THM-10

Carnot efficiency

η = 1 − Tc/Th for a reversible engine between two reservoirs.

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First lawCarnot

Governing equation

\eta=1-T_c/T_h

where

T_h: Hot reservoir (K)
T_c: Cold reservoir (K)
\eta: Efficiency (—)

Lecture brief

Historical brief

Carnot (1824), Clausius entropy, the first law and later van der Waals and Gibbs potentials turned heat into a state science. The sheets compute work, efficiency and vapour pressure. This sheet (THM-10 — Carnot efficiency) is the form associated with Carnot. Working symbols: $T_h$ , $T_c$ $\rightarrow$ $\eta$ . No engine between the same two temperatures can beat Carnot. Equality for reversible cycles.

Purpose

Purpose: compute

\eta

from

T_h

T_c

in Thermodynamics via

\eta=1-T_c/T_h

η = 1 − Tc/Th for a reversible engine between two reservoirs. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T_h = 600.000\,\mathrm{K}

T_c = 300.000\,\mathrm{K}

, the governing relation

\eta=1-T_c/T_h

yields

\eta = 0.500\,\mathrm{—}

. Two baths, a cycle lozenge, an efficiency bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Hot reservoir T_h600 KCold reservoir T_c300 K

Outputs

Efficiency \eta0.500 —

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Narration of this film

Two baths, a cycle lozenge, an efficiency bar.

No engine between the same two temperatures can beat Carnot. Equality for reversible cycles.

Reading speed

Watch on YouTube