Re: Paper: Solid-State Thermal Rectifier
- From: "Sorcerer" <Headmaster@xxxxxxxxxxxxxxxxxx>
- Date: Sat, 18 Nov 2006 16:43:48 GMT
Top posted not to detract from your post, Davidson, since I agree
with the "temperature" of what you say.
Much as you love to snip for whatever vague purpose, I have more
consideration for the preservation of data.
What this leads us to is Maxwell's demon [daemon], where the demon is
now a "diode".
Maxwell's demon was concerned with pressure, the demon opening
a door that allowed a molecule into a chamber but closed the door
if a molecule was about to escape. The matter really comes down to
how fast the demon can close the door, for if a slow (cold) molecule
takes too long entering, a fast (hot) molecule can tunnel out while
the door remains open to allow passage for the slow. The demon
cannot close the door without guillotining the incoming molecule.
Hence I disagree with your statement
"This assymetry will *never* cause heat to frow [flow] from cold to hot."
I will insist: "Assymetry will *never* cause *temperature* to flow from
cold to hot", and disregard your abuse of the word "heat".
Call it nit-picking if you will, but appropriate nit-picking leads
to discovery and I approve of YOUR nit-picking "temperature".
Androcles
"tadchem" <tadchem@xxxxxxxxxxx> wrote in message
news:1163858280.626511.284360@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
|
| Robert Karl Stonjek wrote:
|
| > RKS:
| > If you placed such a thermal diode between two chambers that are in
thermal
| > equilibrium, will the temperature in one chamber rise and the other
fall??
|
| Since heat flow is driven by the temperature *difference*
| http://scienceworld.wolfram.com/physics/NewtonsLawofCooling.html
| where there is no emperature difference there is no heat flow.
|
| > The electrical equivalent might be thought of as a diode between two
| > capacitors that are charged to some voltage. Let the capacitors have no
| > leakage and the negative terminals connected together. Connect the
positive
| > terminals together via a diode.
| >
| > In this analogy we would expect the diode to have no effect.
|
| Correct.
|
| > But if the
| > *average* voltage of the capacitors is some value then the voltage will
rise
| > in one and fall in the other (if the capacitors are in a filter circuit,
for
| > instance, then there will be some fluctuation around an average value).
|
| Depending upon how the circuit with two capacitors and one diode are
| wired in to the flutuating voltage of the filter circuit, you will get
| asymmetric filtration. The diode is inherently an asymmetric resistor.
| That means that, assuming the capacitors are equal, the filtration of
| voltage fluctuations will encounter different RC time constants
| depending on the voltage bias across the diode. The net effect is that
| voltage excursions in one direction will be filtered more quickly than
| voltage excursions in the other direction.
|
| > In
| > the case of the two chambers in thermal equilibrium there will be
| > fluctuations such that temperature will be slightly high on one side of
the
| > thermal diode and slightly lower on the other side at some frequency and
| > some amplitude (the greater the differential amplitude the lower the
| > frequency of that occurrence and so on). Thus the thermal diode should
| > cause an accumulation of thermal energy on one side.
|
| The heat will always flow from the warmer chamber to the cooler one.
| The 'fluctuations' in temperature arising from stochastic processes
| will only become *significant* (i.e. measurable) of the chambers have a
| statistically *INsignificant* number of molecules inside.
|
| Temperature is an *average* quantity. The *average* will not display
| statistical fluctuations.
|
| > For thermodynamics not to be violated the subsequent lowering of
temperature
| > in the now higher temperature chamber must occur through the diode
before
| > further thermal energy passes through the diode into the higher
temperature
| > chamber (on average).
|
| Disregarding for the moment your abuse of the word 'temperature' by
| applying it to a system with a statistically insignificant number of
| particles, you will find that once the system has passed from the
| macroscopic realm to the microscopic realm in which stochastic
| fluctuations become significant you will find that the 'rectifying'
| properties of your device also become irrelevant as it is no longer
| able to have a statistically significant effect on a statistically
| insignificant number of particles. The transfer of energy through the
| barrier must be considered on a molecule-by-molecule basis as either
| occurring or not occuring with each individual impingement of a
| molecule upon the barrier.
|
| Think of it as the transition between the analog and digital realms. By
| failing to recognize which realm you are in, you have tried to apply
| the physics from one realm to the problems of another. This has led
| you to the absurd conclusion that you have discovered Maxwell's Demon.
| A rather novel and somewhat subtle example of a 'reductio ad absurdum'
| argument:
| http://en.wikipedia.org/wiki/Reductio_ad_absurdum
|
| If anything the absurdity of your conclusion is a disproof of your
| premise.
|
| > Thus in an open system, thermal energy flows across
| > the diode in one direction more than the other
|
| In a diode (of any kind) the asymmetry appears as a directional
| assymetry in the material constant, K in the case of cooling (see Eq.
| 2):
| http://scienceworld.wolfram.com/physics/NewtonsLawofCooling.html
|
| This assymetry will *never* cause heat to frow from cold to hot.
|
| > but in the two chamber closed
| > experiment the chambers remain at equilibrium (on average). A true
diode
| > would not allow heat energy to flow back.
|
| There are no *perfect* diodes in the real world. Examine the
| characteristic curve of a diode such as the ones here:
| http://www.physics.csbsju.edu/trace/CC.html
|
| Current (electron flow) is plotted against voltage (potential
| difference), which would be analogous to 'heat flow' and 'temperature
| difference' for your case. The slope (dI/dV) at any point in the range
| is proportional to the conductance - inversely proportional to the
| resistance R.
|
| When the applied voltage is positive, conductance is high (i.e.
| resistance is low) and ehen the applied voltage is negative,
| conductance is low (i.e. resistance is high). In *either* case, the
| current will flow in such a direction as required to reduce the applied
| voltage.
|
| If your thermal rectifier finds itself confronted with a temperature
| difference, the net flow of heat will *only* act to *reduce* that
| temperature difference.
|
| Try the math:
| If T is the average temperature of your system and you examine it at
| a time when there is a small difference dT between the two sides, the
| chance that a molecule on the cooler side will be able to transfer heat
| to the warmer side is proportional to T-dT, and the chance that a
| molecule on the cooler side will be NOT able to transfer heat to the
| warmer side is proportional to T+dT.
| Similarly while the chance that a molecule on the warmer side will be
| able to transfer heat to the cooler side is proportional to T+dT, and
| the chance that a molecule on the warmer side will be NOT able to
| transfer heat to the cooler side is proportional to T-dT.
|
| Tom Davidson
| Richmond, VA
|
.
- References:
- Re: Paper: Solid-State Thermal Rectifier
- From: Greg Neill
- Re: Paper: Solid-State Thermal Rectifier
- From: Robert Karl Stonjek
- Re: Paper: Solid-State Thermal Rectifier
- From: tadchem
- Re: Paper: Solid-State Thermal Rectifier
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