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Unformatted text preview: Lecture 6 — Changing the State Recall “equation of state”: for pure systems, only two independent properties, so a third may be given in terms of the other two. For example, v = f ( T,p ). How does v change when we change T and p ? Recall that v t is a state function, so dv is independent of path. We may therefore use any convenient path to compute dv . dv = ( ∂ v/ ∂ T ) P dT + ( ∂ v/ ∂ P ) T dP (graphical interpretation of this: tangent plane) What we would need to know to compute dv , then, are the values of the partial derivatives ( ∂ v/ ∂ T ) P and ( ∂ v/ ∂ P ) T as a function of T and P . What are these two quantities physically (and how would we measure them)? Isothermal compressibility Fractional change in volume induced by pressure change at fixed T . K T =- 1 /v ( ∂ v/ ∂ P ) T (We include a minus sign in the definition of K T , because v decreases with increasing P , and we want K T to be positive.) Comments: gases are much more compressible than liquids, and liquids more than solids.Comments: gases are much more compressible than liquids, and liquids more than solids....
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This note was uploaded on 04/01/2008 for the course CHE 220 taught by Professor Prof.marannas during the Spring '08 term at Penn State.
- Spring '08