Thinking Engineering

The PhD viva I did last week went differently from what I thought: my examiners asked many questions about basic chemistry and physics, rather than the specifics of my research work. And I realized that I could not remember promptly certain equations, but nevertheless I knew the physical meaning of those equations, and after some thinking I was able to write them in the proper form.

An undergraduate student needs to know equations by heart, too, and there’s a reason: they are learning the basics and fundamentals of their disciplines, so it is legit to ask them more than strictly necessary – just to be sure they know their stuff. Instead, engineers on their job do not need to remember by heart all possible equations; it doesn’t really take lonk to look them up into manuals or databases. But what engineers need to know is the physical meaning of the various equations and formulas, and in what conditions they can be applied.

Another question y examiners asked was the intermolecular separation distances for solid, liquid and gas phases. Yeah, what are those distances? Before giving numbers, let’s reason a bit: in solids, molecules are closely packed together: the distance between one another is of the same order of magnitude of atom-atom bonds. Also in liquids molecules are packed together rather closely, so the separation is of the same order of magnitude. In gases, molecules are much father away: at room temperature and atmospheric pressure, the density – number of molecules per unit volume – of a gas is roughly 1/1000 of the density of water; given that volume is a length cubed, intermolecular separation must be roughly ten times larger. Atom-atom bond lengths are typically 100 – 300 pm (1-3 Angstrom, an unit I never really mastered), so all the rest can be estimated easily. The separation between molecules for gases at atmospheric pressure is in the order of nanometers.

And order of magnitude also means “a factor ten”; what engineers must be able to do is to provide quick estimates (also known as back-of-the-envelope calculations) accurate within one order of magnitude. There is always time to crunch numbers through computers nowadays, but if the orders of magnitude are off, it is completely useless to have calculations accurate to the sixth decimal digit. For example, when boiling water is used as coolant, at least for a first estimate the specific heat of liquid water is trascurable compared to the heat of vaporization, which is about 500 times, 2 – 3 orders of magnitude, bigger.

So, what is the practical manifestation of the intermolecular distances discussed above? Solids are dense and scarcely compressible; liquids are slightly less dense (in reality, liquid water at 277 K is denser than ice, but water is a rather unusual liquid, despite being the most common) than solids but equally not compressible; gases are much lense dense and very compressible. Compressing a gas means packing more molecules in the same volume by forcing them closer together; this also means that theh igher the pressure the less ideally a gas will behave.

A problem with universities is that students are often taught to be pedantically precise; they know the numbers well, but they find it hard to place these numbers in a context – while in the industrial practice is more important to place numbers in the right context rather than knowing them with great accuracy. On the other hand, young minds may become sloppy if the students (erroneusly) become convinced that accuracy is not important and rough estimates are enough. As usual, a tradeoff is required.