Irreversibility destroys exergy. The Gouy-Stodola relation connects that loss directly to entropy generation:

$$\dot E_{x,dest}=T_0\dot S_{gen}\ge0.$$

Energy is not destroyed; the ability to convert energy into useful work is.

An exergy balance accounts for exergy carried by heat, work and mass streams together with accumulation and destruction. For heat transferred at boundary temperature $T_b$, the associated exergy transfer is

$$\dot E_{x,Q}=\left(1-\frac{T_0}{T_b}\right)\dot Q.$$

A second-law efficiency compares actual useful performance with the reversible performance permitted by the same resources. Its precise definition depends on the device, but it always asks how effectively available exergy is converted into the desired product.

For example, if a process receives $100\ \mathrm{kW}$ of input exergy and produces $65\ \mathrm{kW}$ of desired product exergy, its second-law efficiency is $0.65$ if no other useful products are credited.

Exergy analysis therefore locates where improvement is physically possible: large entropy generation identifies large lost-work potential.