Gouy-Stodola relation

The expansion of the natural gas is a spontaneous process and thus work must have been lost. According to the Gouy-Stodola relation, this lost work is related to the entropy production of the process. 

Equation 11.3 is occasionally called the law of exergy loss or the Gouy-Stodola s relation (G. Gouy and A. Stodola) who first discovered independently of each other in the late nineteenth century the loss of maximum work due to the irreversibility of thermal processes [Ref. 9.]. 

Generally, a chemical reaction has a nonlinear relation between the rate and the driving force AIT. Chemical reactors are often designed to operate at the maximum rate of reaction. An alternative is a reactor operated with minimum useful work lost. The lost work per unit time in a chemical reactor is given by the Gouy—Stodola theorem, and is obtained by integrating the entropy production rate over the reactor volume ... 

This remarkable, simple relation between the work lost and the entropy produced in a process dates back to close to the beginning of the twentieth century, when it was independently derived by Gouy [2] and Stodola [3]. 

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