The figure illustrates a soap film (shown in gray) supported by a wirc frame. Because of surface tension the film exerts a force 2ol on the cross wire. This force is in such a direction that it tends to move this wire so as to dscrense the ares of the film. The quantity o is called the "surface tension" of the film end the factor 2 occurs because the film has two surfaces. The temperature dependence of o is given by where o and a are constante independent of T or z. (a) Suppose that the distance z (or equivalently, the total film area 2!z) is the only external parameter of significance in the problem. Write a rolation expressing the change dE in mean energy of the film in terms of the heat đo 197 2nl bsorbed by it and the work done by it in an infinitesimal quasi-static process in -hich the dietance z is changed by an amount dz. (6) Calculate the change in mean energy AE E(x) – E(0) of the film when it is stretched at a constant temperature T. from a length z -0 to a ength z. (c) Calculate the work W(0 → x) done on the film in order to stretch it at his constant temperature from a length x = 0 to a length z.

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When a metal is heated, its atoms vibrate more about their position in the lattice (a network of crossed bars). This causes them to take up more space, so the solid metal expands from its original shape. Calculate the heat needed to expand a ring made of copper with an internal diameter of 50mm to fit over a shaft of diameter 50.05mm.  The shaft is measured at a temperature 20 degrees c

0.4 kg water is at room temperature 23 degrees in an aluminum container. An unknown metal with 0.5 kg mass is placed inside the water raising its temperature to 40 degrees. A)What is the specific heat of the unknown metal. B) Would the equilibrium temperature greater, less or the same if the system was not properly isolated.

Common automatic fire alarm system uses bimetalic strip of brass and iron, with iron tacing the wire external to the alarm system. Have you checked the coefficients of linear thermal expansion of these materials? How do these metals in the bimetalic strip behave when exposed to heat? HINT: You may imagine which expands first and how this expansion result into behavior of the whole strip. You may write your explanation in the blank provided. Cutat tle