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Any thermodynamic quantity can be calculated if we

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Unformatted text preview: entropy: ⎛ ∂A ⎞ U = A + TS = A − T ⎜ ⎟ ⎝ ∂T ⎠V If we wish now to compute the heat capacity we use: ∂⎛ ⎛ ∂U ⎞ ⎛ ∂A ⎞ ⎞ CV = ⎜ ⎜ A − T ⎜ ⎟ ⎟ ⎟= ⎝ ∂T ⎠V ∂T ⎝ ⎝ ∂T ⎠V ⎠V So the equation of state and the heat capacities are not independent: They all can be derived from the same fundamental quantity A(V,T) (or G(P,T)). Any thermodynamic quantity can be calculated if we know either A or G. In principle, one can calculate A or G if the interaction energies among the molecules are known – this is the main goal of statistical mechanics. Unfortunately, in practice this is not easy except for very simple, idealized systems. In some (rare) cases, such as an ideal gas, A and G can be calculated analytically from first principles. Thermodynamics takes a different approach and starts...
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