Carnot efficiency of a heat engine

The Carnot relation comes from an entropy balance using absolute thermodynamic temperature. Celsius has an arbitrary zero and gives a false ratio. Convert both reservoir temperatures to kelvin first and check that TH exceeds TC. Use absolute reservoir temperatures; this is a reversible upper bound, not predicted plant performance. Application: Estimate the thermodynamic upper bound for an engine at specified reservoir temperatures. The numerical example Between TH=600 K and TC=300 K, ηC=1−300/600=0.50; a real engine delivers less than 50% anchors the idea in a concrete measurement case.

No. The Carnot engine is a reversible idealization with no friction, finite-temperature-difference heat transfer or other entropy generation. Every real plant falls below it. The equation shows the limit imposed by reservoir temperatures; it does not measure a particular plant. Use absolute reservoir temperatures; this is a reversible upper bound, not predicted plant performance. The corresponding units are η dimensionless; T in K. Between TH=600 K and TC=300 K, ηC=1−300/600=0.50; a real engine delivers less than 50%. This checks that the reference quantities are compatible.

Then the temperature difference is small and ηC approaches zero. A heat engine can extract little work from a small thermal gradient. If TC equals TH, ideal work output vanishes. This shows why temperature difference matters in thermal power cycles. Use absolute reservoir temperatures; this is a reversible upper bound, not predicted plant performance. Scope: The limit follows from the entropy balance of a reversible cycle between two reservoirs. Use absolute temperatures in kelvin, not Celsius. Real engines fall below it because of irreversibilities; the expression does not include engineering losses or finite heat-transfer rates. A practical application is Estimate the thermodynamic upper bound for an engine at specified reservoir temperatures.

Write the quantity and unit from the variable list next to every value: η dimensionless; T in K. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example Between TH=600 K and TC=300 K, ηC=1−300/600=0.50; a real engine delivers less than 50%. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Use absolute reservoir temperatures; this is a reversible upper bound, not predicted plant performance.

The background states this starting condition: The limit follows from the entropy balance of a reversible cycle between two reservoirs. Use absolute temperatures in. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Use absolute reservoir temperatures; this is a reversible upper bound, not predicted plant performance.