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In thermodynamics, entropy (differences) is (are) defined, at least at first, only for two states which can be connected by a reversible transformation. Hence, those two states have to be equilibrium states. Yet, sooner or later, one always runs into the example of two boxes of gasses, at different temperatures, separated by an insulating wall. The ...

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Here is part I of the answer. Part II will be so controversial, although standard, that I want to mull it over a little more. Anyway, chew on this. In the good old days, Newtonian Mechanics was taught carefully and slowly in three stages. First was kinematics, how to describe positions and motions. Then was statics, how to analyse a configuration of ...

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Static equilibrium requires that the sum of all forces is 0,$$\sum F=0$$ and the sum of all torques is 0, $$\sum \tau =0$$ Be aware that force and torque is a vector; they have both magnitude and direction. You will usually want to separate a force into its components such that all forces are either parallel or perpendicular to each other. Then apply the ...

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In the canonical situation, you have a total system , which is made of a heat reservoir "HR" (with constant temperature $T$) and the systeme to be observed "OBS". If we call $E_{total}$ the total energy of the system (HR + OBS), it can be shown that the total entropy of the system (HR + OBS) $S_{total}$ could be written : S_{total} = S_{HR}(E_{total}) ...

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Take the points held by the trestles one at a time and consider it as being the pivot. ----------------------------------- ^ | ^ A V B W W is the weight of the wooden board. Say we consider A as the pivot, then work out the moments at W and B. $0 = |AW|\cdot W - |AB|\cdot B$ $|AW|$ is the ...

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The ideia is which constraints you are dealing with. When you have a system with have Fixed Energy, Number of Particles and Volume (which we will end up calling micro-canonical ensamble), what you seek is to maximize entropy while respecting these constraints. So when you extremize entropy, you can't really extremize (internal) energy. When a system can ...

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