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Gibbs Free Energy: Why ΔG = ΔH − TΔS Makes Sense

Derive the spontaneity criterion from the Second Law instead of memorising a four-case table.

By Anil Sir · 2026-10-10

Most students memorise the table of signs for ΔH and ΔS. You never need to — the result comes straight from the Second Law.

Start from the universe

A process is spontaneous when ΔS_universe > 0. Split it: ΔS_univ = ΔS_sys + ΔS_surr. At constant T and P, the surroundings absorb heat −ΔH_sys, so ΔS_surr = −ΔH/T.

Multiply by −T

−TΔS_univ = ΔH − TΔS_sys. That quantity is defined as ΔG. Since ΔS_univ > 0 means −TΔS_univ < 0, spontaneity becomes simply ΔG < 0.

Now the four cases read themselves

• ΔH < 0, ΔS > 0 → always spontaneous.
• ΔH > 0, ΔS < 0 → never spontaneous.
• ΔH < 0, ΔS < 0 → spontaneous at low T.
• ΔH > 0, ΔS > 0 → spontaneous at high T.

Link it to equilibrium with ΔG° = −RT ln K and to cells with ΔG = −nFE, and three chapters collapse into one idea.