A Modern Treatment of the Second Law

Abstract

In our study of the thermodynamics of homogeneous fluid bodies, we saw that the First and Second Laws implied relation (3.24) of Chapter I:

$$\int\limits_{0}^{1}{\frac{{\bar{h}(\tau )}}{{\bar{\theta}(\tau )}}}d\tau=0$$

((1.1))

which holds on each cycle of a homogeneous fluid body. Conversely, granted the First Law, (1.1) was shown to imply the Second Law as well as the general efficiency estimate (4.4) in Chapter I. In other words, the content of the Second Law is contained in relation (1.1). In Chapter I, we could have used (1.1) from the outset had we not wanted an approach to the Second Law which had intuitive appeal and reflected the history of the subject. Indeed, use of (1.1) would offer two advantages: (1) it is mathematically more explicit than the version adopted in Chapter I; and (2) it requires only the concepts of heating and temperature. The second fact is important for the treatment of the Second Law which we present in this chapter, because it motivates an approach to the Second Law based solely on the notions of hotness and heat. In this approach neither the concept of work nor the First Law plays a role.