A6. Notation

Appendix A6 319

A6 Notation¶

Numbers are written with a dot as the decimal separator and a thin space as a thousands separator. Digits are grouped by three so that $12.3456 \times 10^{3}= 12 345.6$. When only four digits are present, grouping is omitted. This follows the recommendations of the bipm in the 9th edition of the SI Brochure [50]. In tables, in order to increase readability, integers are always grouped, and decimals never grouped. Rounding is done as late as possible and never in series. Leading and trailing zeros are not indicated.

Units are in upright characters and colored in gray $(1 kg)$. In sentences, units are written out in full and in lowercase (one hundred watts). The liter is written with a capital $(L)$ to make it more readable $(1 L \equiv 10^{-3}m^{3})$. The units in equations are from the International System of Units (SI) [50] unless otherwise indicated, and non-si units are listed in Appendix A5 p. 317.

Special symbols:

$\equiv$ means “by definition”. The symbol $\equiv$ sets the definition of the term on its left (which does not depend on previous equations).

$\dot{}$ (dot above a symbol) means the time rate: $\dot{} \equiv \frac{d}{dt}$. For example, $\dot{Q}$ is the power as heat (in watts) representing an amount $Q$ (in joules) per second.

$\Delta$ means the net difference between two state quantities: $(\Delta X)_{\mathrm{A}\rightarrow \mathrm{B}}= X_{\mathrm{B}}- X_{\mathrm{A}}$. It can be negative. See the Appendix A4 p. 316.

δ means the inexact differential. See Appendix A4 p. 316.

$d$ means the exact differential. See Appendix A4 p. 316.

Italics are used for physical quantities (mass $m$, temperature $T)$. The symbols are all named in the list on page 328.

Indices:

• In upright characters: points in time or in space (temperature $T_{\mathrm{A}}$ at point A). The index “cst.” denotes a quantity that remains constant, the index “rev.” indicates that the calculation is carried out along a reversible process, “in” denotes “incoming” and “out” denotes “outgoing”.

• In italics: $T_{H}, T_{L}$, and the indices $TH$ and $TL$ denote respectively a high and low temperature, as detailed in section §7.2.2 p. 179. The indices $L$ and $V$ indicate the saturation points of a liquid-vapor mixture, as detailed in section §5.3.2 p. 126.

Lowercase is used for mass-specific values (energy or power). See section §1.1.5 p. 14.

Operators: the exponential is written $\exp x \equiv e^{x}$, and the natural logarithm is $\ln x \equiv$

Arrows in drawings are drawn according to conventions explained in §2.2.2 p. 34, §3.2.1 p. 61, and §6.1 p. 151.