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An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.
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Temperature meaning
Temperature is also related to the entropy as the partial differential. It is a measure of the energy of the atoms within but which types of energy? …
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Slope of constant pressure line on $T$-$S$ plot
We know $T=\frac{\partial U}{\partial S}$, so $\frac{\partial T}{\partial S}$ is the second derivative of the internal energy with respect to entropy. …