I know my posts are usually walls of text, but I am trying to improve!
In his landmark physics course, the Feynman Lectures on Physics, Richard Feynman tries to explain what an explanation in physics actually is. You can always understand “the math” and follow a proof step-by-step. But deep, yet intuitive, understanding becomes harder and harder the more abstract the concepts become. Feynman claims that physicists do not really understand on a fundamental level what cannot be explained to undergrad students. He has invented ingenious twists and lines of reasoning in order to explain seemingly old and dull physics.
I second that. Trying to find those brief, intuitive but exact explanations is an obsession of mine, and I plan to report on my attempts as a would-be-Feynman in my blog.
I start with an arbitrary question: A heat pump is often said to work like a refrigerator, but “just the other way round”. I do not like this explanation: “the other way round” is misleading. A heat pump is, in some sense, also a steam power plant just working “the other way round”. It depends to which sides or which cycle you refer to, and it does not explain how a refrigerator works.
Heat pumps sort of enhance the energy retrieved from the “cold” ambient environment. You put in electric energy and typically gain about 4 times as much heating energy , the energy available to internal heating devices. A super optimized machine would be able to enhance energy by about a factor of 8. Where does this energy come from? Is this sort of a perpetuum mobile?
The marvellous enhancement is due to so-called cold environment is still being rather hot – hot compared to the absolute zero (0 Kelvin, 0 K) temperature of -273,15°C. There is some amount of internal energy connected to virtually anything, and this energy reaches a zero point when all of this energy has been extracted.
Only if we would try to multiply heat from a 3 K cold, dark asteroid in outer space the multiplication factor would be very close to 1. In winter (on earth) a heat pump transfers heat from actually warm 273K (0°C) to a little bit warmer 298K (25°C). If the heat pump would operate on the surface of the sun (5000K) and increase the temperature to 5020K, the multiplication factor would be 251!
A perfectly operating heat pump could be used to explain what temperature actually is and why it is just natural to measure the temperature in Kelvin. The limit of -273,15°C has originally been discovered on studying the thermal expansion of gases, extrapolating backwards to low temperatures. You can start from looking a perfectly operating heat pump at some temperature above absolute zero, and zero is where the multiplication capabilities of the heat pump come to an end.
But why is there a limited amount of internal energy? Haven’t we learned that energy is something that makes sense only if measured in relation to another “state” anyway? Yes, but only as long as you do not consider the freezing of degrees of freedom at absolute zero. Quantum mechanics forces you to do that.