Search online and you can find videos of machines that lift cogs or turn wheels that are powered by the steam rising off a coffee. You can see an example here and find instructions for how to build your own here (a “stay at home” hobby project perhaps?).
Although such machines are very much for the hobbyist, the principle of the steam engine drove the industrial revolution. And, even now, much of our power network relies on somehow heating water which then drives a turbine that generates electricity. Underlying this is the principle that energy can be transformed from one type to another but is, ultimately, always conserved.
The concept is easiest to visualise with a pendulum or a swing. At its height, the pendulum has a maximum of potential energy but is not moving (so its kinetic energy is zero). As it passes through its minimum height point, the speed of the swing (or pendulum) is maximum and the potential energy at a minimum. Indeed, the amount of potential energy lost by the pendulum is equal* to the amount of kinetic energy gained. The same can be extended to “work” which, in the language of physics is always energy. If a certain amount of energy is put in, a certain amount of work can be produced. In a closed system and without loss, the amount of energy you put in is the amount of energy you get out. In any real system, some of that energy is lost to heat or other methods of loss.
To use a more coffee related example, in an espresso machine, work is done to put the water under high pressure (and separately to heat it). This pressurised water is then allowed to escape through the coffee puck where the work originally done pressurising it gets transformed into the kinetic energy (speed) of the water going through the group head. Changing the pressure changes the speed at which the water goes through the puck in an analogous way to how changing the height of the pendulum drop affects the speed as it goes through its central point. Of course you won’t always see this because changing things like the grind size in the espresso puck will also affect the route that the water takes as it travels through the puck and so the actual speed at which you see the coffee-infused water leaving the espresso basket will be affected by that too. The real world is never quite so easy as the ideal.
A pour over works in a different way. Here, the energy is stored in the water ‘bath’ in the filter as gravitational potential energy. As the water falls, it gains kinetic energy at the expense of this gravitational energy (or height). As the espresso machine also works with gravity, the conclusion would be that the water will move much faster through the espresso puck than the pour over bed. That this often doesn’t seem to be so is again because of the effects of the resistance of the coffee bed or espresso puck, on the espresso and the pour over.
This concept of the conservation of energy has been engrained into us from an early age. And so it may be surprising that it is a fairly recent principle in physics. For although versions of this principle had been considered for many years, it had not been recognised until the 1840s (by James Joule and Robert Mayer in 1843 and 1842 respectively) that work and heat were interchangeable. And it wasn’t until 1847 that Helmholtz recognised that all energy was conserved. Although at that time he was using the word ‘force’ for what we now call ‘energy’, and what we now call kinetic energy was thought of as a ‘living’ energy. He wrote:
“… the loss in the quantity of potential force is always equal to the gain in living force, and the gain of the first is the loss of the second. Thus, the sum of the existing living and potential forces is always constant.”**
So, among the many contributions to physics that he made, Helmholtz also has a claim to being among those who developed the field of thermodynamics which remains crucial both for physics and for our industrial and technological progress.
There is perhaps a cautionary note here for any who are tempted to think that science and religion are always somehow in opposition. For the British scientists who contributed to the development of the idea of conservation of energy (such as Joule and William Thomson (Lord Kelvin)), the concept was founded on the idea of a Creator God: as only God could create or destroy, so it followed that energy of itself, could never be either created nor destroyed, it could only be transformed from one form to another. The idea of a God was, for them, implicit in the idea of the conservation of energy**.
Helmholtz had a philosophical disagreement here. For him, the principle was founded on a Kantian understanding of philosophy***. Certainly certain things had to be assumed at the beginning (such as the principle of causality and the existence of matter outside of our perception of it). But once these assumptions had been made, the principle of conservation of energy followed in a deterministic manner.
Does this matter? In our everyday experience of engines and the way things work, conservation of energy certainly seems to be crucial. We no longer question the principle but assume that one form of energy is transformed into another and is continuously conserved even as it is dissipated into the universe as heat as our coffee cools. But nonetheless, Helmholtz’s understanding was founded on certain assumptions, beliefs, just as Joule and Kelvin’s. It helps to be aware of the philosophical underpinning of our science so as to ensure we don’t have over confidence in what we can, and cannot, know.
So Helmholtz can teach us something else as we gaze into our coffee. Our world is multifaceted, and what we believe about what the world is, influences and informs our understanding of how the world works. Our challenge is to look into ourselves as we sip our coffee and to start to see what we believe we know and what we can actually know. And if we were to really do that, what conflicts would we find?
*With the usual caveats of no energy being lost to friction etc.
**”Helmholtz and the British Scientific Elite: from force conservation to energy conservation”, David Cahan, Notes Rec. R. Soc (2012), 66, 55-68
***”Helmholtz: from enlightenment to neuroscience”, M Meulders, MIT press, 2010