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Q & A: explaining thermodynamic efficiency

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Most recent answer: 01/22/2015
When people are informed that an airconditioner can produce twice as much "cool" for the energy (electricity) consumed they look at me as if I am a liar. Even when I explain the tech specs that come with the airconditioner they still think I am full of crap.It is difficult to explain to people that aircondtioners do not make HOT and do not make COLD and that the hot and cold experienced is a consequence of the process.Airconditioners like refrigerators are heat pumps, they transport energy. The two processes:gas compression leading to condensation andevapouration back to a gas.Both these processes create a thermal gradient for heat to be loaded into or out of the transport system.This maybe clear to you and I but explaining this to people is difficult...... how can you get something for nothing ..... it may look like this but it is not the case ....... there are no perpetual motion engines!We now see devices coming out from Japan that have efficiencies of 1:7, that is for 1000 watt of power consumed the equivalent of 7000 watt of heat is made available.How can this be explained to average people?Projecting thermodynamics and graphs of Entropy/Enthalpy is very very unproductive.How would you explain the thermodynamic efficiency of refrigeration systems so it makes sense to non scientists and non engineers?
- Pato (age 61)
Darwin, NT, Australia

How to explain thermodynamic efficiency of heat pumps to laymen? A great question! You can help us out here. We'll suggest some explanations, and you can let us know how well they go over.

It might help rhetorically to start with an acknowledgement that you aren't proposing magic, there are real thermodynamic limits. It's yucky, but you might even try to  bolster your credibility by some appeal to authority, e.g. us.  (We are physics professors and, more importantly, don't sell heat pumps.)

Ok, now for the real argument. Let's pick one direction to discuss, say heating.  I'll borrow shamelessly from Sadi Carnot, since he was able to get these ideas without any sophisticated modern background back around 1820. 

Your friends surely recognize that when it's hotter out than in you don't need any power at all to get heat to flow in. Heat flows in just like water would flow in from higher ground. It happens spontaneously. So since you get what you want with zero input, the efficiency is infinite. Say it cools down outside, just a bit cooler than inside. Now you have to pump heat out. Will tyor friends acknowledge that how hard it is to pump it doesn't suddenly change drastically when the temperature outside is just a little higher than inside? Doesn't the amount of energy required to pump water depend not just on how much you pump but on how high you're pumping it? The same goes for pumping heat, where temperature is like height.

Let's say you're pumping energy around in the form of gravitational potential energy of water, starting from zero at sea level. One kg of water at 1 m height has about 10 J of that energy. It takes 10 J of work to pump 1 kg from a height of 100 m to a height of 101 kg. In the process you've pumped 110 J of energy to the tank at the greater height, pumped 100 J  from the lower tank, and bought 10 J from the power company. The ratio of the amount of that type of energy that you pump to the amount of energy you pay for depends on the ratio of the height of the lower tank to the difference in heights of the two tanks. When that ratio is big, you can pump a lot without much input. As Carnot realized, exactly the same principle applies to heat. Here, unlike our somewhat arbitrary sea-level baseline, absolute zero of temperature provides the starting point. In principle, efficiencies can be high because room temperature is about 295 K above absolute zero, and a quite cold day is usually not lower than about 265 K. The temperature differences are small compared to the absolute temperature. So in principle heating efficiencies of over 10 are reachable, although no commercial device does that well. A very hot day is rarely above 310 K, so in principle even greater cooling efficiencies are possible.

Let us know if this works at all or if you figure out improved versions.

Mike W.

posted without vetting until Lee returns

(published on 01/22/2015)

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