Definition

Entropy change

Δ S = \int \frac{d Q}{T}

Statement

The change in entropy for a reversible process, from heat exchanged divided by the temperature at which it occurs.

Symbols and units

$Δ S$	entropy change	J/K
$Q$	heat exchanged	J
$T$	absolute temperature at which it is exchanged	K

When it applies

A reversible process; for an irreversible process, ΔS is still well defined but cannot be computed from this integral along the actual path.

Don't use when

The integral form applies along a reversible path only — for an irreversible process, ΔS is still well-defined but must be computed along an equivalent reversible path between the same states, not the actual irreversible one.

Derivation

Defined so that entropy change accumulates heat exchange weighted by the inverse of temperature, along a reversible path between two states:

Δ S = \int \frac{d Q}{T}

Watch out for

For any real (irreversible) process, ΔS ≥ 0 for an isolated system, with equality only for a reversible one — heat flowing spontaneously from hot to cold always increases total entropy; the reverse would decrease it, which is why it never happens on its own.