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Some rulebound thoughts on energy

March 31, 2012

The study of mechanical work produced by heat (such as in a steam engine) or heat produced by mechanical work (such as in friction) is called thermodynamics. Like asimovian robotics, thermodynamics is governed by three laws. And like asimovian robotics, a zeroth law is sometimes added.

The zeroth law of thermodynamics says that temperature is a physical property. Actually, it says that if both A and B are in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. Yes, this is important. Assume that C has a temperature of 15 °C. Saying that A is in thermal equilibrium with C is fancy talk for “even if we connect A and C, no heat will flow from A to C, nor from C to A”. This would mean that A has the same temperature as C, so A is also 15 °C. Likewise, B being in thermal equilibrium with C would mean that B has the temperature 15 °C too. Suppose that the zeroth law doesn’t hold, so A and B does not have to be in thermal equilibrium. Now we have two bodies, A and B, both at 15 °C, but not in thermal equilibrium. This doesn’t make sense. Temperature suddenly has no meaning.

Thankfully, the zeroth law does hold, temperature is a thing, and so is thermodynamics. The zeroth law could be jokingly expressed as “the game exists”.

The first law of thermodynamics is a variation of the law of conservation of energy. Conservation of energy is more or less what it sounds like: in a system that exchanges neither mass nor energy with its surroundings, the amount of energy is always constant. No energy is produced, no energy is consumed. Thermodynamics frequently deal with systems that allow energy transfers to and from the surroundings. So the first law of themodynamics states that in a system that doesn’t exchange mass with its surroundings, the change in energy of the system is equal to the heat delivered to the system from the surroundings, minus the work done by the system on the surroundings. Take for instance a steam engine in a locomotive: the change in energy of the engine is equal to the heat it recieves from the fire, minus the work it performs in pulling the train. If we study the steam locomotive for a work day, at the beginning of its shift the engine is cold and silent. Then the fireman arrives and starts up the fire, entering heat into the system. The engine gets hot – it has gained energy. The driver starts the locomotive, and the engine pulls the train, using the energy to get work done. At the end of the day, the crew parks the locomotive on a side track and goes home. A while after the shift is over, we have arrived at the same state as we had in the morning: engine cold and silent, resting at the same low energy as before. The change in energy, seen over the full work day from early morning to late evening after cooldown, is zero. First law now says that since no energy was taken from the engine itself, it must all have come from the heat of the fire. We can’t create any energy to do work for us. It has to come from somewhere.

In other words: “you can’t win the game, the best you can hope for is a draw”.

Enter the second law of thermodynamics. It says that heat will never flow spontaneously from a cold body to a hot body. From this follows that extracting heat from a hot body and converting it completely into work is impossible. Proof by contradiction again: suppose we could do it. Suppose further that we use this work to drive a refrigerator, that takes heat from a cold body and puts it into the same heat reservoir that our hypothetical perfect engine draws its energy from. The net result of the whole system would be heat flowing from the cold body to the hot body, with no work being consumed, which is impossible. Hence, we can’t convert all the heat into work. Some of it has to go into heating something else. Every thermodynamical engine needs a heat sink.

So, we have shown that the heat energy available for work in a hot body doesn’t really depend on that body’s own temperature. Rather, it depends on the temperature difference between heat source and heat sink. The greater this difference, the less energy needs to be wasted in heating the cold body. To not lose any work, we would need a heat sink that’s as cold as possible. 0 K. -273,15 °C. Absolute zero.

In other words: “you can’t get a draw either, except on a very cold day”.

Then comes the final blow, in the form of the third law of thermodynamics. In its non-mathematical form it says, succinctly:

“Nothing ever gets that cold.”

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