well, you are right that the experiment is a test of analytical skills. unfortunately you fail again.
Well someone failed, unfortunately for you, since you believe yourself to be the smartest guy in the room you don't realize that it was you.
the conditions are that the bars are in a cooled thermos with a vacuum to represent outer space. the bars arent touching so there is no conduction, there is no air so there is no convection. that leaves only radiation. heat loss through radiation is proportional to difference in temperature between the radiator and the absorber.
It doesn't matter whether it was in a vaccum or not Ian. The second law and the law of conservation of energy are laws of nature, not laws of systems or laws of vacuums, or laws of anything else you care to name. They apply everywhere.
The electrical energy coming into the heated bar establishes the maximum temperature. It can not go higher than that because to do so would be to create energy. You were shown mathematically that it can not happen and instead of grasping what you saw, you reverted to your faith that cool objects can heat warmer objects.
Here is the proof that was shown to you Ian. What precisely do you find to be wrong with the math?
Re: Vacuum Chamber with plates.
First, identify the ONLY energy source in the Vacuum Chamber with an electric heater.
The ONLY energy source is the ELECTRIC HEATER that heats a plate with electricity to a temperature of 150 deg F or 338.56 K.
Asuume an emissivity = 1 and a surface Area for the plate = 1 m^2
Using the Stefan-Boltzmann Law, the Watts provided by the Electric Heater is:
P = e*BC*A*T^4
Where P = net radiated power (Watts), e = emissivity, BC = StefanÂ’s constant 5.67 X 10^-8, A = area and T = temperature of radiator in K
P = (5.67X10^-8) X 1m^2 X (338.56 K)^4 = 744.95 Watts
(***ThatÂ’s ALL the Energy Available and cannot be exceeded without CREATING ENERGY***)
The EM field produced by the plate is 744.95 Watts/ 1 m^2 = 744.95 w/m^2
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If another identical “non-heated” and colder plate is inserted into the Vacuum Chamber next to the heated Plate then:
The 2nd Plate also has an emissivity = 1 and a surface Area for the 2nd plate = 1 m^2
We can easily determine the equilibrium temperature of both plates by using the Stefan-Boltzmann Law and The Law of Conservation of Energy.
The TOTAL amount of energy available is 744.95 Watts and both plates will have the same temperature at equilibrium, so they can be considered to be a single radiating body with double the radiating surface area.
The area of both plates = 2 m^2 so the Radiation emitted by both plates at equilibrium = 744.95 Watts / 2 m^2 = 372.48 w/m^2
And the equilibrium temperature for both plates will be 284.69 K or 53 deg F.
————-
NOTE:
This is simple effect is demonstrated every day and is happening in your Computer right now.
It’s called a “Heat Sink” and is used to cool the microprocessor in your computer by increasing the radiating surface area of the microprocessor.
Here was the mathematical proof that in order for the heated bar to reach a temperature of 160, additional energy would have to be created.
PROOF:
160 deg F = 344.11 K and that means it would require:
P = (5.67X10^-8) X 1m^2 X (344.11 K)^4 = 795 Watts!
795 Watts exceeds the TOTAL Energy available which is 744.95 Watts.
An obvious violation of The Law of Conservation of Energy.
You were shown that in order to get the heated plate to 160 degrees, an additional 50.05 watts above and beyond what is available is required. Where do you believe that additional energy came from? The plate that had no power source? Well of course you believe that is where it came from because you also beleive that the atmosphere, which is not an energy source, provides energy to the surface of the earth.
the earth's surface and atmosphere are much more complicated, with conduction convection and water-based effects coming into play. so what?
Hell yeah it is more complicated but you are fooled by a very simple thought experiment in which it is claimed that by placing a non powered bar next to a powered bar you can somehow coax 6.7 more watts out of the system than is going in. If that is possible, why aren't we doing it on a large scale and making use of that excess energy? Someone should be making billions off of the process.
The question was 'can something cooler make a warm thing warmer'. the answer to that is yes, depending on the conditions
The answer is no Ian. You accept that it can happen on faith, not on the basis of any physical law and there is no condition that we can create in which the second law of thermodynamics or the law of conservation of energy is violated. Hell Ian, that experiment violates the 2nd law of thermodynamics even if you throw in the fictitious "net" energy flow allowing energy from cool objects to be absorbed by warm objects but the net result is that more energy is radiated to the cooler object because the net result of that experiment was that the heated bar actually got hotter.