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Question 31054
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Kinetic Theory and Thermodynamics: Carnot Cycle MCQ

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Carnot CycleHardQuestion 31054

Question

Two Carnot engines A (between T₁ and T) and B (between T and T₂) have same efficiency. Temperature T is:
  1. A
    (T₁+T₂)/2
  2. B
    √(T₁T₂)
    Correct
  3. C
    T₁T₂/(T₁+T₂)
  4. D
    T₁/T₂

Correct answer

√(T₁T₂)

Explanation

η_A = 1−T/T₁ = η_B = 1−T₂/T. So T/T₁ = T₂/T → T² = T₁T₂ → T = √(T₁T₂) (geometric mean).

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