Internal Energy -- from Eric Weisstein's World of Physics

Thermodynamics "> Thermodynamic Functions v

Internal Energy

The first law of thermodynamics states that

where is the heat added to system, dW is the work done by system, and dE is the energy change of the system. Rewriting,

where T is the temperature, dS is the entropy change, P is the pressure, dV is the volume change, is the heat capacity at constant volume, is the isothermal bulk modulus. Therefore,

Including chemical potential energy,

where is the chemical potential energy for species i.