Question

This is an extract of Lecture 1 (page-67) of Rational Thermodynamics by Truesdell.

The irreversibility of natural processes is represented by the existence of an a priori least upper bound B for the heating Q. The term "irreversibility" is justified because Q, the rate of increase of energy not accompanied by mechanical working, is bounded above but not necessarily below. There is no limit to the magnitude of negative values of Q which represent conversion of energy into heating without performance of work, but there certainly is to positive ones. Work and energy may always be converted into heat, but each body is limited in the rate at which it can convert heat into energy without doing work. That is the content of the second axiom: Q≤B.The first axiom was (the first law) : E˙=W+Q, where E is the energy, W is the rate of working.

My question is, how does saying there is an upper bound for positive values of Q correspond in any way to the second law ? Loosely, the second law is supposed to imply that you cannot completely convert Q>0 into working W.

Furthermore, the statement

Work and energy may always be converted into heat, but each body is limited in the rate at which it can convert heat into energy without doing workseems incorrect. I do not see why there is a limit on converting heat into energy without doing work. Surely, one can simply keep supplying heat and raising the energy without doing work ?
This second axiom is critical to the rest of the chapter, so I am very confused.

Answer 1

The upper bound B for the heating rate Q corresponds to the second law of thermodynamics by acknowledging the limitations of converting heat to work. Entropy, which always increases in real processes and signifies unavailability of energy for work, provides a fundamental reasoning for the existence of this upper bound.

Step-by-step explanation:

Your question concerns how the concept of an upper bound for the heating rate Q relates to the second law of thermodynamics. The second law implies that there is a limit to the efficiency of converting heat into work. This law also introduces the concept of entropy, which increases in all real (irreversible) processes. The statement that there is an upper bound B for Q corresponds to the second law because it acknowledges that a system cannot convert heat into energy with perfect efficiency; some of the energy will always be 'lost' to irreversibility.

Furthermore, when we say that converting heat into energy without doing work is limited, it's not about simply supplying more heat; it's about the efficiency and the directional nature of energy transfer governed by entropy. The increase in entropy signifies that not all energy from heat can be used for work, and so there is indeed a practical limit to how much energy you can get from heat without performing work. This limit is what underlies the role of the second axiom in describing natural processes in thermodynamics.