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based on casual observation, believes that coffee will cool faster than ordinary hot tap water Let's revisit the "casual observation" part. Are the initial conditions the same? Water from a kettle will usually be hotter than from a coffee machine. And we tend to do things to coffee that we don't do to water, like add 10% of another liquid (milk) at low ...


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Internal Energy = Heat - Work, or U = Q - W. By definition an adiabatic process has constant heat, so when finding the rate of change of each in a process by taking the time derivative: dU = dQ(0) - dW Q goes to zero, and U = W.


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There's no violation of the second law here. You have a system that is out of thermal equilibrium. That black bodies absorb and radiate is the driving mechanism that tries to move this system toward thermal equilibrium. By way of analogy, suppose you are from a southern clime and take a trip at this time of year to a northern clime. You, as a southerner, ...


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Not all the radiation from the outer shell reaches the inner shell. When you take into account the intensity distribution of radiation from the outer shell (Lambertian distribution, i.e. $\propto\cos\theta$) you will see that the amount of radiation for the inner to the outer shell is the same as in the other direction. No violation of the second law.


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Your function $I(\lambda,T)$ is the spectral radiance. It's the intensity per steradian per square meter per unit wavelength. To get the total intensity radiated per steradian per square meter over all wavelengths between $\lambda$ and $\lambda + d\lambda$ you multiply it by $d\lambda$, as you've done in your second equation (strictly speaking you integrate ...


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Resolution of the ellipsoid paradox in thermodynamics: the finite sizes of the black bodies lead to a resolution of the apparent paradox


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I have discovered the source of the discrepancy with help from the researcher (thanks Dr. Lipinski!). It seems that many sources (including Wikipedia, the undergraduate heat transfer texts by Incropera & DeWitt and Lienhard & Lienhard) mention only breifly, or not at all, the dependence of the speed of light in the medium on the refractive index, ...


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In addition to the other answers, "bright light can never hurt your eyes" has to be false -- you up the intensity of the light enough, and the energy density can get arbitrarily high. In principle, it's possible to have light so bright that it collapses to a black hole. Before then, you'll get pair production in the light beam.


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You're question is one of the canonical questions that inevitably led to Quantum-Mechanics. It is true that in Classical Mechanics the electron is rotating -> radiating, but if that were true the system would be losing energy all the time, until the electron collapses into the proton. by the same token a proton would be radiating since it also rotates ...


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Let us try to clear up terminology here: A black body is classically defined as a perfect absorber of radiation. No, it is not. The classical description of the perfect absorber also includes an emitter black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A ...



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