Brendan wrote:
Hi,
Owen wrote:
Brendan wrote:
"The temperature of the cosmic microwave background radiation gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvins), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperature."
I can't see what any of this has to do with what I wrote. What I wrote has nothing to do with temperatures at all. For a simple example, imagine a system of iron balls being pushed by electro-magnets made out of superconductors in a perfect vacuum (energy converted from electricity to momentum, and energy converted from momentum to electricity).
And if you do this experiment you fill find that, yes, there is no energy loss from the superconductors. However, you will also find that your magnets are heating up.
Owen wrote:
This talks about speed of computation. It has no relevance.
See section
Box: The role of thermodynamics in computation..
Brendan wrote:
Owen wrote:
(Or: You can't break even except at absolute zero, and you can't ever reach absolute zero)
Also assumes temperature is involved in some way.
Of course it does. Temperature increases entropy. Entropy increases errors. You need to expend energy to minimize entropy in order to reject errors.
Brendan wrote:
Owen wrote:
Brendan wrote:
You already stated that CPUs convert 100% of electrical energy into heat energy (I implicitly agree). Converting heat back into some other form of energy (e.g. electricity) is the only part where we disagree, which is what the Carnot engine does.
The Carnot engine converts a
difference in temperatures to energy, not heat.
Same end result.
No it isn't, because in the process your heat sink is warming up. (The entropy of your heat sink is increasing. While energy is conserved, the entropy of a closed system can only ever
increaseBrendan wrote:
Owen wrote:
Brendan wrote:
Given that it's possible to use heat pumps to shift the heat back (and that the inefficiency of the heat pump just creates more heat that can be reclaimed), the efficiency of both the heat engine and the heat pump are irrelevant. For example, you could have 3 objects (CPU, heat store and cold store) where heat pumps are used to ensure that the temperatures of the CPU and cold store remain constant (by pumping excess heat into the heat store).
Mostly, there are only 2 ways to show that this setup isn't possible. Either you prove that conservation of energy is false (e.g. energy is destroyed), or you prove that it's impossible to prevent energy from escaping out of an isolated system.
The energy required to pump heat against a temperature gradient ΔT is greater than the energy that a carnot engine can recover from temperature gradient ΔT. In other words, your heat pump would consume all the energy from your carnot engine in order to not maintain the temperature gradient.
The energy required to pump heat against temperature... is stolen by invisible magic ninjas riding unicorns when you're not looking? You're attempting to prove the law of conservation of energy is false. That energy doesn't vanish, so where do you think it goes?
Into the hot reservoir.
Brendan wrote:
Also note that I strongly suspect you've screwed that up by confusing "is greater than" with "is not less than".
Sorry, I will confess a mistake: The Carnot engine is a theoretical model which defines a maximally efficient reversible engine (In my defense, it's been a long time since I've had to deal with Carnot Engines). That is, yes, by injecting energy into a Carnot engine, you could indeed pump energy from cold to hot with the same efficiency as it would extract energy from the process. If you hooked up one of these to the other, you would produce a perpetual motion machine.
Of course, a Carnot engine is an
idealized engine. You cannot actually build a reversible engine, because it is impossible for a real material to undergo an isentropic change of temperature. What this means, in other words, is that the entropy of the system must increase in the process.
All heat engines and pumps you can produce have η different from that of a Carnot engine. Actually, for an engine, η must be less than that of a Carnot engine; meanwhile, for a heat pump, η must be higher (Heat pumps normally use a figure called the Coefficient of Performance, which when operating against the thermal gradient is 1/η). If you want, go and do the calculations for what happens when this isn't true; what you will find is that you have just violated the 2nd law of thermodynamics (i.e. conservation of energy)
Anyway, you can go and do the calculations for this, and what you will find for ηengine < ηpump is that your hot reservoir is getting colder, and your cold reservoir is getting hotter...
Of course, eventually, Tc == Th will occur, and (1 - Tc/Th) will equal zero, and therefore even if you did have a perfect engine you would be unable to extract energy because you no longer have a temperature gradient to extract it from.
Which is good. We Physicists don't like having random perpetual motion machines randomly running around in perpetuity.