# Thread: Electricity from ambient heat

That's what I remember as well. And as bad as that is, it's still not THE big kicker/killer of this idea.

What REALLY dooms it is the fact that even *if* you could extract a minute amount of energy from such a device, doing so would reduce the energy (motion) of the molecules inside. And even assuming you could continue to reduce said energy (which is still a BIG stretch) you would eventually reach a point - at zero K - where there was no energy left inside the system.

Just as there is no such thing as a free lunch, there's no free energy either. If you want to ride the train you *must* buy a ticket.
That's definitely not a killer, since finding enough waste heat to dump back in is never going to be a problem for current energy uses. Note that the vast majority of energy used ends up as waste heat anyway.

2. If all our energy comes from the sun and the energy from the sun comes from fusion then every thing would fuse and turn into a giant black hole. There could be no big bang without energy coming from somewhere.

Doesn't the fact that the universe exists at all violate the law of thermodynamics? I mean, if there was nothing to start out with where did the energy come from?

3. Originally Posted by Pete
That's definitely not a killer, since finding enough waste heat to dump back in is never going to be a problem for current energy uses. Note that the vast majority of energy used ends up as waste heat anyway.
Then pardon my intrusion, please, Pete. Somewhere along the line I got the impression that you guys were talking about a totally closed system. Just two chambers with a a gate and isolated from anything/everything external.

Then pardon my intrusion, please, Pete. Somewhere along the line I got the impression that you guys were talking about a totally closed system. Just two chambers with a a gate and isolated from anything/everything external.
Well, I believe we were discussing a closed system regarding the energy source without referring to what was done with the recaptured energy itself, which would presumably be used externally, eventually being turned back into...ambient heat. I think his point is that there will "always" be more energy available in the form of heat because that's basically the last bastion of energy reservoirs, presuming we can consider ambient heat an energy reservoir (which is the whole point of the thread!!).

5. Originally Posted by angryScientist
If all our energy comes from the sun and the energy from the sun comes from fusion then every thing would fuse and turn into a giant black hole. There could be no big bang without energy coming from somewhere.

Doesn't the fact that the universe exists at all violate the law of thermodynamics? I mean, if there was nothing to start out with where did the energy come from?
For some reason, I'm not so bothered by the idea of the Universe "bootstrapping" itself from nothingness. Maybe I haven't given it enough thought. If you want something to pontificate about regarding the Big Bang, ask yourself how material was apparently ejected from it when it basically was the prototypical black hole.

6. ## Tesla's Ambient Heat Engine

Interestingly Nikola Tesla wrote an article on this subject published in Century Illustrated Magazine, June 1900

(The forum will not allow me to post links as yet sorry)

Some extracts:

A DEPARTURE FROM KNOWN METHODS—POSSIBILITY OF A "SELF-ACTING" ENGINE OR MACHINE,(...) —THE IDEAL WAY OF OBTAINING MOTIVE POWER.

When I began the investigation of the subject under consideration,(...)

I was vainly endeavoring to form an idea of how this might be accomplished, when I read some statements from Carnot and Lord Kelvin (then Sir William Thomson) which meant virtually that it is impossible for an inanimate mechanism or self-acting machine to cool a portion of the medium below the temperature of the surrounding, and operate by the heat abstracted. These statements interested me intensely. Evidently a living being could do this very thing, and since the experiences of my early life which I have related had convinced me that a living being is only an automaton, or, otherwise stated, a "self-acting-engine," I came to the conclusion that it was possible to construct a machine which would do the same. As the first step toward this realization I conceived the following mechanism. Imagine a thermopile consisting of a number of bars of metal extending from the earth to the outer space beyond the atmosphere. The heat from below, conducted upward along these metal bars, would cool the earth or the sea or the air, according to the location of the lower parts of the bars, and the result, as is well known, would be an electric current circulating in these bars. The two terminals of the thermopile could now be joined through an electric motor, and, theoretically, this motor would run on and on, until the media below would be cooled down to the temperature of the outer space. This would be an inanimate engine which, to all evidence, would be cooling a portion of the medium below the temperature of the surrounding, and operating by the heat abstracted.

DIAGRAM b. OBTAINING ENERGY FROM THE AMBIENT MEDIUM
A, medium with little energy; B, B, ambient medium with much energy; O, path of the energy.

But was it not possible to realize a similar condition without necessarily going to a height? Conceive, for the sake of illustration, [a cylindrical] enclosure T, as illustrated in diagram b, such that energy could not be transferred across it except through a channel or path O, and that, by some means or other, in this enclosure a medium were maintained which would have little energy, and that on the outer side of the same there would be the ordinary ambient medium with much energy. Under these assumptions the energy would flow through the path O, as indicated by the arrow, and might then be converted on its passage into some other form of energy. The question was, Could such a condition be attained? Could we produce artificially such a "sink" for the energy of the ambient medium to flow in? Suppose that an extremely low temperature could be maintained by some process in a given space; the surrounding medium would then be compelled to give off heat, which could be converted into mechanical or other form of energy, and utilized. By realizing such a plan, we should be enabled to get at any point of the globe a continuous supply of energy, day and night. More than this, reasoning in the abstract, it would seem possible to cause a quick circulation of the medium, and thus draw the energy at a very rapid rate.

Here, then, was an idea which, if realizable, afforded a happy solution of the problem of getting energy from the medium. But was it realizable? I convinced myself that it was so in a number of ways, of which one is the following. As regards heat, we are at a high level, which may be represented by the surface of a mountain lake considerably above the sea, the level of which may mark the absolute zero of temperature existing in the interstellar space. Heat, like water, flows from high to low level, and, consequently, just as we can let the water of the lake run down to the sea, so we are able to let heat from the earth's surface travel up into the cold region above. Heat, like water, can perform work in flowing down, and if we had any doubt as to whether we could derive energy from the medium by means of a thermopile, as before described, it would be dispelled by this analogue. But can we produce cold in a given portion of the space and cause the heat to flow in continually? To create such a "sink," or "cold hole," as we might say, in the medium, would be equivalent to producing in the lake a space either empty or filled with something much lighter than water. This we could do by placing in the lake a tank, and pumping all the water out of the latter. We know, then, that the water, if allowed to flow back into the tank, would, theoretically, be able to perform exactly the same amount of work which was used in pumping it out, but not a bit more. Consequently nothing could be gained in this double operation of first raising the water and then letting it fall down. This would mean that it is impossible to create such a sink in the medium. But let us reflect a moment. Heat, though following certain general laws of mechanics, like a fluid, is not such; it is energy which may be converted into other forms of energy as it passes from a high to a low level. To make our mechanical analogy complete and true, we must, therefore, assume that the water, in its passage into the tank, is converted into something else, which may be taken out of it without using any, or by using very little, power. For example, if heat be represented in this analogue by the water of the lake, the oxygen and hydrogen composing the water may illustrate other forms of energy into which the heat is transformed in passing from hot to cold. If the process of heat transformation were absolutely perfect, no heat at all would arrive at the low level, since all of it would be converted into other forms of energy. Corresponding to this ideal case, all the water flowing into the tank would be decomposed into oxygen and hydrogen before reaching the bottom, and the result would be that water would continually flow in, and yet the tank would remain entirely empty, the gases formed escaping. We would thus produce, by expending initially a certain amount of work to create a sink for the heat or, respectively, the water to flow in, a condition enabling us to get any amount of energy without further effort. This would be an ideal way of obtaining motive power. We do not know of any such absolutely perfect process of heat-conversion, and consequently some heat will generally reach the low level, which means to say, in our mechanical analogue, that some water will arrive at the bottom of the tank, and a gradual and slow filling of the latter will take place, necessitating continuous pumping out. But evidently there will be less to pump out than flows in, or, in other words, less energy will be needed to maintain the initial condition than is developed by the fall, and this is to say that some energy will be gained from the medium. What is not converted in flowing down can just be raised up with its own energy, and what is converted is clear gain. Thus the virtue of the principle I have discovered resides wholly in the conversion of the energy on the downward flow.

Some of the statements made by Tesla have been echoed here in this forum. For example, that Heat is converted into other forms of energy in passing through or into a heat engine and so effectively "disappears". The so-called "cold hole" or heat "sink" therefore never being filled or never receiving the heat or receiving so little of it that what does pass through can be removed by the energy generated by the engine itself - such as, perhaps, some form of heat pump driven by the engine. If the engine were very efficient, the heat pump would have little work to perform and so there would be a net gain.

Sounds logical, though I'm not sure that removing such a SMALL amount of heat from a very cold "sink" back to the relatively HOT Ambient would be as easily accomplished as Tesla seems to have imagined.

7. ## Drinking Bird = Ambient Heat Engine

Again, I'm not able to post links as yet, being new to the forum, but there are many articles and YouTube videos of the toy "drinking bird" or "dippy bird".

Is not this relatively simple toy proof that a heat engine can, in at least one way generate enough energy to operate its own cooling system so as to maintain the "cold hole" or "sink" indefinitely ?

Yes, it uses evaporative cooling as a means of trapping heat energy and carrying it away but the evaporative cooling system itself requires energy to operate. The bird must continue to move and repeatedly dunk its head. That kinetic energy to keep the bird in motion is ultimately derived from the inflowing ambient heat that powers the engine not the heat energy being carried off. Why not a more powerful engine operating some more efficient cooling system, more efficient that is than a bit of wet felt on a toy bird's beak ?

Is not this toy bird at least a kind of "proof of concept" that some form of "Self Acting Engine" as Tesla described is a demonstrable possibility ?

8. Originally Posted by Tesla
If the process of heat transformation were absolutely perfect, no heat at all would arrive at the low level, since all of it would be converted into other forms of energy. Corresponding to this ideal case, all the water flowing into the tank would be decomposed into oxygen and hydrogen before reaching the bottom, and the result would be that water would continually flow in, and yet the tank would remain entirely empty, the gases formed escaping.
I'm confused here. How does removing all of the energy from liquid water ideally break the water down into gases?

9. How does removing all of the energy from liquid water ideally break the water down into gases?
Tesla was not suggesting that, I don't believe. Not literally.

He was using it as an illustration.

That is; His point is that HEAT-energy behaves differently than a fluid.

In reality, water itself, as a "fluid" going over a water wheel for example, to produce energy is NOT converted into some other substance or some other form, but he says:

Heat, though following certain general laws of mechanics, like a fluid, is not such; it is energy which may be converted into other forms of energy as it passes from a high to a low level. To make our mechanical analogy complete and true, we must, therefore, assume that the water, in its passage into the tank, is converted into something else
That is, if Water DID behave like HEAT/ENERGY being CONVERTED to another form in a heat engine... then for the sake of argument... it would have to be assumed or conceived that in the water wheel analogy, the water entering the tank would be, like heat entering a heat engine - CONVERTED into something else.

For example, if heat be represented in this analogue by the water of the lake, the oxygen and hydrogen composing the water may illustrate other forms of energy into which the heat is transformed in passing from hot to cold.
Clearly it is an analogy or illustration or example intended to convey the idea of how HEAT behaves differently from a "Fluid" and is not to be taken too literally. But IF a FLUID DID behaved like heat then ideally the water would all be converted into some other form, like gas. When Tesla stated:

For example, if heat be represented in this analogue by the water of the lake, the oxygen and hydrogen composing the water may illustrate other forms of energy into which the heat is transformed in passing from hot to cold. If the process of heat transformation (such as in a heat engine) were absolutely perfect, no heat at all would arrive at the low level, since all of it would be converted into other forms of energy. Corresponding to this ideal case (heat engine analogy stated above), all the water flowing into the tank would be decomposed into oxygen and hydrogen before reaching the bottom, and the result would be that water would continually flow in, and yet the tank would remain entirely empty, the gases formed escaping.
I think he was using the term IDEAL CASE in the sense of IDEA, that is, in other words it could have been stated: "Corresponding to this thought experiment..." or abstraction.

A perfect heat engine under IDEAL circumstances would convert all the heat into some other form of energy. Correspondingly, IF water behaved like heat, then in the analogy, all the water passing over a water wheel or through a turbine would "disappear", having been converted into something else or some other form, such as, for purposes of illustration, a gas. Of course it doesn't turn into gas, but if water powering a turbine behaved like heat in a heat engine it would change or be converted into some other form. Or so goes Tesla's argument.

Since heat behaves differently than a fluid in actuality the analogy breaks down. The way it breaks down, according to Tesla's argument, allows for the possibility of a heat engine which could maintain its own heat sink and so operate continuously, or so Tesla believed.

10. Originally Posted by RJBeery
For some reason, I'm not so bothered by the idea of the Universe "bootstrapping" itself from nothingness. Maybe I haven't given it enough thought. If you want something to pontificate about regarding the Big Bang, ask yourself how material was apparently ejected from it when it basically was the prototypical black hole.
RJ

You might read Guths papers on Eternal Inflation Theory. Inflation describes how our universe evolved from a soliton in a quantum scalar field. Guth and Linde [behind the iron curtain] both hypothesized 'what would happen' if they made the cosmological constant component, of the FRW metric, 'big dominant'. This domination will cause the soliton to expand in a false vacuum until it stabilizes as the true vacuum. At least we hope that's the case. I think it settled slightly false and thats why we see the universe expansion accelerating now. The mini false vacuum.

11. Again, I think the silly "drinking bird" apparent "perpetual motion" toy is a working example.

The ambient heat/energy that enters the bird to make it operate is ultimately converted into another form or other forms of energy - Kinetic energy, friction, and finally the excess locked up in the escaping water molecules evaporating from the birds head. As some of the ambient energy that powers the contraption is used to operate a cooling system throwing off excess heat an on-the-fly heat sink can be maintained. The "cold hole" is never filled as the heat reaching it is continuously "pumped out".

In a way, I suppose the energetic water molecules that escape in evaporation or the process of evaporation itself constitutes a kind of natural "Maxwell's Demon" separating out the most energetic molecules . If so, or if that were all that were involved, I would say that this could never be scaled up and the amount of energy that could be derived would never be more than infinitesimal. However there is the factor of some of the mechanical energy being used to replenish the water or power the "cooling system". The bird keeps dipping its beak in the water, otherwise there would be no evaporative cooling in the first place.

As Tesla stated; Some energy must be expended to create the initial "sink".

To get the bird started one must first dip its head in some water to create a sink, it wont get going on its own. Once initiated however, some of the energy extracted by the engine can be used to operate this mechanical aspect of the cooling system and so maintain the sink indefinitely.

Is it necessary to use evaporative cooling or some other natural process ?

I think that perhaps some other more efficient cooling system might be utilized so that more energy could be extracted. The idea is to convert as much ambient-heat energy as possible into some other form before it reaches the sink and then use some of that energy extracted to throw off the excess heat that does reach the "sink" so that it never warms up.

Possible ? It would seem so. Practical ? As a novelty item at least. Could the principle be scaled up to a practical level to produce useable power ? I don't really see why not. Compare the drinking bird to a child's toy pin wheel. Not very practical as a power source, but it can be scaled up to a 50 megawatt wind generator. The drinking bird is simply a heat engine with a built in cooling system to throw off excess heat reaching the sink. Why could not a more powerful and efficient heat engine be coupled with a more powerful and efficient cooling system ? A combined Stirling Engine / Heat Pump for example. If the engine were provided with controlled doses of ambient heat being otherwise thermally well insulated to exclude excess heat infiltration and also very efficient at converting heat to electricity the heat pump would have little work to do so as to maintain the sink. In other words, only allow as much heat into the system as can be converted into some other form such as electricity. Any heat/energy not converted that reaches the sink could be easily removed by the heat pump.

This would not be a "closed system" so I don't think that the 2nd law actually applies. Personally, I don't see how any Ambient Heat engine could ever be a "closed system", ultimately it would be the indirect utilization of solar energy stored in the atmosphere.

12. Originally Posted by Tom Booth
Again, I think the silly "drinking bird" apparent "perpetual motion" toy is a working example.
A working example of an inefficient heat-engine, perhaps.

http://en.wikipedia.org/wiki/Drinking_bird#How_it_works

13. A few points. The reference states: "The initial state of the system is a bird with a wet head" - not exactly true.

The initial state is a bird with a dry head that does nothing. I had one of these drinking bird toys as a kid. You have to push the beak down into the glass of water to get it started. Afterwards it just sits there for a while until enough water evaporates to get the head cooled down. Otherwise I more or less agree, it is a "heat engine" and probably not all that efficient which is my point. It is inefficient yet it works. What if a more efficient heat engine with a design based on the same principles were constructed ?

Also: "The liquid in the bottom bulb is heated by ambient air"

Most heat engines are the reverse. That is, heat above ambient such as a flame is applied and ambient is the sink. The bird has no heat sink initially, it must be artificially created, someone has to mechanically force the head down into the water to initiate the cycle. Once a sink has been created then ambient heat is drawn in as a heat source rather than a heat sink. The energy extracted from ambient heat to run the engine keeps the bird moving so as to repeatedly wet the beak and maintain the sink.

"the system efficiency is about 0.01%"

A Stirling engine can be 30% to 50% but is not generally designed to run on ambient as the heat source.

14. I think you are being deliberately obtuse. Your objection about the definition of "initial state" is without merit, as you are describing a state not part of the operating cycle. It as is irrelevant to analysis of the heat engine whether the bird's head is wetted by manual dunking or if the moisture is the tears shed from a temple priestess as it is irrelevant to analysis of a piston engine if the starter is electric or hand cranked.

The heat source is the ambient dry air and the heat sink is the non-equilibrium state of the water which has a high heat of vaporization which can only be exploited when the relative humidity is below 100%. In a small, airtight enclosure the finite volume of the system causes the heat sink to become exhausted. One Earth, the effective volume is still finite, but the heat of the Sun drives large air movements which keeps much of the atmosphere far from 100% relative humidity.

If I put a kettle of liquid nitrogen on a block of ambient temperature rock (or even a block of ice), the vapor exhaust from the spout of the tea kettle can be made to do work. In the exact same way as the volume of artificially cooled liquid nitrogen, the evaporative cooling of the head of the bird is a finite reservoir of cold. There is nothing magic about making heat engines run off of ambient. It's engineering and thermodynamics, not magic and not a loophole in physics.

15. Originally Posted by rpenner
There is nothing magic about making heat engines run off of ambient. It's engineering and thermodynamics, not magic and not a loophole in physics.
I wasn't sure if that was the point but you nipped it in the bud for anyone who might go there.

Other ways for folks here to think of an "ambient engine" is a "differential ambient" engine--where there are two masses of air, water, whatever--one being the source and the other being the sink.

And another way to think of direct conversion of electricity from a hot and cold well is by way of a thermoelectric device.

16. Originally Posted by rpenner
I think you are being deliberately obtuse. Your objection about the definition of "initial state" is without merit, as you are describing a state not part of the operating cycle.
I think it is important in relation to Tesla's explaination regarding how an ambient heat engine can be made to work.

For a heat engine to operate there must be a temperature differential. A relative Hot side and a relative cold side. A heat source as well as a heat sink - somewhere to dump the EXCESS heat.

In a normal heat engine heat is applied by combusting fuel and ambient is the sink, so there is no need to CREATE a sink, it already exists, but where ambient is the heat source there is no sink, one is surrounded by heat on all sides so a sink must first be created artificially and then somehow maintained by the engine itself as it runs.

As Tesla wrote:

...The question was, Could such a condition be attained? Could we produce artificially such a "sink" for the energy of the ambient medium to flow in? Suppose that an extremely low temperature could be maintained by some process in a given space; the surrounding medium would then be compelled to give off heat, which could be converted into mechanical or other form of energy, ... But can we produce cold in a given portion of the space and cause the heat to flow in continually? To create such a "sink," or "cold hole," as we might say, in the medium, would be equivalent to producing in the lake a space...
Do you think Tesla was being "deliberately obtuse" in putting emphasis on the point that to get energy from the ambient medium a sink or "cold hole" must first be artificially created and then maintained ? Tesla considered it the KEY to the whole problem. So do I.

If I put a kettle of liquid nitrogen on a block of ambient temperature rock (or even a block of ice), the vapor exhaust from the spout of the tea kettle can be made to do work. In the exact same way as the volume of artificially cooled liquid nitrogen, the evaporative cooling of the head of the bird is a finite reservoir of cold.
Sure you can run a heat engine on ice, snow, dry ice, liquid nitrogen, evaporating water etc. but it takes energy to make these things and a wet head on a bird dries out, ice melts, etc.

To continue to run the engine would have to use the ambient energy to MAINTAIN the "cold hole" initially created. Generally speaking, this is or always has been considered impossible, a violation of the second law of thermodynamics. Tesla explained how he believed it was possible by first creating a sink artificially, then as the heat flowed in it could be converted into other forms of energy so the "HEAT" would effectively "disappear" from the system

...some heat will generally reach the low level, which means to say, in our mechanical analogue, that some water will arrive at the bottom of the tank, and a gradual and slow filling of the latter will take place, necessitating continuous pumping out. But evidently there will be less to pump out than flows in, or, in other words, less energy will be needed to maintain the initial condition than is developed by the fall, and this is to say that some energy will be gained from the medium. What is not converted in flowing down can just be raised up with its own energy, and what is converted is clear gain.
Tesla repeatedly emphasized that point that the initial cold hole or sink had to be created and reasoned that since in the process of heat conversion some of the heat leaves the system in a different form it is possible to use some of the energy created to maintain the sink and still have a net gain.

Calling me obtuse does not refute Tesla's reasoning. If he was right then a very efficient heat engine "running on ice" should be able to power a freezer that would keep the ice from melting and so run on and on indefinitely so long as the ambient heat was available and the ice was otherwise well insulated against heat infiltration from the surroundings.

So I think the point that the initial sink has to be created in order to get the ball rolling in the first place is worth emphasizing.

17. Originally Posted by Tom Booth
... Tesla repeatedly emphasized ... it is possible to use some of the energy created to maintain the sink and still have a net gain. ...
No that is impossible:
This is the Carnot cycle.
As an ideal (frictionless) engine the cycle runs clockwise around the loop. It takes in all the heat at the same high temperature source, Th, (A to B part of cycle) and rejects all the waste at the same lower (colder) temperature, Tc, (C to D part of the cycle).

The efficiency, E, is (Th –Tc) / Th where all temperatures are on the absolute scale. Any engine that takes in part of the thermal energy at less than Th or rejects waste heat at a higher temperature than Tc will be less efficient.*

Thus when a Carnot engine takes in thermal energy H the work, W, produced is: W = ExH and the waste heat is H-W. (Simple conservation of energy law.)

Now this work W is exactly what is required (still assuming there is no lost to friction, etc.) to drive an identical Carnot cycle counter clockwise around the loop. I.e. make a Carnot refrigerator. However, there is always some friction, so an input of W to the Carnot refrigerator will pump LESS thermal energy out of the cold source than (H-W) even a perfect Carnot engine MUST put there. (A real Carnot engine, with friction, will of course make less W and more waste heat. So (H-W) added the cold sink is the LEAST heat flow into it possible, even in principle.)

Thus, two of the most efficient possible identical Carnot cycles, one running loop clockwise (the engine) producing W and other counter clockwise (the refrigerator) using W input energy will result in a net transfer of heat to the cold source. (Engine adds more heat to it than any real refrigerator can pump out and of course there is zero net work produced.)

Hence: “…a very efficient heat engine "running on ice" should be able to power a freezer that would keep the ice from melting and so run on and on indefinitely so long as the ambient heat was available …” is false. Or crudely put: There is no free lunch.
-----------
*Easy to prove – just imagine that the right side of curve A to B, before B is reached, drops down an adiabatic curve to temperature Th´ where Th > Th´> Tc, and then goes over to the original, but lower point on the adiabate B to C along a lower isothermal curve. I.e. full cycle is two Carnot cycles but the right one operates between Th´ and Tc so is less efficient.

18. Originally Posted by Tom Booth
To continue to run the engine would have to use the ambient energy to MAINTAIN the "cold hole" initially created.
So you need a refrigerator that moves at least as much heat out of the cold sink as the heat engine moves in and you need to run this off the energy generated from the heat engine. The same thermodynamics that accurately models the drinking bird says that this is impossible.

Say the resevoirs were arbitrarily large and at $T_{\tiny \textrm{Cold}}$ and $T_{\tiny \textrm{Hot}}$, and that each cycle of the the machine transferred $Q$ heat from hot to cold. Then a perfectly efficient extraction of work would be $W = \left( \frac{T_{\tiny \textrm{Hot}}}{T_{\tiny \textrm{Cold}}} -1 \right) Q$.

( For $Q_{\tiny \textrm{out}} \equiv Q, \; Q_{\tiny \textrm{in}} = W + Q$ we see that $\frac{W}{Q_{\tiny \textrm{in}}} = \frac{W}{W+Q} = \frac{ \left( \frac{T_{\tiny \textrm{Hot}}}{T_{\tiny \textrm{Cold}}} -1 \right) Q }{\left( \frac{T_{\tiny \textrm{Hot}}}{T_{\tiny \textrm{Cold}}} -1 \right) Q + Q} = \frac{ \left( \frac{T_{\tiny \textrm{Hot}} - T_{\tiny \textrm{Cold}}}{T_{\tiny \textrm{Cold}}} \right) }{\left( \frac{T_{\tiny \textrm{Hot}}}{T_{\tiny \textrm{Cold}}} \right)} = \frac{T_{\tiny \textrm{Hot}} - T_{\tiny \textrm{Cold}}}{T_{\tiny \textrm{Hot}}} = \eta_{\tiny \textrm{Carnot}}$ is the usual expression for maximum thermal efficiency. )

So if we had a refrigerator, then if you insert $W$ work, then a certain amount of heat, $Q'$ is pumped out of the cold reservoir and $Q' + W$ enters the hot reservoir. Assuming a perfect refrigerator, then we have the relation $Q' = \frac{ T_{\tiny \textrm{Cold}} }{T_{\tiny \textrm{Hot}} - T_{\tiny \textrm{Cold}}} W$ and from above's assumption of perfectly efficient heat engine we have $Q' = \frac{ T_{\tiny \textrm{Cold}} }{T_{\tiny \textrm{Hot}} - T_{\tiny \textrm{Cold}}} \times \frac{T_{\tiny \textrm{Hot}} - T_{\tiny \textrm{Cold}}}{ T_{\tiny \textrm{Cold}} } Q = Q$. But in this case, all of the energy is being used by the perfect refrigerator, so no work is being extracted. (Conservation of energy at work!)

Naturally, if some of the work is diverted or the refrigerator or heat engine are not maximally efficient, the net effect is a transfer of heat from hot to cold.

http://en.wikipedia.org/wiki/Heat_pump
http://en.wikipedia.org/wiki/Carnot_heat_engine
http://en.wikipedia.org/wiki/Carnot%...rmodynamics%29
http://en.wikipedia.org/wiki/Thermal_efficiency

19. Not *totally* related, but this entire business reminds me of a VERY old thread I read through a couple of years back.

Some bonehead (his name was something like "Metakron") was insisting there was no such thing as a heat pump! Despite the fact that hundreds of thousands of them are in use worldwide AND the fact that common household refrigerators and air conditioners both operate on the same principle.

Several people tried in vain to educated him. His argument was that such a device would violate the 2nd law of thermodynamics and that you could NOT "pump heat uphill." I nearly split my sides laughing!!!

20. Originally Posted by rpenner
So you need a refrigerator that moves at least as much heat out of the cold sink as the heat engine moves in
I appreciate the efforts at explaining the mathematics involved, unfortunately it is largely over my head. But taking the non-mathematical statement above: "So you need a refrigerator that moves at least as much heat out of the cold sink as the heat engine moves in" I think Tesla's point is - No you don't.

Let's say that 500 BTU's per minute go into the heat engine (arbitrary numbers).

Say that the engine is 35% efficient at converting that heat into electricity. That leaves 325 BTU's to be removed by the refrigeration system. Less to take out than went in right ? But if all the electricity created at 35% efficiency were used to run the refrigerator there would not be enough power to remove all the excess heat. Under ideal conditions I would think that the engine would have to be at least 50% efficient just to break even.

But if a heat engine could reach say 75% efficiency then there would be just 125 BTU's left over to be removed. You would have a theoretical net gain of 250 BTU's converted to electricity not needed for refrigeration. In other words, the more efficient the engine the less heat will reach the sink and the more power will be available to remove it. Of course with friction, losses due to conversion etc. this could probably never be realized in practice but this would seem to be Tesla's reasoning.

Theories and mathematical derivations aside, we have a toy bird that appears to be doing that very thing. Converting ambient heat into mechanical energy, some of which is used to run an evaporative cooler or simple refrigeration system with an infinitesimal bit of energy to spare. ("about 1⁄1,000,000 W can be extracted from the bird, either with a coil/magnet or a ratchet used to winch paperclips" - according to the Wiki article cited earlier).

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