From: Robert J. Bradbury (bradbury@aeiveos.com)
Date: Thu Mar 16 2000 - 20:08:00 MST
EvMick, since you are such a cool guy, and I happen to have a
very tall stack of books on thermodynamics on my desk, floor,
in my bookcase, etc. (due to the research on Matrioshka Brains),
I'll take a stab at your question...
On Thu, 16 Mar 2000 EvMick@aol.com wrote:
> All power sources that I'm familar with go from hot to cold.
They must do this. The second law of thermodynamics requires it.
> By that I mean
> that the power source(gasoline, diesel, electric, charcoal, firewood,
> whatever) is concentrated. Using this concentrated heat source and some
> type of mechanism a tempetrure differential is produced with the ambient.
Yep, and the efficiency is commonly expressed as delta(change-in)-T/T,
or (T2 - T1)/T2. The reference on my desk is Nanomedicine, Section 6.3.1,
but it is in all thermodynamics texts. As Robert points out, going from
the human body (310K) to the periphery (307K) {(310-307)/310)} yields a
1% efficiency. Not very good. If you want more energy (from more efficient
conversion) for the nanobots, you are going to have to "burn" glucose at 600K.
That gives you ((600-310)/600) or around 48%. Better than *most* common
power sources (nuclear reactors, coal plants, engines, etc.) today.
I'll offer a point of trivia, that since the differential in temperature
should be greater when you are driving in Minnesota, than when you are
in Florida (lower outside temp), in theory you should get slightly better
gas mileage in those Northern climes. [Caveat, the efficiency may be
masked by many other factors that I'm unaware of.]
>
> My truck has a radiator, electric company generators have cooling towers,
> etc. etc. There must be a tempeture differential for power to be produced.
>
The limit for power conversions on Earth is how hot you can make
the power carrier (burning). If your engine were constructed out of
titanium carbide, it might have an operating temperature of around 2400K,
it would then sink the waste heat into the environment at 294K. That
would yield an efficiency of (2400-294)/2400 or 88%. The reason that
diesel engines are more efficient than gas engines is that they
burn slighly hotter, and therefore have better efficiency. But since
iron has an operating temperature only up to 1400-1500 degrees K
(before it starts getting soft), that makes your efficiency much lower
than if you had a ceramic (e.g. titanium carbide) engine.
I'm sure you could browse the web and find the difference in operating
temperatures between diesel and gas engines that determines the slight
differences in efficiency.
> How about if we go about it backwards?
>
> How much "Coldth" can be concentrated in a mobile source? Is a solid
> nitrogen brick possible?
>
Aha, yes, of course, solid N2 bricks have a temperature of ~60K. And
if you were delivering the heat of your engine to a solid N2 brick
you would of course have higher conversion efficiency (more MPG).
The problem is that creating something cooled *below* the ambient
heat sink temperature (~294K) is very expensive. At least one
figure I've read is that it costs you ~3x as much to create the
cold "sink" as you would get back from using it. So you would have
to burn 3x as much petrol to produce N2 bricks to fill your radiator
as you would get back by using that as the heat sink.
> Assume it is (or something like it).....could usable amounts of electricity
> be developed using "thermocouple technology"? Or merely by letting the
> nitrogen boil off and powering "steam" engines?
Sure, the principles are no different from those at higher temperatures.
The problem is that the laws of thermodynamics kill you in attempting
to create a sink that is cold. Now if you were running your truck around
on Neptune, you would most likely have liquid nitrogen circulating between
the engine and the radiator.
> In this instance the ambient temp. of the atmosphere would heat the nitrogen
> brick causing (hopefully) a useful pressure differential. The only exhaust
> would be nitrogen....chilly nitrogen...no nitrogen dioxides even...
Yep. You could get the energy for free by mining frozen LN2, focusing
the (weak) sun on it and letting it boil off powering your "steam" generator.
However, the efficiency would be much lower. LN2 boils at 77K. So
the efficiency of converting solid nitrogen blocks to nitrogen "steam"
is only (77-63)/77 or 18%. Not very good. The net result, you are
going to have to shovel a lot more N2 bricks into your boiler than
you pump diesel fuel into your tanks currently to go the same
distance. Do you care? Depends on the price you have to pay the
LN2 brick miners. You really want to run your truck inside the orbit
of Venus, using a radiator fluid that has the greatest differential
between the melting point of the solid and the boiling point of the
liquid. And, believe it or not, I have no idea what this substance
would be.... I suspect, since it is commonly used in proposed nuclear
reactors that liquid sodium is good (1156 BP, and 370K MP). So you
could get (~68%) in this system. Note that you can change the MP and BP
by applying pressure to the system, but that makes it much to complex
to discuss here.
Note that the purpose of the radiator fluid is to allow you to "burn"
your engine as hot as possible without allowing a melt-down. But
you tend to be constrained by the properties of the fluid. Since
cars and trucks use water, you are always running at temperatures
over the boiling point. You could run the engines somewhat hotter,
but it would require a more pressurized system (or a different coolant).
More pressurized systems are more expensive, think metal (hydraulic)
coolant pipes rather than rubber hoses. And if one bursts, oh boy....
It cheers my heart to hear you thinkin about this stuff. Clever
people, thinkin about everyday stuff and askin why? Thats what
what made science what it is today and gave us our present
technological ramp and will make things more interesting in
the future as the phase space for creativity expands.
Robert
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