--- title: "The Carnot Cycle and the Ceiling on Efficiency" description: "The reversible Carnot cycle has two isothermal and two adiabatic legs. It sets the maximum efficiency for engines exchanging heat only with two reservoirs at constant temperatures. The limit depends o" canonical: https://lightmysky.com/learn/science/the-carnot-cycle-and-the-ceiling-on-efficiency-mt_aWH0BHM556 source: https://lightmysky.com/learn/science/the-carnot-cycle-and-the-ceiling-on-efficiency-mt_aWH0BHM556.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # The Carnot Cycle and the Ceiling on Efficiency The reversible Carnot cycle has two isothermal and two adiabatic legs. It sets the maximum efficiency for engines exchanging heat only with two reservoirs at constant temperatures. The limit depends on their temperatures in kelvin. Subject: Science · Area: Thermal & Statistical Physics · Ages 19 to 20 Page: https://lightmysky.com/learn/science/the-carnot-cycle-and-the-ceiling-on-efficiency-mt_aWH0BHM556 ## Ready when they can - Describes the four Carnot legs, their heat flows and the work represented by a clockwise pV loop - Computes the Carnot efficiency from the two reservoir temperatures - Argues why no engine between the same reservoirs can do better ## Lesson: The best engine allowed An isothermal leg keeps temperature fixed; an adiabatic leg exchanges no heat. For an ideal gas, the Carnot engine follows four reversible legs: hot isothermal expansion absorbs heat; adiabatic expansion cools the gas; cold isothermal compression releases heat; adiabatic compression warms it back to its starting state. A reversible process can be undone with no net change left in the system and surroundings. *(drawing: Follow two expansion legs, then two compression legs. Only the isothermal legs exchange heat.)* On a pV diagram, pressure is vertical and volume is horizontal. Expansion moves right; compression moves left. For an ideal-gas Carnot engine, the hot isotherm lies above the cold one. Adiabats connect them and are steeper than the isotherms at their meeting points. The engine follows a clockwise loop. The enclosed area gives net work done by the gas per cycle, not efficiency. Let Th and Tc be the hot and cold reservoir temperatures, with 0 < Tc < Th. For heat exchange only with these two fixed-temperature reservoirs, maximum efficiency is 1 - Tc/Th. Use kelvin: add 273.15 to each Celsius value. If Qh is absorbed heat, maximum work is (1 - Tc/Th) times Qh. A reversible engine reaches the limit. Raising Th at fixed Tc, or lowering Tc at fixed Th, raises the limit. **Example.** Between 900 K and 300 K, maximum efficiency is 1 - 300/900 = 2/3. With 900 J absorbed per cycle, maximum work is 600 J and minimum rejected heat is 900 - 600 = 300 J. The bars show operation at this limit. An engine producing less work from the same heat input rejects more heat. Energy amounts are in joules; efficiency at the limit is 600/900. Suppose a rival beats Carnot between the same reservoirs. Run it forward and drive a reversed Carnot machine with all its work. Match their work amounts. For the same work, the rival absorbs less heat from the hot reservoir and rejects less heat to the cold reservoir. Together, the machines move heat from cold to hot with no net work. This violates the second law. Reversibility allows this comparison. All reversible engines share the limit; irreversible engines fall below it. **Recap.** Two isotherms plus two adiabats set the ceiling of one minus cold over hot, measured in kelvin. *This lesson and its questions were written for this dataset. OpenStax thermodynamics material was consulted for scientific facts; its prose and figures are not reproduced.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Heat Engines and the Second Law](https://lightmysky.com/learn/science/heat-engines-and-the-second-law-mt_M7CDvIi4Vs) ## Opens up - [Entropy as a State Function](https://lightmysky.com/learn/science/entropy-as-a-state-function-mt_bg_K5nU-GZ)