Tim May graciously wrote:
The physics cited by Anonymous is hand-waving.
Absolutely. It's my weak understanding of a beginning physics book. Thank you for your reply.
If a block of a metal is hollowed out and a small port is drilled to see in, the radiance of the cavity is substantially higher than that of the surface of the metal. As if that weren't shocking enough, it turns out that the radiance of cavities is the same no matter what kind of metal is used. (This is so counterintuitive that I almost don't believe it!)
It is not correct to say the radiance is either higher or lower than some other material: the radiance approximates that of a perfect black body.
My book defines "radiance" in terms of the amount of energy radiated per surface area. (It likes to use W/cm^2.) The radiance of the surface of different materials at various temperatures can be compared. The radiance of a cavity to the surface material can be compared and it is higher. The radiance of two cavities is the same, but this is not immediately obvious to the uninitiated. It's a reasonable thing to measure and discuss.
Nothing mystical at all.
If you don't already know, it's actually surprising.
The "perpetual motion" part is a non sequitor.
There are many cases where a material of higher radiance, e.g. the surface of the earth, is "looking at" (in the sense of the drawing above) a material or thing of lower radiance, e.g., deep space.
And guess what: the earth radiates more energy toward deep space than deep space radiates toward the earth. This is one reason deserts get so cold so fast at night.
It's not surprising when a hot body and a cold body approach the same temperature. But, in the case described the two bodies start out at the same temperature. One radiates more energy towards the other one at that particular temperature. So, you would expect that one body would become hotter than the other. This effect (if it really occurred) could be exploited to make an engine which would return the two materials back to the same temperature, but also do some work in the meantime - a perpetual motion machine.
From the hints you've dropped I see the general outline of the solution. The photons going between the two blocks of metal will "thermalize" and the volume between the two blocks will look like the inside of a cavity. The rate of energy transfer in each direction will then be the same.
In fact, if the two blocks were contained in a large thermos which perfectly reflected the photons, the same effect would occur. It would be like an inside out cavity. Each block would end up at the same temperature. (Perhaps slightly lower than the start temperature because it must take some energy to fill the space with thermalized photons.)
On 17 Aug 2001, at 16:17, An Metet wrote:
But, in the case described the two bodies start out at the same temperature. One radiates more energy towards the other one at that particular temperature. So, you would expect that one body would become hotter than the other.
The important fact that you seem to be unaware of is that the body that radiates faster also absorbs more (reflects less). A black plate will radiate faster than a white one, but the white plate is reflecting almost all the light that hits. Cavity radiation and blackbody radiation are used synonymously. George
From the hints you've dropped I see the general outline of the solution. The photons going between the two blocks of metal will "thermalize" and the volume between the two blocks will look like the inside of a cavity. The rate of energy transfer in each direction will then be the same.
In fact, if the two blocks were contained in a large thermos which perfectly reflected the photons, the same effect would occur. It would be like an inside out cavity. Each block would end up at the same temperature. (Perhaps slightly lower than the start temperature because it must take some energy to fill the space with thermalized photons.)
On Friday, August 17, 2001, at 01:17 PM, An Metet wrote:
It's not surprising when a hot body and a cold body approach the same temperature.
But, in the case described the two bodies start out at the same temperature. One radiates more energy towards the other one at that particular temperature. So, you would expect that one body would become hotter than the other.
Radiative transfer goes as the fourth power of the temperature difference between two bodies. The hot object will radiate energy to the cooler object roughly as (delta T)^4. When the temperatures are equal, radiative transfer is equal in both directions. Think of "radiance" as being a bit analogous to thermal conductivity. Heat transfer still depends on a driving force (temperature difference). All heat transfer functions have something like this form: Heat Transfer is proportional to a (power per unit area) x (area) x (temperature)^(some exponent) This is of course the same form Ohm's law takes: current = voltage/resistance current = voltage x "conductance" Here, current plays the role of heat transfer. Voltage is the potential difference, or delta T. Conductance plays the role of emissivity, radiance, etc. This is just the very basic flux equation, seen in physics, geology, even economics. The "perpetual motion machine" envisaged would no more work for two metals of differing emissivities than such a machine woudl work by placing two metals of different conductances together.
From the hints you've dropped I see the general outline of the solution. The photons going between the two blocks of metal will "thermalize" and the volume between the two blocks will look like the inside of a cavity. The rate of energy transfer in each direction will then be the same.
In fact, if the two blocks were contained in a large thermos which perfectly reflected the photons, the same effect would occur. It would be like an inside out cavity. Each block would end up at the same temperature. (Perhaps slightly lower than the start temperature because it must take some energy to fill the space with thermalized photons.)
Yes, you've got it right. --Tim May
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Tim May