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Thermodynamics Equation

Thermodynamics texts use the relationship (dy/dx)(dz/dy)(dx/dz) = -1

Prove that this equation is true.

(Hint: Start with a relationship F(x,y,z)= 0 that defines x = f(y,z), y = g(x,z), and z = h(x,y) and differentiate implicitly.)

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Thermodynamics texts use the relationship (dy/dx)(dz/dy)(dx/dz) = -1

Explain the meaning of this equation and prove that it is true (Hint: Start with a relationship F(x,y,z)= 0 that defines x = f(y,z), y = g(x,z), and z = h(x,y) and differentiate implicitly.)

Instead of calling the functions f, g, and h, I'm going to call them X, Y, and Z. The capital X, Y, and Z are functions, and the lower-case ones are variables. I think it's less confusing this way. If you don't, just replace all the X, Y, and Z's with ...

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