1→2: isothermal expansion (T_H)2→3: adiabatic expansion3→4: isothermal compression (T_C)4→1: adiabatic compression1234Net work done by the gas = area enclosed by the loop 1→2→3→4→1

The Carnot cycle alternates two isothermal steps (heat absorbed at TH, released at TC) with two adiabatic steps (no heat exchange); the enclosed loop area equals the net work output, and η = 1−TC/TH is the maximum possible efficiency between those two temperatures.

Concept context

Laws of thermodynamics, heat engines, entropy, and gas processes.

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