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Efficiency question

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LAN_403

Dr. Dark Current

Mon Apr 16 2007, 01:52PM

Registered Member #152 Joined: Sun Feb 12 2006, 03:36PM
Location: Czech Rep.
Posts: 3384

This question has been lying for months in my mind. I must be missing something.
Lets say I have a heat pump that can move 5 times more heat from one place to another than is the input power. Now I place a heat engine between these 2 places with efficiency greater than 20% and now I have generated more power than is inputted, and this is obviously a paradox.
Where is the problem? I think it does have something to do with the efficiency of the heat engine? (btw I asked this question to my physics teacher and he had no answer

)

Steve Conner

Mon Apr 16 2007, 02:07PM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

According to the second law of thermodynamics, it's impossible to have a heat engine with a higher efficiency than a heat pump, when they are operating between the same source and sink temperatures.

This is Carnot's statement of the second law of thermodynamics: see wikipedia for more information @

(if your physics teacher didn't know this, that's pretty shocking)

AndrewM

Mon Apr 16 2007, 02:31PM

Registered Member #49 Joined: Thu Feb 09 2006, 04:05AM
Location: Bigass Pile of Penguins
Posts: 362

been eyeing peltier performance plots eh? if so, I had the exat same thought in highschool. frankly i recieved this explanation then, but i didn't understand it until years later.

Pete

Mon Apr 16 2007, 04:16PM

Registered Member #106 Joined: Thu Feb 09 2006, 09:39PM
Location: Portland, OR and Istanbul, Turkey
Posts: 47

It's an interesting thought experiment and I was actually going to ask the same question to the forum as well. Mine was slightly different.

Mine involved a Ground source heat pump system. So lets try this one. The average ground temperature below 5 meters is approximately 10 Degrees C or 50 degrees Fahrenheit. You have a refrigerant that gets cooled to this temperature and then the liquid refrigerant goes through the process of evaporation in the air conditioner absorbing, lets say 20,000 BTUs. your pump is a very nice one, rated at 4 to 1 COP so your power usage is only 5,000 BTUs or 1400 watts.

The heat pump then compresses the gaseous refrigerant which is now at a nice 21 degrees C or 70 Degrees F to a higher temperature, or I think to about 60 Degrees C or 140 Degrees F. You would only have the temperature difference between the outside air and the hot side. Or you could have a cold closed water loop running in the ground for a 50 degrees/140 degrees difference. That only gives you a temperature difference of 90 degrees.

You might be able to get a large low temp Sterling Engine to generate some power, but like Steve said the laws of thermodynamics limits that cycle itself to only 30% efficiency and in no way will generate 1.4Kw of power. You can just envision the losses. You can always use that excess heat, like they do now with extra water heating but maybe I should look at my figures better. I've been staring at them for too many days lately anyway. I'm starting to drive myself crazy.

Pete

Bjørn

Mon Apr 16 2007, 06:10PM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

The maximum efficiency possible is: ((Thot-Tcold)/Thot)*100%. You need to have to use Kelvin as the unit for temperature.

Any heat pump or heat engine that actually does anything will have losses so the efficiency will always be less than 100%. If you apply this correctly you should arrive at the correct answer. If your system has more than 100% output you either did the math wrong or you forgot to consider that something somewhere got colder.

Steve Conner

Tue Apr 17 2007, 10:30AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

BTW, I just wanted to remind everyone that the Second Law does not "prove" that perpetual motion is impossible. In fact, the derivation of the Second Law starts from the assumption that perpetual motion is impossible. We treat that assumption as a valid starting point because it agrees with what we see by observation and experiment.

So, the world shows us that you don't get something for nothing, and the Second Law is just a formal statement of that in a way that lets us use it in our engineering calculations. But if someone somehow made a perpetual motion machine tomorrow, the Second Law would have to go. I don't expect this to happen, though.

Pete: You do indeed get considerably more heat out of your heat pump than the amount of electricity you put in. Maybe 3 times as much. That doesn't violate any law of thermodynamics, because the electricity driving your heat pump was made from heat in a power station that was only about 30% efficient.

Pete

Wed Apr 18 2007, 07:20AM

Registered Member #106 Joined: Thu Feb 09 2006, 09:39PM
Location: Portland, OR and Istanbul, Turkey
Posts: 47

Steve, I don't disagree with you, otherwise COP ratings of heat pumps wouldn't be worth anything. I was thinking of the waste heat that could be reused to generate power before the cooling cycle takes place.

Steve Conner

Wed Apr 18 2007, 09:00AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

What waste heat? I don't see any in the operation of a heat pump. It sucks heat out of the already-fairly-cold ground, and delivers it to your already-warmer house, against the normal tendency for heat to flow from a hot place to a colder one. The electrical power used to drive the compressor all ends up as heat delivered to your house too.

A COP of 4 means that for each 1 unit of electrical power you supply, you get 4 units of heat: 3 of them pumped from outside and the remaining 1 from the electricity you put in. Or maybe it's 5 units (4 and 1) I can't remember.

Pete

Wed Apr 18 2007, 09:49AM

Registered Member #106 Joined: Thu Feb 09 2006, 09:39PM
Location: Portland, OR and Istanbul, Turkey
Posts: 47

ohh I just realized our miscommunication. I was thinking of when a heat pump is used for Air Conditioning. The compressor exit temperature would be a bit higher than the the ground. IF you could put a Sterling engine or some kind of recovery system between the compressor outlet and the ground, you would get a nice temperature difference to use. That way we are extracting extra energy before the gas reaches the ground loop to be condensed to a liquid for use in the air conditioner.

But for Heating applications I agree with you.

Bjørn

Wed Apr 18 2007, 10:19AM

Registered Member #27 Joined: Fri Feb 03 2006, 02:20AM
Location: Hyperborea
Posts: 2058

The direction of flow does not matter. The formula above is still valid, in worst case you just swap the pipes to your stirling engine. When you heat your house instead of cooling it the hot and cold just change place. Only the temperature difference matters when it comes to the efficiency of the energy extraction.

So yes you can regain some energy but since the temperature difference is small the efficiency will be poor unless you need air/water at that specific temperature.

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