# Conservation

This week in physics lab my students are testing the principle of conservation of energy by dropping a marble through a photogate and comparing the kinetic energy the marble gained with the gravitational potential energy it gave up as it fell. In a perfect world, these quantities would be equal, and thus total energy conserved. Since we don’t live in a perfect world, energy is continually dissipated by insidious forces like air resistance et al. Regarding this points, I had Serendipitously just read the following comic from xkcd.com and asked my students to write about it:

What I wanted them to think about is the divergence between the tools, powerful and useful they may be, that we use to describe the world (total energy always stays the same) and what is really practical to do. According to the principle of conservation of energy (also known as the first law of thermodynamics for those keeping track at home) the scheme shown in the comic should be a perfectly acceptable way to “transport wind,” with no loss of intensity. Of course, this comes with the proviso that the turbine must capture all of the wind energy and be perfectly efficient. The power cable must have zero electrical resistance, and the fan must also have a 100% efficiency rating.

However, we know intuitively (or at least, we should) that, in the real world, nothing is perfectly efficient, and the actions of the cartoon’s protagonist will inevitably lead to a colossal waste,  since each step of converting from wind to electricity and electricity to wind entails a loss of energy.

In case you think that the whole discussion is silly, and that no one in their right would convert so profligately from one form of power to another, consider the case of back-up power for server farms. Google has a patent on a method that saves energy by reducing the number of times electricity has be to converted between AC and DC. Evidently, this was an innovation, and existing server farms were build with inefficiency wired-in:

Now, there are limits, even in principle, to the efficiency of some processes. Once you get past the idyllic world of the 1st law, the second law of thermodynamics puts some upper bounds on what you can do even if you try your hardest to squeeze every last bit of efficiency out of certain ways of converting energy between various forms. However, as one of my students pointed out, there is no reason why you couldn’t drive forever in a “perfect” hybrid car that recaptured all of the energy from braking (and going up hills).