I found an interesting idea for a PM machine suggested by Nikola Tesla, see if you can find a flaw in it...

- The efficiency n of a perfect heat engine, which converts heat flow from a temperature gradient to mechanical work, is
n = 1 - Tc/Th
where Tc is the temperature of the heat sink and Th is the temperature of the heat source.

- The efficiency of a perfect heat pump (like a fridge), which creates temperature gradients, is given by
n = Tc / (Th - Tc) .
Note: n can be greater than 100% for heat pumps, and is actually called a coefficient of performance (COP).

If 100J of heat energy flows from ambient temperature (300 Kelvin) to a heat sink at 50K (liquid hydrogen), the heat pump will transform 100X (1 - 50/300) J = 83.3J of heat energy from this flow into mechanical energy. This leave 16.7J to flow into the heat sink.

If 1 heat pump pumps the 16.7J out to maintain the heat sink at 50K, it will use 16.7/ (50 / (300 - 50))J = 83.3J of energy, exactly balancing out the energy gained by the heat engine.

If instead 5 heat pumps in series are used to pump the heat out, at a temperature gradient of 50K each, they will have an overall COP of 0.5 and will use 16.7/ 0.5 = 33.4J to keep the heat sink at 50K.

Therefore, using 5 heat pumps, the net energy gained is 83.3 - 33.4 = 49.9J

Therefore for every 100J sucked out of the surrounding ambient temperature, 49.9J is converted into mechanical energy. Heat engines/pumps can only be less than 100% efficient even in principle, but real machines could still be made efficient enough for this to work.

Note that the generator is not actually a perpetual motion machine, the heat source (the warm atmosphere) is ultimately provided by the sun.

Frigidaire oder  Kühlanlage heizt den Raum, Keller oder die Umgebung auf = Verlust) (oder kühlt bei Wärmepumpe ab - weil Wärme entzogen wird )Dass heisst:
Eine Wärmepumpe . kühlt die Aussenluft oder Erdreich ab (da wo der Energie-Austausch statt.

Diese Energie ist nicht FREI ( auch wenn man die ( noch ) nicht bezahlen muss. Sonnenlicht ist auch noch gratis, während Wind "entnehmen"  in einigen Staaten schon bezahlen muss !!. (Wie fasst überall die Wasserkraft)
(Das erhöht die Wirtschaftskraft einer Nation, wie auch deren Bürokratie. Dies sind wichtige Faktoren , die dem "sparen" auch Grenzen setzen !


Dieae " dumme " Rechnung. Wärmepumpe bringt xx% Gewinn , ist einfach nicht wahr.
Der Strom der gebraucht wird, dient nur zum Pumpen und ist reiner Verlust. den hiermit wird ja keine Wärme oder Kälte erzeugt !!
(Was auch möglich wäre, aber nicht getan wird !)
Die  Wärme  Kälte-Mengen wandeln (pumpen) um Energie (aus der Umgebung zu erhalten um diese  gratis und unbezahlt wegzunehmen , hat NICHTS mit der PUMPE zu tun, sondern nur mit dem Temperaturgefälle (Input/Output) und günstigen Werten der Verdampfungstemperatur die durch Druck beeinflusst wird). 
Das hier die Natur aus dem Gleichgewicht kommt - ist eine andere Sache.

Frei = unbezahlt die Umgebung nutzen
wäre möglich die Pumpe in eine Windmill zu setzen, so wie es
Lee Bell in seiner URL für  "compresses air"zeigte.
-------------------------
An Frigidaire is als heating the the ambient room !!
So this pump System is only cooling or heating the room, basement or the environment THIS are = losses). Also the Pump himself produce ONLY losses an is not usede to produce Energy in any way

That means:
A heat pump. Outdoor air cools the soil (earth) or from (as where the energy exchange.

This energy is NOT FREE (even if you do not (yet) pay. Sunlight is still free, while (also small)Windmills "shows" in some states already pay!. (Like everywhere summarizes the hydropower)
(This increases the economic strength of a nation, as well as bureaucracy. These are important factors associated with the "save" also set boundaries!


FREE Heat-Pump... :
This is a "stupid" bill, that an heat pump brings xx% profit, is simply not true.
The flow of needed, only serves to pump and is pure loss. This pump never produce an enrergy ! _ ONLY LOSSES" to tranfer stranger engies, by compressing and evaporating !
(What would (with pump only) be also possible, but not done!)
The cold-heat convert quantities (pump) to energy (from the environment to receive these away for free and unpaid, has nothing to do with the PUMP to do, but only with low temperatur-drift (Input v/s Output) and  so ,low values of the evaporation will be influenced by pressure).
BUT the natural-ambient temperature comes out of balance - anyway !!.

FREE  = unpaid the environment
would be possible to set the pump into a Windmill !
The way that Lee Bell done this  in his URL for his "compress air" showed.

G.P.
Google translation, was an little bit "modified" for understanding. I hope thid os OK.

http://www.instructables.com/id/The-Sterling-Engine-absorb-energy-from-candles-c/

Above is the link to the Instructables version of a Sterling Engine.  It has complete plans and photos.  I built mine out of a tuna can and a metal can lid.  Nice little project and with a little care, these can be very efficient.

Bill

FWIW, I remember reading 10 or so years ago about a 17 year old South African lad who had devised a refrigerator using Stirling engine to pump the freon through the its coils. It was touted in the international headlines as the answer to Africa's refrigeration problems in areas where there was no electricity.  The lad's first name was Christian, I believe; I've forgotten his last name.  All of a sudden, the story disappeared, and I have not been able to find it at all on the internet. My guess is that the design was quickly bought up by a energy interests and even more quickly shelved.  My point is that your idea may be worth further exploring, and the Stirling engine application may work well with it.  There's no reason why it shouldn't work.  I believe Groundloop has posted a design for a Stirling engine on a thread about 8 months ago. If I find it, I'll post the link.
Bob Smith

Why not.

See to the compressorless frigudaires.
that work only with an s,all heat-source.
loke 60 watt electric heater - like an small gaz-flame !
why not solarheat (in adrika shure the cheatest source ...
as transfer gaz, you can also use buta filled inside the tubings wit 2.2 bar !

Pese

This technik is not belived by industry, because to simly ...

I found an interesting idea for a PM machine suggested by Nikola Tesla, see if you can find a flaw in it...

Interesting idea as a mind exercise but unfortunately not feasible.
Something is wrong in math. It boils down to nasty sums (or integrals) but spreadsheet may be helpful. Check the quoted part again, please:

If instead 5 heat pumps in series are used to pump the heat out, at a temperature gradient of 50K each, they will have an overall COP of 0.5 and will use 16.7/ 0.5 = 33.4J to keep the heat sink at 50K.

I assume you missed to increment the heat to be removed starting with the second pump in series. The first one indeed pumps 16.66J but the second one pumps more (33.33J), the third pumps even more by again adding 16.66J  and so on.

Cheers,
Tinu

@jandell254,

Pump 1 is COP 1, hence in order to pump 16.66J from Tcold to Tintermediate1 (Tint) it uses another 16.66J. So, you have now 33.33J on Tint1 that has to be pumped to Tint2. Second pump is COP 2 and that’s why it will require again 16.66J to pump 33.33J from Tint1 to Tint2 (If it was COP 1 it would require 33.33J). But also the work consumed by pump #2 is transferred as heat to Tint2, so you’ll have to pump 33.33J plus 16.66J from Tint2 to Tint3.
And so on. It’s already said in my previous post and I don’t think I have time to detail it again.
Problem is math can not be beaten nor cheated…

Cheers,
Tinu