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# hw07 - Homework Assignment 7 Due 30 October 2002...

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Statistical Mechanics Homework Assignment 7 Due 30 October 2002 1. Problem 10.13 – Soap films (Reif 5.15) The figure illustrates a soap film (shown in gray) sup- ported by a wire frame. Because of surface tension the film exerts a force 2 σl on the cross wire. This force is in such a direction that it tends to move this wire to decrease the area of the film. The quantity σ is called the “surface tension” of the film and the factor 2 occurs because the film has two surfaces. l x 2 l σ The temperature dependence of σ is given by σ = σ 0 αT where σ 0 and α are constants independent of T and x . (a) Suppose that the distance x (or equivalently, the total film area 2 lx ) is the only external parameter of significance in the problem. Write a relation expressing the change dE in mean energy of the film in terms of the thermal energy T dS absorbed by it and the work done on it in an infinitesimal quasi-static process in which the distance x is changed by an amount dx .

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hw07 - Homework Assignment 7 Due 30 October 2002...

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