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You would expect it to radiate roughly a black body spectrum, but with lower intensity due to the thinness. You would also be able to see through it to things beyond. So if you had a container like that in front of you, you would see the background with a slight overlay of black body spectrum.

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Terrific question. You had it right in your first sentence: “the same amount of energy must have been released during the Earth's history,” but then it gets a little mixed up when you look at various energies, some of which aren’t related to the question at hand (for example, the current internal energy contributes positive mass-energy to the Earth, rather ...

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The rest of the energy went into space. Without that energy loss the planet would not even have condensed and the gas/dust cloud would have stayed a cloud. Having said that, the details of these condensation processes in planetary clouds seem to be non-trivial and, from what I have read, are not fully understood, as of yet.

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Other small effects that you may be ignoring are heat conduction to the air and temperature drop along the pipe. If the fluid is a gas, its temperature may drop by some small amount due to pressure drop along the pipe. The fluid temperature will also drop due to the heat transfer that you calculate. An old reference for these effects is Chapter 8 of ...

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theoretically yes. If the white garment on the outside is opaque enough, it will block more of the sun's light from reaching the inner black garment. The black garment will actually help you keep cooler if you have both garments made properly. This is because black does not actually absorb heat, it traps it therefore not allowing the "cooler" air to heat it ...

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I'm just learning this myself, but for the the first one, the thermal state I think just means that if you throw any field in the resulting space-time, it will immediately acquire the specified temperature. In Hawking's original calculation, he shows that this radiation will be dominated by the massless, lowest-spin particles available, which in our universe ...

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As an example, the International Space Station (ISS) has external thermal radiators. They looks similar to solar panels, but instead of pointing the flat side towards the sun, they point towards empty space. An ammonia loop carries heat from various parts of the space station to the radiators. This is a picture of a radiator: (source) External Active ...

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The satellite itself can do with radiative cooling but some instruments on board, e.g., IR sensors, require temperatures as low as than 4 K for which Helium dewars are used. Bolometers require even lower temperatures (in the mK range). A good summary is available here.

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Typically, satellites use radiative cooling to maintain thermal equilibrium at a desired temperature. How they do this depends greatly on the specifics of the satellite's orbit around Earth. For instance, sun-synchronous satellites typically always have one side in sunlight and one side in darkness. These are particularly easy to keep cool because you can ...

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The microwave answer given above is good, especially if you have only one paper wrapped in foil because it would transfer a large fraction of the energy produced to the sample. If you have many of these (for example as a step on an assembly line) then immerse it in a hot medium. This would provide really efficient transfer of heat energy for each sample ...

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Heat a batch of high temperature silicone to 250°C, then drop in your foil wrapped paper.

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Put it in a microwave at the right power, and it will quickly heat up withouth burning (and heat whatever is inside). But do not try this at home. Too much power and you will get the microwave oven on flames.

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Not sure how hot you want it, but a hairdryer or heat gun would be quick, but not very energy efficient while it was blowing - but it turns on and off quickly so might be efficient by not having to be on for long. edit - ok for 250 degrees C - heat gun probably not hot enough. I would put an oven on at close to max temp and put the foil in, but even then ...

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Suppose we have a drum. When you bang on the drum it will vibrate. When you look at any point on the surface of the drum head, you will see it go up and down, similar to if to take a mass hanging from a spring attached to the ceiling and watch it bob up and down. However, there is also an important difference between these two situations. In the situation ...

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Spectrum of waves in 1D is described with one numerical parameter. It may be either frequency, or wavelength (propagation speed divided by frequency *), or wave vector (inverse wavelength, multiplied by 2π ; hence proportional to frequency *). In three spatial dimensions the wave vector becomes 3-dimesional and frequency is proportional to its magnitude. ...

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Edited and simplified on behalf of the crowd (useless at this point of other very good answers): Consider a cube of edge length L in which radiation is being reflected and re-reflected off its walls. Standing waves occur for radiation of a wavelength λ only if an integral number of half-wave cycles fit into an interval in the cube. In other words, ...

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You need to look at the idea of Separation of Variables for Partial Differential Equations. You consider a toy universe comprising oscillators in a box: let's think of a cuboid microwave cavity with electromagnetic fields losslessly confined within perfectly reflecting walls. The Cartesian components of the electric field all fulfill Helmholtz's equation: ...

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The "modes" in this case refer to the standing waves that can exist in a cavity. A very nice diagram / explanation is given at http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html To summarize: if you consider a cavity of dimension $L$, the modes that fit inside the cavity have wave numbers $n_1$, $n_2$, $n_3$ such that n_1^2 + n_2^2 + n_3^3 = ...

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Blackbody radiation assumes thermal equlibrium with surroundings. For example if you have a hollow sphere heated up with a small hole in it the radiation that comes out of the hole will have blackbody distribution of intensity vs wavelength / frequency If you have a wire heated the spectrum would not look like blackbody radiation. I am afraid that I do ...

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