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Lastly, since you ask about thermodynamics and the formula graven on Boltzmann's headstone, the logarithm is the grounding of the natural encoding of the idea that numbers of possibilities (volumes of …

Your question cannot be answered in its present form. The RHS is simply the heat flux out of the system, and that will be different depending on what your system is surrounded by and how those surroun …

See my answer to Why are the laws of thermodynamics “supreme among the laws of Nature”? for further discussion of these ideas. …

You'll need to read up on a little bit of mathematics to numerically solve problems like this. You need to solve the heat diffusion equation for the temperature $T(\vec{r},\,t)$ as a function of time …

I think you should accept Nathaniel's answer, because the process you cite does indeed fulfill $\Delta\,S<0$, thus by the second law is impossible. Another way to show this (less general and elegant …

The Boltzmann distribution is the main and fundamental result you use here; see the Wikipedia article on the Microcanonical Ensemble. This is: $$p(E) = \frac{1}{\mathcal{Z}}\,g(E)\,\exp\left(-\frac{E …

You're problem is not fully defined, but let's begin to define it. Firstly, you're looking for something with a high emissivity $\epsilon$, so that it will absorb most of the incident light. This fa …

Intuitively, this makes entropies add when we calculate the number of microstates for the combination of two systems: if the two systems are independent (uncorrelated), we simply multiply these number …

Firstly, the laws of thermodynamics have very different origins and putative theoretical justifications and indeed the Eddington quote only talks about the second. … This, of course, is a "laboratory form" of the second law of thermodynamics. …

Wood is mostly cellulose, which burns to yield carbon dioxide and water, so this indeed can "burn fully". The rest - particulate matter in smoke and wood ash is made of minerals that the tree either d …

You're on the right track. Your statement can be true in special cases. More generally, the entropy is defined by the Boltzmann-headstone-equation you write down if $\Omega$ is the number of different …

The temperature does not depend linearly on the radius because the flow lines of heat flux are not parallel. This means that the heat flux, and therefore the temperature gradient, decrease as the flux …

Out of interest, is this method cited as a "proof" in a thermodynamics text? It fails when you want to extrapolate to wider intervals, so that the higher order terms are important. …

Maybe the following will help thinking about what is a really quite a complex question: it would be a fantastic last question for an undergrad thermodynamics exam BTW: You can abstract detail away by saying …

However, this system still complies with the second law of thermodynamics through Landauer's Principle. … One of the best references around on this stuff is Charles Bennett's review paper: Charles Bennett, "The Thermodynamics of Computation: A Review", Int. J. Theo. Phys., 21, No. 12, 1982 …