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S s p s dv t dt t dv t dt v t

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Unformatted text preview: = (∂/∂y) ∂F/∂x = ∂2F/∂x∂y = (∂/∂x) ∂F/∂y = (∂B/∂x)y This is a very important relationship that will allow us to derive many useful formulas. It can also be used to test whether A(x,y) dx + B(x,y) dy represents an exact differential of some function. Exercise: verify the validity of the above identity for F ( x, y) = x 2 y 7 How to calculate the entropy as a function of (V,T). Below we will be considering only equilibrium processes so instead of inequalities we will have equalities. We have previously learned two relationships: dG = V dP – S dT (1) dA = - PdV – S dT (2) Consider the second one. We have also established that ⎛ ∂A ⎞ P = −⎜ ⎟ ⎝ ∂V ⎠T (3) and ⎛ ∂A ⎞ S = −⎜ ⎟ ⎝ ∂T ⎠V Applying Maxwell’s trick: ⎛ ∂P ⎞ ⎛ ∂S ⎞ ⎜ ⎟ =⎜ ⎟ ⎝ ...
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