The usefulness of entropic average temperatures

The second law Carnot efficiency, entropy balances, and many other principles of the second law are stated with assumed constant temperature heat sinks and reservoirs; i.e., assuming heat transfer across a boundary at a constant temperature. However, real world heat exchangers reject and receive heat transfer to a flowing fluid with a varying temperature making the application of many aspects of the second law inappropriate or complex. For such varying temperature cases, an entropic average temperature can be defined and easily calculated that can be substituted for the varying temperature heat sink or source temperature. The constant temperature restricted second law statements can then be used with this entropic average temperature. This entropic average temperature concept is simple to understand and is very useful in the presentation of thermodynamic concepts to new students, making it seem less abstract and more applicable to real world processes with which they are familiar. This paper serves to develop the concept and details of the entropic average temperature and show its usefulness while emphasizing its benefit for inclusion in engineering thermodynamics syllabi.