Thermoeconomic consideration of a refrigeration system

From the second law consideration, the annual cost of fuel CF is given by 

The following derivations are from Szargut (1990). The total consumption of natural resources involved in the production of a product can be expressed by the overall index of cumulative exergy consumption rp 

Exergy consumption of resources that are renewable should also be considered. The overall cumulative exergy consumption index may help in assessing various energy utilization problems for a specified product, such as the relationships between the amounts of raw materials and the products, or the cost of raw materials and the alternative production technologies available. 

In analyzing the production of materials and energy flows, the values of r can be compared with the exergy of the product. The ratio of the specific exergy of the product ex to is called the cumulative degree of thermodynamic perfection 17 for a certain production network 

r is the cumulative exergy consumption index for a specified product. For the manufacturing of major products, we have 17 1. Sometimes, for a byproduct we may have 17 1, if the exergy of the product is greater than the exergy of the substituted product of a certain process. It would not be useful to calculate 77 for certain products, such as cars and airplanes, because their usefulness results mainly from their system features, not from the chemical composition of their components. However, the calculation of r may be beneficial for all kinds of products, because the values of r can be used to compare various design variables and production technologies. 

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