Energy is conserved, but not all energy has the same ability to produce useful work. Exergy measures the maximum useful work obtainable as a system comes reversibly to equilibrium with a specified environment.

The environmental reference state, often described by temperature $T_0$ and pressure $p_0$, is called the dead state. At the dead state the system has no physical exergy relative to its surroundings.

For a closed simple compressible system, neglecting kinetic and potential contributions, a useful physical-exergy expression per unit mass is

$$e_x=(u-u_0)+p_0(v-v_0)-T_0(s-s_0).$$

For a flowing stream, the corresponding flow exergy is

$$\psi=(h-h_0)-T_0(s-s_0)+\frac{V^2}{2}+gz.$$

Exergy depends on the environment as well as the system state. A hot body has exergy in a cool room because it can drive a heat engine while cooling; once it reaches room temperature, that opportunity disappears although its internal energy is not zero.

Exergy therefore quantifies useful-work potential rather than total energy.