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. ..ZZMaxwell Relations

Properties of an exact differential


A state function can be an exact differential

Thermodynamic processes can be described by state functions. Enthalpy, Internal Energy, Entropy, and Free Energy are all examples. However, we must be aware of the variables of state that are appropriate for the state function to have the property that known as an exact differential. An exact differential means that the derivatives of the function are related in a specific way. The functions are generally expressed as a function of two variables, F(X,Y). Examples are U(S,V), H(S,P), A(T,V) and G(T,P). Mathematically we can say that the order of differentiation does not matter for the second cross derivative. This statement will be true only if we express the function in terms of appropriate variables. For example, if we express the internal energy as a funciton of T and V (rather than S and V) then it is not an exact differential. This distinction is important for the physics since the derivative of (dU/dV)S = P, but (dU/dV)T = pT.

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