# Tag Info

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Your teacher's explanation is incorrect. A simple counterexample can be constructed to illustrate this by considering what happens when the role of your arm is replaced by that of a rubber band. When a weight is suspended from the ceiling by a rubber band, the band stretches and its polymer chains become more ordered, in exact analogy to your teachers ...

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You will almost never encounter a calculation that is intended to account for every detail of a phenomenon with perfect accuracy. That isn't possible, and in fact many times adding more detail to a calculation only takes away from the insight it grants. Why make a complicated calculation when a simple one tells you everything you want to know? Gamow is ...

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So my question is, "Why should the change in entropy be zero, even if the particles are distinguishable?" In statistical physics, entropy can be defined in many different ways. One possibility is to define it as log of the accessible phase space, given the macroscopic constraints (volume). Such entropy is not a homogeneous function of energy, volume ...

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Two obvious desirable features of this definition are: When you put two systems next to each other, considering them as one system, the total number of possible microstates $\Omega_t$ is equal to the product of $\Omega$s of the two systems, $\Omega_t=\Omega_1\times \Omega_2$. But for this system the entropy is the sum of the entropies, indicating the ...

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Entropy was first met in classical thermodynamics and was defined as , where Q comes from the first law of thermodynamics and T is the temperature, W work done by the system. Once it was established experimentally that matter at the micro level is discrete, i.e. is composed of molecules the statistical behavior of matter became the underlying ...

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It's important to distinguish between time and the flow of time. In any universe we need four numbers to uniquely identify a spacetime point, and we conventionally choose one of the coordinates to be time and the other three space so the location of a spacetime point is given by $(t, x, y, z)$. Assuming the universe doesn't hit a singularity then for every ...

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The expression $$k_B \frac{\Omega}{\bar{\Omega}}$$ equals $$k_B\frac{1}{\bar{\Omega}}\frac{d\bar{\Omega}}{dE}$$ which equals $$\frac{dS}{dE}.$$ In thermodynamics, where $S$ is the Clausius entropy, this is equal to $1/T$ where $T$ is the Kelvin temperature. In statistical physics, this expression can be taken as a definition of $1/T$ of a system from ...

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You should use $U=q\epsilon_1$. With the total number of particles $N$ being constant, we have: $$\frac{\partial S}{\partial q}=\epsilon_1 \frac{\partial S}{\partial E}=\frac{1}{T}\epsilon_1\tag{1}$$ As you said: $$\frac{\partial S}{\partial q}=k_B\ln(N/q - 1)=k_B\ln(N\epsilon_1/q\epsilon_1 - 1)=k_B\ln(N\epsilon_1/U - 1)\tag{2}$$ $$\to ... 2 No, in fact you could even view the spontaneous evaporation as being driven by the fact that it increases entropy. Basically what's happening is the liquid particles have random speeds (with distribution characterized by temperature), and they bump into each other. Every once in a while, two particles near the interface will collide in just such a way that ... 1 It depends on how you define your system or your control volume. If only the container is considered then indeed the entropy has decreased due to cooling. On the other hand if you account for the container plus the escaped vapour the entropy has increased, as the randomness of the molecules in the vapour state is larger than compared to in liquid state at ... 1 Temperature is a macroscopic concept, so you're bound to run into some problems when you apply it on a molecular scale (what does temperature and equilibrium (or for that matter, friction) even mean on such a small level?). A thermal equilibrium does not mean all the molecules have the same energy. The distribution of their energies looks like this (normal ... 1 Exactly as you said: "(5) seems to say that the entropy change for an irreversible process is 0 for the case of the system itself, but is > 0 for the case of the surroundings." After the cycle is finished, by definition of the "cycle", the system returns to its original state irrespective of all the irreversibilities that may have taken place within it ... 1 I read somewhere that if the reservoir is infinite then any heat added is actually occurring infinitely slowly. Is this true? No, infinite reservoir does not imply infinitely slow transfer of heat. There is no direct relation. Equation (4) is incorrect; if the integral is over closed path in the state space of the reservoir, its value is 0. If the ... 1 If we accept that black holes do not indeed destroy information and that they follow the second law of thermodynamics (this is how the entropy-is-proportional-to-area formula was derived, after all) then we can forget about their being black holes and simply think of them as some object radiating black-body radiation. From this standpoint, the entropy of the ... 1 It isn't true that the entropy of the black hole must always increase. Prior to the discovery of Hawking radiation there was a second law of black hole thermodynamics:$$ \frac{dA}{dt} \ge 0  and because the entropy is proportional to the area this means the entropy must always increase. However since the discovery of Hawking radiation this has been ...

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Mustafa's answer gives one important reason for the logarithmic dependence: microstates multiply, whereas we'd like an extrinsic property of a system to be additive. So we simply need an isomorphism that turns multiplication into addition. The only continuous one is the "slide rule isomorphism" aka the logarithm. The base $e$ is arbitrary as you can see from ...

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You have to realize that depending on the dimensions of the variables under consideration the laws of physics change. When the dimensions are of order of h_bar, the Planck constant, it is the framework of quantum mechanics, and this is the underlying framework from which all other physics frameworks emerge. Quantum mechanics sees elementary particles, ...

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I am going to address the question as to why energy and information have time symmetric conservation properties whereas entropy does not. According to the Wikipedia entry on entropy - "The entropy of an isolated system never decreases, because isolated systems spontaneously evolve towards thermodynamic equilibrium, which is the state of maximum entropy." ...

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This question seems to me harder and more interesting than either of the answers take into account. A) GR has an analogue of Newton's First Law: the geodesics. B) The OP doesn't wish to consider the Universe as a whole. @Jerry is taking the OP in reverse. The OP is: since none of the usual bodies we study is the whole Universe, none of them are closed ...

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