Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Geezer on 15/02/2012 06:08:28
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FLAME ON:
A certain geezer by the name of Carnot made it perfectly clear (a very long time before a lot of other brilliant physicists) that the efficiency of any heat engine, be it nukeular, thermo-mumbo-jumbo or even quanto-solaristic, is determined by the DIFFERENCE in temperature between the "hot side" and the "cold side".
Why do so many people think they might be able to "get around" this limitation? To me, it's pretty much the same as saying that e=mc^2 is only a minor inconvenience.
FLAME OFF.
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About 5 and 6 years ago I surveyed my advanced undergraduate chemistry students, who had just audited a "Fuels and Energy" module in their Chemistry or Environmental Science subject.
The majority of them seemed to think that the second law of thermodynamics (in its Carnot cycle and similar manifestations) was a limitation to our present state of knowledge rather than an inevitable "law of nature". This may or may not be a reflection on the quality of my teaching!
A few pedantic points:
- the Carnot equation is an inequality -- it represents a maximum efficiency that can never quite be achieved in a practical heat engine, and usually the efficiency is quite a bit less.
- it is not universal, in that there are situations where there is no effective "temperature" because there is not a Boltzmann distribution (e.g. lasers). In these situations an equivalent and equally severe restriction applies, but it can not be so simply expressed.
- the actual maximum efficiency is given by (Thi-Tlo)/Thi which means that the best way to achieve a high efficiency is to relocate to the Antarctic or to a crater well near the lunar pole [;)]
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Quite right!
I should have said maximum efficiency. In practice, we would be fortunate to get anywhere near that limit.
The sad thing is that many people seem to assume that it's "just a matter of time" before we get there. The reality is that we will get there at about the same time as we can travel at the speed of light.
Basically, that's my point. No amount of technomumble can overcome the limitations imposed by thermodynamics, but that does not seen to be universally accepted.
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The problem is that...
Say one has a resistance electrical heater.
One puts in 1kWh, and I get out about 3,412 BTU's of heat.
However, working a little smarter, one can run that same 1kWh into a heat pump with a good low-grade heat source, and get back the equivalent of about 15,000 BTU's of heat.
The question is if we take the 3,412 BTU's of resistance heat, or the 15,000 BTU's of Heat pump heat, and tried to generate electricity with it, how much electricity would we get back?
And, I assume that is where the Carnot efficiency comes into play. In the first case of the resistance heater, we don't do very well. In the second case with the heat pump, assuming our heat source and cooling source is the same, we can come closer to recovering our energy investment.
So, the only way we can actually have a net electricity output is if we have independent heating and cooling sources. I.E. gaining energy from solar heating, geothermal energy input, or perhaps chemical energy input.
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The problem is that...
Say one has a resistance electrical heater.
One puts in 1kWh, and I get out about 3,412 BTU's of heat.
That's your problem, right there. What you get out is 1kWh of energy (aka heat). You can measure it it in kWh, BTU, or megaJules, but it is still energy.
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It seems there is a similar mind block when thinking about The Uncertainty Principle - too many people, even science journo.s appear to think that this is a solely measuring problem that could/will be solved by greater technology, clever experiments, powerful statistical methods (ie that there is a clearly defined and exact position, momentum, time, energy etc and we are just too stupid to find it).
I feel your pain
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"The question is if we take the 3,412 BTU's of resistance heat, or the 15,000 BTU's of Heat pump heat, and tried to generate electricity with it, how much electricity would we get back?"
It would depend upon how good a cold sink you had available , if you were on the ISS with a large radiator pointing to the darkness of space I presume from your 15000 btu,s (what ever they may be) you could get more than 1Kw output.
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The problem is that...
Say one has a resistance electrical heater.
One puts in 1kWh, and I get out about 3,412 BTU's of heat.
However, working a little smarter, one can run that same 1kWh into a heat pump with a good low-grade heat source, and get back the equivalent of about 15,000 BTU's of heat.
The question is if we take the 3,412 BTU's of resistance heat, or the 15,000 BTU's of Heat pump heat, and tried to generate electricity with it, how much electricity would we get back?
And, I assume that is where the Carnot efficiency comes into play. In the first case of the resistance heater, we don't do very well. In the second case with the heat pump, assuming our heat source and cooling source is the same, we can come closer to recovering our energy investment.
So, the only way we can actually have a net electricity output is if we have independent heating and cooling sources. I.E. gaining energy from solar heating, geothermal energy input, or perhaps chemical energy input.
Clifford,
What Carnot basically says is that the thermal efficiency of any heat engine cannot exceed 1 minus the ratio of the low/high absolute temperatures.
For example, suppose we have a heat source at 50C and an ambient heat sink at 25C, the ratio turns out to be a pretty big number (298/323 = 0.92). So, a perfect heat engine would only be able to produce 80 watts of power by processing 1000 watts of heat.
Even more depressing, just because the temperature difference is large, it might not help the efficiency. If the high temp is 1500K and the low 1000K, that's a pretty big gradient, but the Carnot efficiency is still only 33% because 1000/1500 is still a large part of 1. That's why running a heat engine "hotter" won't necessarily make it do any more work from the energy supplied.
Things get a lot better as the cold side gets closer to absolute zero, but our ambient (even at the poles) is far above zero.
Sadly, what all this means is that to extract work from "warm" sources, the mechanism has to process huge amounts of the warm stuff and process it with hardly any losses, otherwise no work will be extracted at all!
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"The question is if we take the 3,412 BTU's of resistance heat, or the 15,000 BTU's of Heat pump heat, and tried to generate electricity with it, how much electricity would we get back?"
It would depend upon how good a cold sink you had available , if you were on the ISS with a large radiator pointing to the darkness of space I presume from your 15000 btu,s (what ever they may be) you could get more than 1Kw output.
cough dimensions! cough.
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Apologies for dimensions muddle I don't realy know what BTU,s are of course if energy is being produced at so many BTU,s per second or minute or what have you then we could talk about KW,s or maybe horse power or CV or PF.
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Probably best to stick with megajoules (MJ). I don't know about you, but expressing energy in terms of power in time (as in kWH) always confuses the heck out of me.
Power is derived from energy. Energy is not derived from power, although the the electric companies might want you to think that it is to make it harder to understand what you are actually getting for your money.
Petrol/gasoline should really be priced in megajoules too.
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Well, I believe there is nothing wrong with thermodynamics and its basic principles.
All these comments on Carnot cycle efficiency and delta T as measure of conversion efficiency are, in a way, secondary arguments. The primary one is the second law of thermodynamics stating that whatever amount of internal energy is used to produce desired work, part of it inevitably is converted into entropy. The faster the conversion the higher the entropy waste. So, the entropy waste is inevitable. Unless the targeted activity is to warm the Universe and bring it to its thermal death.
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As far as what we are purchasing from the energy sources- it is amount of work we can produce, and the amount of energy one can spend to produce the desired work... In this sense it is not that important what units are agreed to be used in day-to-day practice (J, KJ, MJ, Wsec, or kW h, or GW sec, or any other abbreviation. All this is matter of agreement and convenience. Everybody likes to deal with numbers containing just few digits (certainly except the basic constants) within the set of circumstances he is running his activities. Say, a physicist cosmologist, while interpreting the Black Hole mass/energy absorption will use BW sec, in the same time discussing the sub-atomic transformation will use, I guess, pW/event, but will use KWh while estimating how much his electric bill is going to be
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No one has commented on my idea to increase the power available on the ISS with the aid of a Stirling engine and a large space cooled heat sink, I expected heavy criticism to fall on me
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Well, I believe there is nothing wrong with thermodynamics and its basic principles.
All these comments on Carnot cycle efficiency and delta T as measure of conversion efficiency are, in a way, secondary arguments. The primary one is the second law of thermodynamics stating that whatever amount of internal energy is used to produce desired work, part of it inevitably is converted into entropy. The faster the conversion the higher the entropy waste. So, the entropy waste is inevitable. Unless the targeted activity is to warm the Universe and bring it to its thermal death.
YG,
You obviously understand what is going on, so you are not in the least surprised by the Carnot limits. However, a large number of people, some of whom are well versed in many scientific fields, do not seem to be aware of the Carnot limits. If they were, they might have a better appreciation of how difficult it can be to convert heat into work.
That was the point of this topic. I was encouraging people to appreciate that there are fundamental limits associated with thermodynamics that are not dissimilar from another fundamental limit that is very well accepted; the speed of light.
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As far as what we are purchasing from the energy sources- it is amount of work we can produce, and the amount of energy one can spend to produce the desired work... In this sense it is not that important what units are agreed to be used in day-to-day practice (J, KJ, MJ, Wsec, or kW h, or GW sec, or any other abbreviation. All this is matter of agreement and convenience. Everybody likes to deal with numbers containing just few digits (certainly except the basic constants) within the set of circumstances he is running his activities. Say, a physicist cosmologist, while interpreting the Black Hole mass/energy absorption will use BW sec, in the same time discussing the sub-atomic transformation will use, I guess, pW/event, but will use KWh while estimating how much his electric bill is going to be
It's not the amount of work we can produce.
What we are buying is energy. How we choose to use that energy is up to us. If we could easily compare the prices we are paying for different forms of energy, we might be sufficiently shocked to consider alternative sources, or alternative methods of utilizing that energy.
Most people have not the faintest clue how to compare what they are getting from various suppliers, and the suppliers really like it that way because it preserves their revenue. The SI unit of energy is the joule. Other than the usual inertia and protection of self-interests, there is absolutely nothing to prevent all energy from being priced in joules (probably MJ).
For example, how many people would continue buying premium gasoline if they realized they would get more energy by buying regular gasoline?
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No one has commented on my idea to increase the power available on the ISS with the aid of a Stirling engine and a large space cooled heat sink, I expected heavy criticism to fall on me
OK - so you want a beating? I'll give you a beating. The BTU is the BRITISH THERMAL UNIT! (Not to be confused with the brutish thermal unit, which is a different thing entirely.)
Actually, I think you are right on the money. Space is a great place for heat engines because the cold side can be incredibly cold, and because of that, the Carnot efficiency can be high. After that, it's only a matter minimizing any parasitic and entropic losses!
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There is a major and fundamental problem with the concept of buying energy. It relates to the first law of thermodynamics. When we "use" energy, we do not consume it: it is all still there! Where? Well it might be spread around a bit, but perhaps we could collect it all up, and use it over and over without having to pay for any more?
That is where the second law comes in. It is stated in many ways, most of them pretty obscure and impossible to understand. What it is really saying is that energy comes in forms of different quality, and that in anything we do, we are turning, useful, high quality energy into useless, low quality energy.
The ultimately low quality energy is low grade heat. It is easy to add 1 litre of water at 100°C to 79 litre of water at 20°C to make 80 litre of water at 21°C. It is impossible to take 80 litre of water at 21°C and make 1 litre of water at 100°C for coffee all round (along with 79 litre at 20°C) without using energy, high quality energy, from elsewhere!
So our aim in energy conservation should always be to march down that usefulness hierarchy as gradually as possible, making good use of energy all the way down. Using LED or compact fluorescence lighting rather than incandescent is a good step for example -- more light output, and less heat for a given amount of energy.
It might also be a good move to use the hot water that is a low quality energy offshoot of nearly any heavy industry for neighbourhood domestic heating but that would depend on the energy cost of setting up and maintaining the necessary infrastructure, which would need to be calculated on a "dust to dust" basis.
Capital energy cost of compact fluorescent or LED manufacture and safe disposal must similarly be factored into consideration of replacing incandescent lamps.
What about premium gasoline? Well, you are not just buying the energy content of the gasoline, because the energy quality of the gasoline is an important factor. And that is not just a property of a particular blend of gasoline, but also of how it matches the design of the particular engine it is to be consumed in, on an effective efficiency basis. Any vehicle engine has manufacturing design specifications: if your car engine is designed to run on standard petrol, you are wasting your money and energy resources to fill up with premium. But if it is designed to run on premium blend, you will get much better performance if you do not switch to standard, because although the fuel energy content may be lower, the efficiency factor will be significantly higher.
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Actually, I think you are right on the money. Space is a great place for heat engines because the cold side can be incredibly cold, and because of that, the Carnot efficiency can be high. After that, it's only a matter minimizing any parasitic and entropic losses!
I am not nearly so sure about that! Actually, you do not just need a low temperature, you also need a large heat sink or "thermal bath" to dump the waste low grade energy that you will produce. And space is incredibly empty!
Also space, at least in the inner solar system as far out as the orbit of Jupiter, is really very hot! The prevailing temperature is thousands of degrees. Basically, the molecules and ions that are there, many of them from the "solar wind", will not hit you very often, but they will hit you very hard when they do -- high temperature, low heat content.
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The ultimately low quality energy is low grade heat. It is easy to add 1 litre of water at 100°C to 79 litre of water at 20°C to make 80 litre of water at 21°C. It is impossible to take 80 litre of water at 21°C and make 1 litre of water at 100°C for coffee all round (along with 79 litre at 20°C) without using energy, high quality energy, from elsewhere!
Which is the purpose of the Heat Pump, but yes, it does require some additional energy.
Sorry to those purists when I suggested using BRITISH UNITS on a BRITISH WEBSITE to indicate the conversion from electrical energy to thermal energy.
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Also space, at least in the inner solar system as far out as the orbit of Jupiter, is really very hot! The prevailing temperature is thousands of degrees. Basically, the molecules and ions that are there, many of them from the "solar wind", will not hit you very often, but they will hit you very hard when they do -- high temperature, low heat content.
It is really hot in the sunshine, but really cold in the shade.
The polar craters on the moon, in mid-winter have been measured at a balmy 25K, (http://www.diviner.ucla.edu/blog/?p=232) at least on the surface, which would be excellent for a cold sink. I think there was a discussion earlier about heat sinks to radiate heat which could be a problem on a free floating object in space though.
Looking for references I bumped into this. Could we generate electricity directly from the polar craters? (http://www.nasa.gov/topics/moonmars/features/electric-craters.html)
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Is this a British web site ?, are we to exclude non Brits from publishing ?, perhaps we true Brits could use blue text while lesser types could be made to use red.
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Sorry to those purists when I suggested using BRITISH UNITS on a BRITISH WEBSITE to indicate the conversion from electrical energy to thermal energy.
Clifford, you may or may not be aware that BRITISH UNITS like BTUs along with calories, imperial measures, avoirdupois weights have long been abandoned by scientists in every country of the world except the US, as well as by engineers in the old British Empire (but not sure about Britain itself). The United States of America is the last stand out bastion of British weights and measures (and manages to have the odd space program disaster as a consequence of unit mismanagement). There is a certain irony in that!
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Sorry to those purists when I suggested using BRITISH UNITS on a BRITISH WEBSITE to indicate the conversion from electrical energy to thermal energy.
further to Damocles' point - you are not even allowed to sell fruit and veg here in the UK without metric masses displayed. Everyone from a few years older than me learnt only the metric system at school. I know there are 12 inches in a foot, 3 feet in a yard, but would struggle to remember how many yards in a mile. The only imperial measurement that I can think of that is still in common and official use is the mile - the foot is still common but not I think officially used by the powers that be
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but would struggle to remember how many yards in a mile.
It is easy enough.
440 yards to the quarter mile (which used to be the track standard until someone changed it to a metric equivalent to the mile, 1600 meters), out of which you can derive the rest.
The only imperial measurement that I can think of that is still in common and official use is the mile
Don't you still use the gallon over there.
Which the British conveniently changed AFTER the US Adopted the British Queen Anne Gallon.
Do you use Calories for nutrition?
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but would struggle to remember how many yards in a mile.
It is easy enough.
440 yards to the quarter mile (which used to be the track standard until someone changed it to a metric equivalent to the mile, 1600 meters), out of which you can derive the rest.
The only imperial measurement that I can think of that is still in common and official use is the mile
Don't you still use the gallon over there.
Which the British conveniently changed AFTER the US Adopted the British Queen Anne Gallon.
Do you use Calories for nutrition?
Here in Oz we use only litre for buying petrol or drinks, and we have also long abandoned the mile -- all distances are in km and speeds in km/h (not m/s but you cant have everything!). Everyone has long forgotten their weight except in kilogram, but most (older) people still think of their height in feet and inches, although timber, cloth, rope, etc is bought in metres or centimetres with gauge, widths etc in cm or mm. All property measurements are in hectare or sq km, though older people still think in acres. Pints, gallons of either variety are long forgotten, although a 200 litre drum (what might be called a barrel in the US?) is still called a 44 gallon drum. And food and dieting always work in kilojoule, or "killer-joule" as they are sometimes known.
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Don't you still use the gallon over there.
Which the British conveniently changed AFTER the US Adopted the British Queen Anne Gallon.
Do you use Calories for nutrition?
Confusingly, the gallon (Imperial) is only quoted w.r.t. fuel economy, but petrol and Diesel are sold in litres on the forecourt! I learnt quite young that a gallon is about 4.5 litres, so is one of the few everyday tests of mental arithmetic :)
Oh, and beer barrels (firkins and kils) are also still derived from the gallon and obviously the pint still survives... for now [::)]
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How about the planet Mercury as the ideal heat engine 'platform'?
Am I right in thinking it has a permanently dark side? The cold dead rocky surface would act like the ideal cold reservoir 'sink' as well (following on from Damocles' point about a lack of thermal mass in space).
How one would transfer the 'work' back to our little blue sphere is an exercise I leave for the reader .... [:D]
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What about the Pound Sterling? Which can't buy a Pound of Sterling anymore?
Isn't Britain the only country in the EU that chose to keep the Pound Sterling rather than adopt the Euro. I wonder how long that will last?
What units are gold and silver measured in?
We commonly use 55 gallon drums, which is about 200L, but apparently it is bigger than a barrel of crude oil.
What about measurements for alcohol?
Pints? Ounces?
Here in the USA, there is a fifth, which apparently was initially 1/5 of a gallon, but converted to 750ml.
Of course, I wouldn't be surprised if the British call something a pint that isn't really a pint, just like the fifth is no longer based on a gallon.
(oh, I see Peppercorn got that squeezed in).
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How about the planet Mercury as the ideal heat engine 'platform'?
Am I right in thinking it has a permanently dark side? The cold dead rocky surface would act like the ideal cold reservoir 'sink' as well (following on from Damocles' point about a lack of thermal mass in space).
How one would transfer the 'work' back to our little blue sphere is an exercise I leave for the reader .... [:D]
Unfortunately Mercury does not have a permanently "dark" side. It is locked into a resonance, with a long day of about 58 days that is just 2/3 of its year of about 88 days.
The floor of a polar moon crater where a permanent shadow might fall is probably the best place to set up. It is also conveniently(?) (well, marginally less inconveniently!) local. The energy costs of the infrastructure to set up there could possibly be recovered in a millennium or two.
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If we ever get around (and don't destroy our home or ourselves first) to building the fabled space elevators there's potential for a pretty serious thermal gradient there! And there's no need to come up with a fancy way to transport the power either.
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One of the most annoying measures with have to put up with is the emasculated half Kilo, many things that are normally sold in 1/2 1/4 kilo packs in England come as 454 or 227 grams, in many stores for products that you normally buy by the Kilo the price is diplayed in large letters as so much the pound.
We are supposed to have gone metric by 1960 but we still have miles, pints, horse power pounds, stones and ounces, when I look for England on the map it seems we should be about where the Azores are.
Clifford there are quite a few countries in the EU that don't use the Euro off the top of my head they are Sweden, Denmark, Hungary, switzerland, Iceland, Czech Republic and maybe some of the ex soviet block countries.
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What about the Pound Sterling? Which can't buy a Pound of Sterling anymore?
Isn't Britain the only country in the EU that chose to keep the Pound Sterling rather than adopt the Euro. I wonder how long that will last?
The UK (which includes England, Wales, Scotland and Northern Ireland) did not buy into the Euro and it was not the only country that didn't drink the Coolaid opted out rats!I cant turn off strikethrough.
Based on recent events, I have a suspicion that the GBP might be around a lot longer than the Euro :)
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The gallon is waning in popularity (petrol is sold in litres - and that was about the only thing you bought in gallons apart from beer for a party). But I think the calorie or kilocalorie is still popular - although I think foodstuffs have the energy content in both calories and joules.
The pint is of course still used on a regular basis - as regular as possible in fact. Although the barmaid managed to charge me over 14 quid for three pints at lunchtime so maybe it is time we moved to the slightly smaller demi
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Although the barmaid managed to charge me over 14 quid for three pints at lunchtime so maybe it is time we moved to the slightly smaller demi
Fourteen quid!! It might be time you moved to another country (either that, or open a pub.)
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Dear me! You weren't buying pints of Scotch again were you imatfaal?! [::)]
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Fourteen quid!! It might be time you moved to another country (either that, or open a pub.)
Or not be a pillock and stop going to pubs in Mayfair - but watching the world (well half of it) walking past in their finery is almost worth it. Don might like to add one his bespoke little yellow men as a shameless ogler here.
Dear me! You weren't buying pints of Scotch again were you imatfaal?! [::)]
That's the ticket; pint of Scotch with lager shots as a chaser. Nope; I was with oiks who liked weird european lagers (who drinks a pint of peroni? apart from the ad man's perfect target) - without my pint of young's ordinary it would probably have been worse. Although if you are in the area I would still recommend it - their shepherd's pie won best in the country about 5 years on the trot, and the young's is too good
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That's all very well, but you could probably buy an an entire island in the Aegean for fourteen quid at the moment.
We trust that HM Inland Rev. would agree this was a "business lunch".
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That's all very well, but you could probably buy an an entire island in the Aegean for fourteen quid at the moment.
We trust that HM Inland Rev. would agree this was a "business lunch".
It was indeed a business lunch and I will be avoiding the cost entirely. If you want an island with running water you might need to think over 20 quid - it's worth the extra investment
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Actually, you do not just need a low temperature, you also need a large heat sink or "thermal bath" to dump the waste low grade energy that you will produce. And space is incredibly empty!
Also space, at least in the inner solar system as far out as the orbit of Jupiter, is really very hot! The prevailing temperature is thousands of degrees. Basically, the molecules and ions that are there, many of them from the "solar wind", will not hit you very often, but they will hit you very hard when they do -- high temperature, low heat content.
Could you explain how you mean there in more detail Damocles? I've been wondering about that one. The sun is said to carry 'heat' to earth by EM radiation, but for a smaller heat source (thermos bottle) it seems as if the vacuum isolates? Why does that differ. Is it that radiation is a generally poor transmitter of 'heat/IR', or is there some another explanation to it, like different combinations of frequency's?
I'm not thinking of it as being just one part of the Radiation, Convection, Conduction cycles here, just asking about radiation.
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In your "Thermos" the transmission of heat by radiation is inhibited by reflective silvered surfaces, the heat would soon leak in or out without these.
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From Yor-on
Could you explain how you mean there in more detail Damocles? I've been wondering about that one. The sun is said to carry 'heat' to earth by EM radiation, but for a smaller heat source (thermos bottle) it seems as if the vacuum isolates? Why does that differ. Is it that radiation is a generally poor transmitter of 'heat/IR', or is there some another explanation to it, like different combinations of frequency's?
As a chemist, I am familiar with situations where "heat transfer" means loss of kinetic energy through the statistics of collisional transfer to vessel walls or surrounding medium. Radiative transfer is a relatively slow and inefficient process and only a tiny perturbation to conductive/convective processes. It can safely be neglected. I am used to neglecting radiation.
In the emptiness of space, there is no almost no opportunity for conductive/convective heat loss, and even if there were, the very thin interplanetary medium is probably at a temperature where heat gain rather than heat loss would follow. That was my point. I might have been wrong in failing to consider radiative heat loss, but I think not.
Radiative loss at a low temperature would involve infrared radiation at around 20 nm wavelength, is a process where spontaneous emission would have a characteristic time of the order of seconds. Spontaneous emission is a process with a characteristic rate that goes as the fourth power of the frequency, other things being equal: double the wavelength means one sixteenth of the emission rate. And radiators with lower temperature emit their radiation at longer wavelength. I would be surprised if any practical heat engine could operate at the low speeds that would be needed if it relied on radiative emission at 20 nm for cooling.
A cold planetary surface that has been continuously shielded from sunlight (solar radiation) for at least several days, and had the opportunity to achieve a really low temperature through its own emissions over that time, would have sufficient thermal mass to allow the possibility of rapid conductive/convective heat transfer -- hence the lunar polar crater floor suggestions.
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In the emptiness of space, there is no almost no opportunity for conductive/convective heat loss, and even if there were, the very thin interplanetary medium is probably at a temperature where heat gain rather than heat loss would follow. That was my point. I might have been wrong in failing to consider radiative heat loss, but I think not.
Maybe you better let these guys know :)
http://en.wikipedia.org/wiki/Advanced_Stirling_Radioisotope_Generator
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In the emptiness of space, there is no almost no opportunity for conductive/convective heat loss, and even if there were, the very thin interplanetary medium is probably at a temperature where heat gain rather than heat loss would follow. That was my point. I might have been wrong in failing to consider radiative heat loss, but I think not.
Maybe you better let these guys know :)
http://en.wikipedia.org/wiki/Advanced_Stirling_Radioisotope_Generator
Wolfekeeper brought up the Stefan Boltzmann Law (http://en.wikipedia.org/wiki/Stefan-Boltzmann_law) here.
http://www.thenakedscientists.com/forum/index.php?topic=42960.msg379543#msg379543
Which will determine the watts per square meter that can be radiated by temperature and energy.
It is not clear how much energy is reabsorbed on a convoluted surface in space, but perhaps if mirrored, the reabsorption would be minimized. One might also design the surface of the entire space probe to be highly heat conductive, and thus use all the surface area of the entire probe as the radiator (and also warm the equipment in the probe slightly).
Anyway, we know that RTGs have been used in space probes for quite a while.
One concern that I have with the sterling engine is that it is rated for "≥14 year lifetime". I guess I'd be a bit worried about moving parts off somewhere where there is little chance of maintenance.
The Pioneer Probes have run out of power (more energy conversion efficiency might have helped, but it also depends on the design tolerances).
The Voyager Probes are now at 34 years and counting, with hopes to keep them operational for another decade or so (perhaps a half century total). Is the Sterling Engine capable of a half century of continuous operation without maintenance?
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btw, it's not Sterling as in money, is Stirling as in this place http://www.nationalwallacemonument.com/ (http://www.nationalwallacemonument.com/)
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I used to work near Smithfield market and always gave a slight shudder when I passed the plaque where Wallace met his awful fate.
(excuse irrelevent post)
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Thanks Damocles. A nice answer. So what is the 'output' of the sun relative the heat/IR we receive on Earth? I guess it might be difficult to answer that one but it would be interesting to know the relation between those two. If we talk about photons the only way they 'annihilate' is through interactions, if we talk about waves we have quenching and reinforcing. And the waves from the sun are polychromatic, of a lot of different wavelengths. So how do the transfer of heat works, and if some get lost, to what does it lose?
I know, maybe for another thread this one, but I like when threads grow :)