A certain engine that operates in a Carnot cycle absorbs 3.347 kJ at 400ºC. How much work is done by the engine per cycle?(The temperature of the sink is 100ºC).
Correct answer: A. 1.49 kJ
- A. 1.49 kJ
- B. 2.51 kJ
- C. 1.85 kJ
- D. 2.98 kJ
Explanation
The Carnot cycle efficiency is calculated using the formula: η = 1 − (Tsink / Tsource), with temperatures in Kelvin. Convert the given temperatures: Tsource = 400ºC = 673 K and Tsink = 100ºC = 373 K. The efficiency η = 1 − (373/673) = 0.446. The work done per cycle (ΔW) is given by the product of efficiency and heat absorbed (q1): ΔW = η × q1 = 0.446 × 3.347 kJ = 1.49 kJ. Thus, Option A is correct. The other options (B, C, and D) do not match this calculated value and are therefore incorrect, as they result from miscalculations or misinterpretations of the Carnot cycle efficiency formula.
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