A4. State Quantities and Process Quantities

316 Appendix A4

A4 State Quantities and Process Quantities¶

Definition

Thermodynamic quantities can be classified into the following categories:

• A quantity is called a state quantity if its value depends only on the current state of the system. Temperature $T$ is an example of a state quantity.

• A quantity is called a path quantity or if its value depends on the path taken. Heat transfer $Q$ and work $W$ are the only two path quantities used in this book.

Using the example provided by Rogers & Mayhew [37], one can illustrate the distinction as follows: a cyclist travels from A to B. Their altitude at the start $z_{\mathrm{A}}$ and at the end $z_{\mathrm{B}}$ are state quantities $(z$ being a state function), and we can quantify $\Delta z \equiv z_{\mathrm{B}}- z_{\mathrm{A}}$ without knowing anything about the route. However, the work $W_{\mathrm{A}\rightarrow \mathrm{B}}$ expended to go from A to B depends on the process: it will be larger, for example, if the route is longer or if there is wind. Quantifying $W$ (a path function) requires knowledge of all intermediate states between A and B.

Quantities are sometimes referred to as variables; state quantities are sometimes referred to as physical properties. Process quantities and functions are sometimes also called transfer or path quantities.

Notation

Infinitesimal changes in state quantities are denoted by the symbol $d$; these are exact

differentials and can be integrated by only knowing their initial and final values. For example, for temperature $T$:

Infinitesimal transfers of path quantities are denoted by the symbol δ; these are inexact

differentials and their integral can only be quantified by knowing all states encountered along the path. For example, for work $W$, one cannot write “$W_{\mathrm{B}}-W_{\mathrm{A}}$”, or “$\Delta W$”, but only:

This notation can be confusing, since it is $d$ and not δ that becomes $\Delta$ upon integration. It may also appear as a complicated way to avoid using partial derivatives. Clifford Truesdell [36] mischievously remarks that because of this notation, equation 8/1 on page 211 might make us believe that some types of differentials are larger than others... Although this notation is widely used in French literature (which is why it is adopted in this book, which is translated from French [51]), it must be recognized that one can fully cover the field of engineering thermodynamics [37, 38] or physical thermodynamics and its history [36] without ever having to use the symbol δ in the above sense.