THM-06

Gibbs free energy

G = H − T S, the isothermal–isobaric potential.

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PotentialsGibbs 1876

Governing equation

G=H-TS,\quad \Delta G=\Delta H-T\Delta S

where

H: Enthalpy (kJ)
S: Entropy (kJ/K)
T: Temperature (K)
G: Gibbs energy (kJ)

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-06 — Gibbs free energy) is the form associated with Gibbs 1876. Working symbols: $H$ , $S$ , $T$ $\rightarrow$ $G$ . Gibbs constructed G so that dG = V dP − S dT + μ dN; at constant T, P a process is spontaneous if ΔG < 0.

Purpose

Purpose: compute

G

from

H

S

T

in Thermodynamics via

G=H-TS,\quad \Delta G=\Delta H-T\Delta S

G = H − T S, the isothermal–isobaric potential. Use it when a real thermodynamics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

H = 40.000\,\mathrm{kJ}

S = 0.080\,\mathrm{kJ/K}

T = 298.000\,\mathrm{K}

, the governing relation

G=H-TS,\quad \Delta G=\Delta H-T\Delta S

yields

G = 16.160\,\mathrm{kJ}

. Closed system, given H, S, T. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Enthalpy H40 kJEntropy S0.08 kJ/KTemperature T298 K

Outputs

Gibbs energy G16.160 kJ

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Narration of this film

Closed system, given H, S, T.

Gibbs constructed G so that dG = V dP − S dT + μ dN; at constant T, P a process is spontaneous if ΔG < 0.

Reading speed

Watch on YouTube