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Why is there zero point energy at absolute zero temperature? Because in a sense temperature is a measure of the motion of matter, whilst at some deep fundamental level, matter is made of motion. You'll be aware of the kinetic theory of gases, wherein the temperature of an ideal gas is a measure of the average kinetic energy of its constituent particles. The ...


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2nd law of thermodynamics has many almost equivalent formulations. The traditional ones always assume closed system, isolation is not needed - heat and work transfer are assumed to be allowed. One formulation: When thermodynamic system goes from equilibrium state 1 to equilibrium state 2, the entropies of these states obey the relation $$ S(2) - S(1) \geq ...


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I think the $\Omega_N$ in your question is the number of states inside an energy sphere $E$; Now we need to consider micro-canonical ensemble, which means we need to get the number of states in an energy shell between $E$ and $E+\Delta$: $\Omega'=\frac{1}{N!h^{3N}} V^N \frac{\pi^{3N/2}}{(3N/2)!}\{[2m(E+\Delta)]^{3N/2}-(2mE)^{3N/2}\}$ Which is equal to: ...


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No, I don't think you have the correct entropy. I think the temperature is incorrect in the numerators, it should be (328 - 313) and (313 - 283).


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The battery in your remote is probably a lithium manganese oxide battery, and these have a shelf life of 10 to 15 years depending on who you believe. I did try Googling for an authoritative figure but without any luck, though this article from Varta (NB this is a 2MB PDF) cites a ten year shelf life. Shelf life means when the battery is not connected to ...


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It continues to work because the battery does not discharge at 5% per month. It's much less. I have batteries with a use by 2019 date, which I have had for some time.


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You state the second law as : The entropy of the universe always increases. In my college textbook it is stated as : Processes in which the entropy of an isolated system would decrease do not occur, or, in every process taking place in an isolated system, the entropy of the system either increases or remains constant.( F.W.Sears an introduction ...


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If you put a gas in a box and wait for it to reach equilibrium, then a) its full behaviour then is described by equilibrium statistical mechanics and b) it will remain in this state - as described by equilibrium statistical mechanics - forever (really forever) if nothing is done to it. The key point is that, although it carries "equilibrium" in it, ...


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The gas could fall into a state of low entropy randomly. It is important to remember that the laws of thermodynamics are probabilistic, and they say not what will happen but what usually will.


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The second law of thermodynamics says that the entropy of an isolated system can increase, but that entropy can not decrease without the addition of energy to the system, or the transfer of entropy to another system. Increasing entropy has been associated with the arrow of time, as entropy seems to be the only quantity in physical processes that requires ...


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Entropy is a state function, correct ! But entropy itself depends upon how you got to that state (final state). In thermodynamics Entropy is considered the quality of heat (hotness/coolness) whereas temperature is considered quantity/degree of heat (hotness/coolness). The reversible processes (and adiabatic i.e. no heat exchange) do not mess with the ...


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It is important to distinguish between the time and the flow of time. The time, $t$, is just a coordinate like $x$, $y$ and $z$ that we use to specify points in spacetime. The time coordinate doesn't have an arrow any more than $x$, $y$ or $z$ have arrows. The time axis has a negative and positive direction, just like the spatial coordinates, but at normal ...


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There is a general formula to get the entropy change between two states $A$ and $B$ for a system, that is: \begin{equation} \Delta S_{A \rightarrow B} = \int_{\Gamma^{rev}(A \rightarrow B)} \: \frac{\delta Q_{rev}(\Gamma)}{T} \end{equation} It states that the variation of entropy of a system between the states $A$ and $B$ can always (even for irreversible ...


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One may still describe the behavior of such a system at maximal entropy using a theory that does use the concept of time, or the time coordinate $t$. But it is true that operationally speaking, the passage of time ceases to exist because the equilibrium associated with the maximum entropy is incompatible with the existence of thinking observers. Note that ...


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Widespread beliefs are not laws. Look to the genesis of thermodynamics: The short range interaction field, the electromagnetic one, that allows the atomic structure and the transfer of energy, heat, in the collisions of atoms and molecules was, for sure, present in the analysis of the thermodynamics since its inception. In this original context the ...


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For gravitational systems one has to be careful making statements about entropy and the second law of thermodynamics. Your example is similar to the gravitational collapse of a gas cloud if you think carefully about it. In that case and in yours, the shrinking of the gas will raise it's heat. Now even though the increase of entropy due to the increased ...


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All energy transfer in an (ideal linear) electrical circuit is a form of work. Its just moving charges in electromagnetic fields. Resistor transfer energy to something external to the circuit, and often this energy will end up dissipated as heat in the surroundings. Inductors and capacitors, however, simply store energy and then release it again. Work is ...


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$1+{R\over C_v}$ is always bigger than 1 as $R$ and $C_v$ are positive. Although I'm not sure you can necessarily put $C_p=C_v+R$, if you can then you can probably say that $R<C_v$ so that $$ 1<1+{R\over C_v}<1+{C_v\over C_v}=2 $$


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The answer is no. Once a black hole is formed you no longer have access to the information stored inside it. The information is not lost, but slowly radiated away as the black hole evaporates. So, the ideal system would be one that is almost near the density for a black hole collapse, but never reach it. Otherwise you loose "easy" access to the information ...



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