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Many materials contain microscopic paramagnetic moments which are free to randomly orient themselves in zero magnetic field. If you apply a magnetic field, then the magnetic moments are able to lower their energy by entering a lower entropy state where they are magnetized. In such a material the entropy tends to decrease as magnetic field increase, at least ...

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I learned I can calculate the entropy $$S=-k_B\sum_jp_jln(p_j)$$ where $$p_j$$=probability at j state but I saw that the entropy is also can be calculated by $$S=-k_Bln(Z)$$ I think this equation applicable for both of isolated system and non isolated system these two equations are same ? Given the number of states $\Omega(E,\Delta ... 2 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 ... 2 To answer your question first we need to know why do we need quantum mechanics in thermodynamics: In Quantum mechanics you can attribute a wave function(to be precise wave-packet) to a particle. . At high temperatures particles can be pictured as billiard balls because their size is much smaller compared to interparticle distance. But as the gas cools down ... 1 Let me show you that there is no contradiction by pointing out e.g. that for ordinary expansion periods (that is away from first order phase transitions, decouplings...) the total entropy is actually constant in time while the universe is getting bigger and cooler. Or, going back in time, the universe is getting hotter while S is kept constant. How is this ... 1 Consider an isentropic (idealistic adiabatic process, with no friction) process, in which the volume of a system is increased. For that to happen, the internal energy of the system would decrease because the system would be performing work. So any gain in the number of available microstates from an increase in volume is negated by the loss of internal energy ... 1 Setting constants to be equal to$1$means that one measures quantities as multiples of that constant. So, for example, if one sets the speed of light,$c$, to$1$,$v=0.5$means that$v\$ amounts to half the speed of light. It may be clearer, especially to people who are not used to these kinds of conventions, to be approach this situation a bit ...

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An intuitive explanation is that entropy is a measure of disorder, so if heat is injected into two exactly identical systems except that one is held at a higher temperature, then you can imagine that the higher temperature system's disorder will increase less because it was more disordered to start with. In other words, its harder to increase the disorder in ...

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I may give you an intuitive example i read before Imagine shouting in a street full of noise and shouting by the same amount in library although the shouting ( dQ ) is the same in both cases it will have a greater effect in the library ( systems with lower temperature. i hope it helps i know only that example and not expert with Thermodynamics.

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In classical mechanics, time is the unique parametrisation of dynamical systems. In relativity theory, one then sees that time is somewhat more than this, because there exists a global symmetry (the Poincaré-group) that involes time and space on an equal basis (called spacetime). Also, one can show that parametrisation by time is not the only way to do ...

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