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CHAPTER THREE

Teaching entropy

3.1 Introduction

The statement of the second law is clear and straightforward: a heat
engine cannot convert the entire heat input to work, or heat cannot be trans-
ferred from a cooler body to a warmer one without external expenditure.
However, the formulation of the second law leads to entropy, which is
one of the most challenging concepts to understand by many. We will first
review the current common method of teaching the second law and entropy
that can be found in most standard textbooks. A part of this common
method relies on the Carnot corollaries and their respected proof. It will
be shown that the proof of the corollaries inherited from Carnot himself
[1] is unsatisfactory and certain objections can be made.

3.2 The common tutorial method
The way entropy is taught in many textbooks includes introduction of
several steps: (i) reversible process, (ii) Carnot cycle and principles, (iii) thermo-
dynamic temperature scale, (iv) efficiency of Carnot cycle, (v) Clausius inequal-
ity. Then, entropy is introduced as a thermodynamic property along with the
principle of entropy increase. This tutorial method has become a standard
approach of teaching entropy to undergraduate students for a very long time.
Compared to other properties such as enthalpy, specific volume, internal
energy, specific heat, or formation enthalpy, entropy is the only property
whose introduction takes a relatively long journey. A whole chapter is usu-
ally devoted to present steps (i) through (iv) whereas the inequality of
Clausius, entropy, and the principle of entropy increase are discussed in a
following chapter. It is not a surprise why grasping entropy is challenging;
one needs to first go through several steps to finally arrive at the definition of
entropy. On the other hand, steps (ii)–(iv) suffer from certain shortcomings:
the proof of Carnot principles and the method of derivation of the Carnot

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