What links a coffee to music by the likes of Eric Clapton and Jimi Hendrix?
As we sit back and enjoy the aroma from our coffee, we may rue the fact that our precious brew is evaporating away. We know from experience that hot coffee evaporates faster than cold coffee and we may dimly remember the physics that explains why this is. But have you ever stopped to consider that it is this bit of your coffee that forms a link between your drink and those famous guitarists?
The link concerns the mechanism behind the evaporation. To evaporate out of the coffee, a water molecule needs to overcome a certain energy barrier, let’s call it W, in order to escape. Given that W is constant, the more energy a water molecule has, the greater its likelihood of escape. So we could say that the probability of a water molecule escaping the coffee goes as exp{-W/kT} which means, the higher the temperature, T, the smaller the ratio W/kT and hence the greater the probability (because the exponential is raised to a negative power and hence is a dividing factor). The k is a constant known as the Boltzmann constant.
Now think about how the amplifiers used by many musicians work. It seems that many guitarists favour valve amplifiers owing to the type of sound they produce. Certainly Clapton and Hendrix were well known for their use of valve amps. A valve amp works by a process of thermionic emission in which electrons are ‘evaporated’ from a hot metal wire before being accelerated to a positively charged plate. This bit is the ‘valve’. In order to escape the metal wire, the electrons have to overcome a certain energy barrier, let’s call it Ω. Just as with W and the coffee, this barrier is a property of the metal that the electron evaporates from. The more energy an electron has (the higher its temperature), the greater the likelihood of it escaping the metal filament and fulfilling its role in the valve amplifier. Hence the mathematics describing thermionic emission is the same as the mathematics describing the evaporation in your coffee cup¹ and the probability of thermionic emission goes as exp{-Ω/kT}.
Now the size of the barrier is of course different in the two cases (Ω is much larger than W) which is why you have to plug in your amplifier to the electricity supply rather than just let it sit on the table top. But this is a difference of size rather than of kind. It is another of those connections between your coffee cup and the world that can be stranger than you may at first think.
If you think of a connection between your coffee and an interesting bit of physics, why not share it in the comments section below.
¹This discussion originally appeared in (and was adapted from) the Feynmann Lectures on Physics, Vol. 1