Thursday 31 March 2016

How not to cut cake

When my wife pointed out Francis Galton's method for cutting a cake to minimise the exposed surface and therefore improve its lifespan, I of course implemented it immediately. I hate stale cake. (I eat it anyway.)

Galton, Nature 75, pp. 173-173 (1906) doi:10.1038/075173c0

The basic principle is that you remove slices from across the middle of the cake, and then press the remaining pieces together so that there is no exposed surface to get stale.

There's an immediate drawback to this method: each progressive slice is taken from a smaller cake of a different shape, so it's hard to judge portions. It's also difficult to make even-sized pieces for multiple guests. (Galton's original publication was meant to maintain the lifespan of a cake that was only being eaten by two people.) The slices are at least neatly cuboid which solves the age-old problem of how to eat a wedge of something with a fork

The bigger problem is that this method is wholly counterproductive when applied to my wife's delicious coffee and walnut cake. It's simply not possible to produce sufficiently crisp parallel edges so that the different sides fit together and exclude the air. In fact, this method results in a greatly increased exposed surface area compared to just cutting out a wedge.

Galton's original method is applied to a Christmas cake, which has a firm texture that might be more conducive to clean edges, but I still think you're going to have difficulty getting a nice tight interface between the two exposed surfaces, even with his suggested rubber band.

Galton is known as the originator of eugenics, so perhaps it's unsurprising that this idea proves to be counterproductive. I'll stick to using the plastic cake cover.

Tuesday 8 March 2016

Melting points and The French Connection

I was watching the classic 1970s crime film The French Connection recently (which is a masterpiece, by the way) and was surprised to see a bit of ordinary undergrad chemistry appear at about the half-way mark.

In lieu of the screencap that Netflix won't let me take, you'll have to load up your own copy and fast forward to the 52-minute mark.

The gang are having their chemist confirm the purity of the heroin shipment around which the whole movie revolves. He's watching for the temperature at which the compound melts - the higher, the purer, with completely pure "product" melting at its own specific melting point. I was really chuffed that the movie went to such lengths to get the technique right, which is just going to be a background detail to most viewers. It really adds to the verisimilitude.

 At the end of my undergraduate organic chemistry labs, we would do a similar procedure to show that we'd done a good job of making whatever compound we were supposed to be making. The hardware was a little different, but we were still tapping the compound into a little glass tube, heating it up, and watching for the temperature at which it melts.

Many a lab session ended with me squinting into these machines. A thermometer and a sample tube go in the top.

You might rightly wonder why impurities lower the temperature at which some chemical compound melts. The intuitive answer is that the molecules of the compound have to fit together like little lego bricks, and impurities get in the way of the molecules bonding (fitting) together, and therefore it melts more easily.

It's intuitive but it's wrong!

Actually, the bonding isn't weakened all that much by the presence of impurities. The real reason has to do with entropy. Understanding this from first principles involves a bit of thermodynamics, but I can cut to the chase a bit and introduce you to one of the neater ideas in physical chemistry.

A process in chemistry happens when the "free energy" G is lower after the process than before. So to melt, the liquid substance has to have a lower free energy, G, than the solid. G has two parts, the enthalpy H, which has to do with things like how strongly molecules are bonded together, and the entropy S, which is to do with the system's capacity for disorder. (Measured by the number of different ways we can arrange the molecules.)

G = H - T x S

The entropy S is multiplied by the temperature as you can see, so it has an additional property that its contribution to the free energy gets larger as the temperature increases.

For a process like melting, the enthalpy H has to increase. The compound is always going to be more stable locked into a neat little solid than with the molecules free to move. So this is a penalty against forming the liquid. (This is known as the enthalpy of fusion.)

However the entropy S will increase upon melting, because we can arrange the molecules in many more different ways in the liquid than in the solid. The entropy increase can be viewed as a sort of a discount on the enthalpy penalty, and because S is multiplied by the temperature, the total discount T x S is bigger at higher temperatures. Melting happens when you reach a sufficiently high temperature that entropy discount T x S is equal to the enthalpy penalty H.

So what happens when we add impurities? Well, the entropy S of the solid is a bit higher than before, because there are now even more different possible arrangements of molecules. However the entropy of the liquid is much higher than before. That means that the entropy increase associated with melting is larger, and therefore the discount we get from the entropy is bigger. Seeing as the enthalpy part H stays more or less the same, the temperature at which the entropy overbalances the enthalpy is lower.

Thinking about chemical processes in terms of thermodynamics isn't always intuitive, but it reveals a lot of subtleties that aren't immediately obvious. Kind of like a good movie.