Physical Sciences

Thermodynamics

Advanced

Entropy Equation

\Delta S = \int \frac{\delta Q_{\text{rev}}}{T}

Entropy change equals reversible heat transfer divided by temperature—a measure of disorder.

By Rudolf Clausius

Physical Sciences

Entropy Equation

1865 · Rudolf Clausius

Human Reviewed

84%

Rabbit Hole Mode

Five doors into the universe behind this equation. Choose your path.

Story PortalWho discovered this?Discover how Rudolf Clausius and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — heat engines.Math PortalWhat does it derive from?Trace the mathematical lineage from carnot efficiency.Future PortalWhere is it going?Quantum thermodynamics

Launch collection — full story, visual, sound & share card

Why it matters: Explains why time has a direction and sets limits on engine efficiency.

Discoverers: Rudolf Clausius (1865)

What does it mean?

Entropy change equals reversible heat transfer divided by temperature—a measure of disorder.

Why should I care?

Explains why time has a direction and sets limits on engine efficiency.

Equation Compass

North — Prerequisites

West — History

Rudolf Clausius

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$ΔS$	Entropy change	J/K	Change in entropy
$Q$	Heat	J	Reversible heat transfer
$T$	Temperature	K	Absolute temperature

Worked Example

Melting ice at 273 K absorbs 334 J/g → ΔS = Q/T per gram.

AI Guide (Pro)

Ask questions about equations and get answers grounded in the Equation Universe catalog.

Upgrade to Pro Try demo (7 days)

Continue your trail

Entropy

Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

Equation Universe