Physic Labs

Classical statistical mechanics

Helmholtz and Gibbs free energies

Visualize the thermodynamic potentials F=U−TSF=U-TS and G=H−TSG=H-TS as functions of temperature and a control parameter, and identify equilibrium states at the minima described by dF=−S dT−p dVdF=-S\,dT-p\,dV and dG=−S dT+V dpdG=-S\,dT+V\,dp.

Undergraduate

Equipment

  • Two synchronized canvases: 3D surface view and normalized quantitative plot
  • Slider “Nhiệt độ” (temperature)
  • Slider “Tham số” (control parameter, volume or pressure)

Procedure

  1. Find the minimum of F

    Fix the temperature slider and drag the parameter to watch the free-energy curve respond on the lower plot. A system held at fixed T and V settles where FF is minimal, because dF=−S dT−p dVdF=-S\,dT-p\,dV vanishes at equilibrium: the minimum is the equilibrium state.

  2. Raise the temperature

    Increase the temperature slider slowly and watch the −TS-TS contribution grow: at higher T the state with larger entropy is favored, so the position of the minimum can shift. Compare the low-T and high-T curves and note where the balance between U and TSTS tips.

  3. Switch to the Gibbs view

    Read the second figure as the pressure-controlled counterpart: at fixed T and p the relevant potential is G=H−TSG=H-TS with dG=−S dT+V dpdG=-S\,dT+V\,dp. Predict whether the equilibrium parameter should move the same way as for F, then check by sweeping the parameter slider again.

Simulation

Experiment history

Hermann von Helmholtz introduced his free energy in the 1880s while extending the energy principle to chemistry: at fixed temperature and volume, F=U−TSF=U-TS measures the maximum work a system can deliver. The name reflects the “free” part of the energy not locked up as unrecoverable heat. Josiah Willard Gibbs generalized the idea between 1875 and 1878 in his memoir On the Equilibrium of Heterogeneous Substances, defining G=H−TSG=H-TS for conditions of fixed temperature and pressure — the natural setting of laboratory chemistry. Gibbs's potentials turned equilibrium criteria into simple minimization rules and founded chemical thermodynamics.

Related physicists

Rudolf ClausiusWilliam Thomson (Lord Kelvin)James Prescott JouleJosiah Willard Gibbs

Related library topics

Helmholtz and Gibbs free energies