The internal energy U of a thermodynamic system is defined by the first law of thermodynamics which states that energy can neither be created, nor destroyed:
ΔU = Q + W
where ΔU is a change in the internal energy, Q is heat received by a system, and W is the mechanical work done on the system.
Internal energy is usually regarded as a thermodynamic function of state rather than a state variable. This is due to the fact that internal energy is not easy to vary experimentally in a controlled fashion — for practical purposes, only changes in internal energy are considered and measured.
For mechanical work against a hydrostatic pressure P the change in internal energy is given by the following differential equation:
dU = dQ - P·dV
If the Gibbs energy is known, the internal energy can be derived as follows:
U = G - T·(∂G/∂T)P,n - P·(∂G/∂P)T,n
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