What is a pure substance?
"Thermodynamics an engineering approach, Cengel and Boles" defines a pure substance as one that has the same chemical composition throughout.


This is the correct definition of a pure substance. However, air, regardless of phase, is not a pure substance. 

All matter is categorized as either a "pure" substance or a mixture. The word "pure" in front of "substance" is unnecessary, since the definition of substance implies purity. A substance is a sample that is chemically uniform in composition. In other words, all particles of that sample are the same chemically (whether they are atoms or molecules or ionic lattices or what have you). Substances cannot be separated into simpler components by any physical process (i.e. without breaking chemical bonds). Mixtures are samples that contain two or more substances. All mixtures can be physically separated, although the means to do so may be neither easy nor practical.

Air is a mixture of nitrogen ($\ce{N2}$), oxygen ($\ce{O2}$), carbon dioxide ($\ce{CO2}$), argon ($\ce{Ar}$), water vapor, and traces of other gases. Each of these gases separately is a substance. Air can be easily (but not in the comfort of your own home) separated into its constituent parts. Cooling air will cause the constituent components to condense out of it at progressively lower temperature: first water vapor, and then $\ce{CO2}$ (195 K), followed by $\ce{Kr}$ (120 K), $\ce{O2}$ and $\ce{CH4}$ (90 K), $\ce{Ar}$ (87 K), $\ce{N2}$, $\ce{Ne}$ (27 K), $\ce{H2}$ (20 K), and $\ce{He}$ (4 K). 

As each substance condenses out of air it can be physically separated from the remaining gas, reducing the complexity of the mixture. Each substance, if returned to the gaseous state separate from the original mixture is physically and chemically distinct from the original mixture (or whatever is left of it). Such physical separations do not need to be easy to make air a mixture, they need to be possible.

A pure substance does not exhibit this behavior. When pure water is cooled, it undergoes a phase change to ice, which is physically separable from liquid water. However, the solid and liquid samples are still water. You have not reduced the complexity of the sample, just changed its form. If you allow the separated solid water to melt, it will be physically and chemically indistinguishable from the original water sample. Pure water cannot be separated into other chemically distinct substances without performing a chemical reaction, which means breaking and forming bonds between atoms.

The majority of matter that we interact with in our everyday lives is comprised of mixtures. 

We encounter a few pure substances in the kitchen. Table sugar is a single compound (sucrose). So is table salt (sodium chloride), baking soda (sodium bicarbonate), and cream of tartar (potassium bitartrate). Water is a pure substance, so long as it has been purified. Most water that we encounter has other substances dissolved in it. 

Gold (as long as it is 24K) is a pure elemental substance. So is diamond (carbon), graphite (also carbon), and the neon in neon lights. All minerals are pure substances, including asbestos. Glass is a pure substance. Most precious stones are pure substances.