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Carnot Engine Work Output: Public Worked Question

A public heat-engine question showing how absolute reservoir temperatures set a Carnot engine's efficiency and per-cycle work output.

Question

A Carnot engine operates between a hot reservoir at 500 K500\,\text{K} and a cold reservoir at 300 K300\,\text{K}, absorbing 1000 J1000\,\text{J} of heat from the hot reservoir each cycle. How much work does it deliver per cycle?

  1. a.1000 J1000\,\text{J}
  2. b.600 J600\,\text{J}
  3. c.400 J400\,\text{J}
  4. d.250 J250\,\text{J}

Correct answer

C. 400 J400\,\text{J}

Full reasoning

  1. 1Carnot efficiency uses absolute temperatures: η=1−Tc/Th=1−300/500=0.40\eta = 1 - T_c/T_h = 1 - 300/500 = 0.40.
  2. 2The work per cycle is W=ηQh=0.40×1000 J=400 JW = \eta Q_h = 0.40 \times 1000\,\text{J} = 400\,\text{J}.
  3. 3Energy balance check: the rejected heat is Qc=Qh−W=600 JQ_c = Q_h - W = 600\,\text{J}, which matches Qc=(Tc/Th)QhQ_c = (T_c/T_h)Q_h for a reversible cycle.

Why each choice is right or wrong

Choice A

This assumes complete conversion of the absorbed heat into work, which the second law forbids for any cyclic engine.

Choice B

This is the heat rejected to the cold reservoir, Qc=(Tc/Th)QhQ_c = (T_c/T_h)Q_h, mistakenly reported as the work output.

Choice C

Correct. η=1−300/500=0.40\eta = 1 - 300/500 = 0.40, so W=ηQh=0.40×1000=400 JW = \eta Q_h = 0.40 \times 1000 = 400\,\text{J}.

Choice D

This comes from the incorrect efficiency formula (Th−Tc)/(Th+Tc)(T_h - T_c)/(T_h + T_c); the denominator should be ThT_h alone.

Related formula

Carnot efficiency

η=1−TcTh\eta = 1 - \frac{T_c}{T_h}

Assumptions: Both temperatures are expressed in kelvin. The engine runs a reversible Carnot cycle between the two reservoirs.

Related topic and practice

Thermodynamics and Heat EnginesSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 2, Section 4.5: The Carnot Cycle — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
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Keiko Study editorial owner
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Reviewer record
Technical reviewer pending
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Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

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