Entropy - A good definition for something that folks frequently do not understand

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peakbagger

Minister of Fire
Jul 11, 2008
6,350
Northern NH
Renewable Heating Design | May 2021 | Plumbing & Mechanical Engineer (pmengineer.com)

I see the entropy being ignored in the popular press often. Thermal power plants in order to work have to reject heat, usually by a cooling tower or air cooled condenser (far less often, they just pull water out of a river, lake or ocean and use the water to cool the plant). Folks take the total flow and multiply by the temperature difference and claim there are millions of BTUs read to go for heating which is technically true. Unfortunately its rarely worth anything to anybody except possibly heating a greenhouse slab or sidewalks in cold weather (they conveniently forget when it warms up the heat has to go somewhere)

I run into this whenever I run my wood boiler with my undersized slant fin radiators, In order to heat the house I need 140 F water minimum. My storage will drop to 140 F but even though its a lot warmer than the house, I can not get the heat out fast enough. Well designed radiant heating or low temp radiant emitters can run down to 85 deg F, so I would get a lot more heat between firing my boiler out of my storage tank if I changed out my radiators. That is not a small undertaking for an existing home and given my wood cost and usage I could never justify it on an existing home but with a new home it would be different story.
 

begreen

Mooderator
Staff member
Nov 18, 2005
88,230
South Puget Sound, WA
Very good design point. Also why most nuclear power plants are built near a large body of water or river. Too bad because the efficiency really goes up when cogeneration is applied.
 

stoveliker

Minister of Fire
Nov 17, 2019
954
Eastern Long Island NY
Good piece that you linked to. But I always use the simple (partial) explanation that energy flow is proportional to the gradient and the surface area. So for a lower energy source (colder hydronic), one would need a larger surface area to reach the same flow (heating). See the radiant hydronic floor example there.

Not as complete an explanation as there, but easier to understand.

However, with respect to the cooling towers, the example of a "1 unit of low entropy energy to move 4 units of high entropy energy" does suggest that combining cooling towers with a heat pump would be able to efficiently use the btus going up there? Indeed, not to power the turbine, but to heat to a lower temperature.
 
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EbS-P

Minister of Fire
Jan 19, 2019
802
SE North Carolina
The Carnot efficiency for and steam or hydronic heating system just isn’t very high.


A lighter look at entropy.

 
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peakbagger

Minister of Fire
Jul 11, 2008
6,350
Northern NH
I usually use the example as having 10000 btus for free to recover, The choice is 10000 pounds of water heated 1 degree F or 100 pounds of water heated 100 F degrees, (same number of BTUS) but the 100 pounds of water is a lot more valuable.
 
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woodgeek

Minister of Fire
Jan 27, 2008
4,373
SE PA
Ah, entropy, my old friend.

Totally agree about the storage-radiation link, but I see it more as diminishing returns for natural convention versus forced convection. A water to air coil in a small air handler could (for the cost of a little fan power, which would also end up as usable heat) extract usable heat from cooler water.

The point here is that we are expending a lot of money and effort for a form of energy (space heating) that is very low worth in terms of its ability to do work. For me, that points to an opportunity to use heat pump technology to turn real energy (i.e. with the ability to do work) like electricity into a far larger amount of heat. In practice, existing HPs get COPs of 4-5 at high outdoor temps (and only 2 in cold weather), and HPWHs get COPs of 3 seasonally (not accounting for heat stealing in heating climates).

The theoretical limits of COP in all these applications are roughly double those figures: https://en.wikipedia.org/wiki/Coefficient_of_performance

So, renewable electricity at $0.10 /kWh (say from offshore wind in winter) X 10e6 BTU/3414 BTU/Kwh = $29 per MMBTU. At a shoulder season COP of 4 in current generation HPs, that is only $7/MMBTU. If you figure that a cord of wood in a modern stove gives 18 MMBTU, that is a match for $125/cord hardwood, or $0.70/gal fuel oil. In January, double those figures at present (COP=2).

The learning curve in offshore wind tech (or grid storage, or long-distance transmission) will drop that scalable winter renewable price in New England. Add in engineering improvements to get higher HP COPs (esp at lower temps) and that (current) price per MMBTU easily has room to fall by 50% to a few $ per MMBTU.

In other words, energy is expensive, but entropy is cheap!
 
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