>> Think how many things YOU could do with a 100
>> Watt external combustion / heat power generator which also had 500 
>> to
>> 1000 Watt of heat output as well.

> I have!  :-)  These days solar heat collectors are getting very 
> efficient - evacuated glass tube types are now coming down to a 
> reasonable price, and
> even in England it's reckoned that a 2m^2 "panel" will provide 
> enough heat to supply an average house's hot water requirements for 
> most of the
> year.  But there's a problem:  when you go away for a while and 
> don't use the hot water, what happens to the excess energy?

Good question. Old style alcathene pipe systems just melted their 
pipes :-).
Worst case you could boil water and recondense it. Boiling takes 
rather more energy than heating all the way from 0C to 100C and the 
steam can be recondensed more easily with air cooling than water 
cooling.

Evacuated glass tubes have got downright cheap here. Chinese heatpipe 
in glass about $NZ20 retail - about 70 Watt in full sun. On my "buy 
one and play with it" list. I want to see if you can air cool the hot 
end at higher than usual temperatures.

> The hot water storage tank can't be big enough to just absorb it 
> indefinately (certainly not over a fortnight's summer holiday) and 
> nobody wants to
> build a radiator just to emit the extra, and covering up the 
> collector is awkward mechanically , so it occurred to me that a 
> Stirling engine could use
> the excess heat to generate electricity, stored in batteries.  Which 
> made me wonder how you'd get rid of the heat from the cold end of 
> the engine -
> and how much would there be?  Thermodynamics' laws say that some of 
> the heat must be turned into kinetic energy, but how much do you 
> "lose", I
> wonder?  How do you calculate the heat output from the cold end?

All "heat" = energy in must flow out as work or from the cold end 
(assuming only hot and cold ends).
For Carnot cycle efficiency is (Thot-Tcold)/THot.
ie efficiency is delta-temperature/Absolute temperature in.
Makes sense.
A practicla Stirling may run at over 50% of Carnot efficiency but many 
run lower or much lower.

If Tcold = 300K = ~ 27C (which is too low for practical purposes but 
makes the arithmetic tidy for examples) then at 600 K = 327C hot end 
Zcarnot = 50%   [ (600-300)/600]
At Thot = 900k = 627C
Zcarnot = (900-300)/900 ~= 66%

2:1 as above is easily done.
3:1 as above is pushing material limits in practice.
Higher and much higher is doable but things die easily.

So for practical "home" use Use 600K Thot = 50% max max.
At 50% of that practical you get 25% efficiency so 75% flows out the 
cold end.
As an excellent rule of thumb starting point assume ALL the heat has 
to flow out the cold end.
Overcooling never hurt a Stirling engine :-)

> Thinking around this lead me to a paradox, at least in my own mind! 
> The useful energy from a Stirling engine is represented by the heat 
> "lost" that is
> converted to kinetic.  But to work you have to keep the cold end 
> cold, which means removing the heat energy that *isn't* turned into 
> kinetic, so a
> 100% efficient Stirling would absorb all the heat and nothing would 
> come out of the cold end - which is impossible!  Going on from that, 
> the most
> efficient Stirlings give off very little heat, so how does the cold 
> end stay cold?  (My brain hurts! :-)

100% efficincy can only occur when (Th-Tc)/Th = 1 so TC = 0 = absolute 
zero.
AZ is impossile to achieve but vv close is achievable.
If you has a Stirling engine in a deep space craft and cooled the cold 
end by radiating into dark space you'd have a 4.3K (AFAIR) sink which 
is ~~~= 0 .
And it;'s very hard to heat up deep space.

The most efficient Stirlings we are liable to see with sinks at 
ambient will seldom have efficiencies over 50% actual so at least half 
the input emergy will exit via the cooling system.

Which is why using any engine system as a power plus heat cogeneration 
system makes such good sense.

> Anyway, what I'm talking about is a sort-of Whispergen with altered 
> functional goals - instead of generating heat for hot water, and as 
> a byproduct
> generating a bit of electricity, I want to "use up" as much heat as 
> possible to generate electricity, to minimise the amount of heat 
> left to get rid of.
> This is starting to look like one of my Maths proofs at school, 
> ending up with  1 = 1  and I never got any marks for those, so 
> perhaps someone can
> explain where my thinking is going wrong...

Nothing wrong with logic - just with what can really be achieved.
Whispergen and any such systems try for as much energy out from SE as 
possible. Heat is ALWAYS a by product. If you ever got "too much" 
energy out it would be trivially easy to convert it to heat again. The 
reason why Whispergen makes about 800 Watt electrical and far more as 
heat is that's the best they can achieve in practice after having made 
suitable compromise3s for lingevity, material limits etc.

Anything over 20% efficiency actual is doing OK. Far more is better.
(Th-Tc)/Th is the limit, but nobody will ever reach that.



            Russell






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