Skip to content
GRE Physics overview

Worked example

Free to read

Carnot Engine Work Output

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 EnginesThermodynamics Domain GuideHeat flow through a thicker wallLinear thermal expansionCreate a free account to practice

This worked example is free to read. A free account unlocks practice questions for this exam.

Sources

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.
Share this worked solution

Sources and corrections

Sources last checked 2026-08-07

Every source cited on this page was checked on the date shown, and we update the page when a source changes. If something looks wrong, tell us and we'll recheck it.

Report an issue with this page