An easier approach to introduce entropy in undergraduate thermodynamics classes

The common tutorial method of teaching entropy is far twisted and complicated. The convention is to first present Carnot corollaries followed by a "rational argument" to justify the corollaries. In the next step, the efficiency of Carnot engine is argued to be solely dependent on the thermal reservoirs temperatures. Then, thermodynamic temperature scale is introduced to show QL/QH equals TL/TH followed by the Clausius inequality, and finally introducing entropy S. It is not surprising why entropy has been one of the most difficult concepts to teach or learn. The way it is taught in textbooks is not straight unlike many other properties and concepts that are comparably much less cumbersome to understand. Interesting to note is that the inventor of entropy; Clausius, derived the famous Carnot efficiency by simply using the p-V diagram of a Carnot cycle operating with an ideal gas. The objective of this article is to shed light to the original method of Clausius and to present a simple and easy-to-digest approach, so students can better understand where entropy is originated from. Furthermore, we will show that the proof of Carnot corollaries is not concrete and certain objections can be raised.