Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Gibbs Free Energy

A thermodynamic potential that measures the amount of energy available in a system to do useful work at constant temperature and pressure.
📜

The statement of the theorem

Let H\mathcal{H} be a system described by a Hamiltonian H(q,p,N)\mathcal{H}(\mathbf{q}, \mathbf{p}, \mathbf{N}) and subject to a volume VV and temperature TT. In the grand canonical ensemble, the system is characterized by the grand partition function Z(μ,V,T)\mathcal{Z}(\mu, V, T), where μ\mu is the chemical potential. The Gibbs Free Energy GG is defined via the relation:\n\nG(μ,V,T)=−kBTln⁡Z(μ,V,T)G(\mu, V, T) = -k_B T \ln \mathcal{Z}(\mu, V, T)\n\nAlternatively, considering the fundamental thermodynamic potential, the differential form is given by:\n\ndG=−SdT+VdP+μdNdG = -S dT + V dP + \mu dN\n\nWhere SS is the entropy, PP is the pressure, and NN is the number of particles. The state variables (μ,V,T)(\mu, V, T) define the equilibrium manifold where GG is minimized for fixed TT and PP.
Source: Wikipedia