Dear Muhammad Ahmad,

In general, the second law efficiency is defined as the product-fuel ratio of a subsystem or the overall system. Fuel refers to what is consumed, and product refers to what is generated by the subsystem or the overall system. Exergetic efficiency is a type of second law efficiency. For many experts, these concepts are synonymous, as you yourself mentioned.

In general, when we look at the literature, there is no widespread definition for second law efficiency, although there are well-established definitions for exergetic efficiency.

Let's take the example of a steam turbine. Many experts agree that the product of this subsystem is the generated power and the fuel is the reduction of the exergy in the steam flow. The ratio between product and fuel is the exergetic efficiency, which can also be understood as the second law efficiency.

However, there are devices that consume exergy but do not generate an exergetic product. These are called dissipative equipment. A typical example is the expansion devices in refrigerators and heat pumps.

Continuing with the example of these expansion devices, we can find in the literature a proposal for second law efficiency: the product is the exergy of the output flow, and the fuel is the exergy of the input flow. Some refer to this as input-output efficiency. However, there are critics of this approach, as such a definition does not represent what occurs in these devices from a productive standpoint.

Defining second law efficiency, especially for dissipative equipment, has been a subject of debate for several years within the niche of exergo-economic and exergo-environmental analysis.

Taking advantage of your question, if you want to read more on the subject, my suggestion is to look for articles published by the Nucleus of Excellence in Thermoeconomics and Energy Sustainability (NETES). Specifically, see the original articles on the H&S, UFS, and A&F Models.

Sincerely,

Atilio.