Lecture_6 - Lecture 6 Changing the State Recall"equation of...

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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. K T > 0 for “stability” — more about this later.
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