The Gouy-Stodola theorem is often applied to refrigeration cycles. These are thermodynamic cycles or mechanical systems where external work can be used to move heat from low temperature sources to high temperature sinks, or vice versa. Specifically, the theorem is useful in analyzing vapor compression and vapor absorption refrigeration cycles. 
The theorem can help identify which components of a system have major irreversibilities, and how much exergy they destroy. It can be used to find at which temperatures the performance is optimal, or what size system should be constructed. Overall, that is, the Gouy-Stodola theorem is a tool to find and quantify inefficiencies in a system, and can point to how to minimize them - this is the goal of exergy analysis. When the theorem is used for these purposes, it is usually applied in its modified form.