Confusion in Thermodynamics

TL;DR

This paper addresses widespread confusion in thermodynamics concepts, clarifies the role of Carathéodory's axiom, and relates it to the First Law to improve conceptual understanding.

Contribution

It clarifies the position of Carathéodory's axiom within thermodynamics and its relation to the First Law, resolving existing conceptual ambiguities.

Findings

Clarified the role of Carathéodory's axiom in thermodynamics

Established the relation between the axiom and the First Law

Resolved common conceptual confusions in thermodynamics

Abstract

For a long time now, confusion has existed in the minds of many over the meaning of various concepts in thermodynamics. Recently, this point has been brought to people's attention by two articles appearing on the well-known archive (arxiv) web site. The content of these two pieces serves to illustrate many of the problems and has occasioned the construction of this answer to at least some of them. The position of the axiom proposed by Carath\'eodory is central in this matter and here its position is clarified and secured within the framework of thermodynamics. In particular, its relation to the First Law is examined and justified.