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.
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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Transcribed Image Text:The figure illustrates a soap film (shown in gray) supported by a wire frame.
Because of surface tension the film exerts a force 20l on the cross wire. This
force is in such a direction that it tends to move this wire so as to dscrease
the area of the film. The quantity o is called the "surface tension" of the film
a.nd the factor 2 occurs because the film has two surfaces. The temperature
dependence of a is given by
where o and a are constanta independent of T or z.
(a) Suppose that the distance z (or equivalently, the total film area 2lx) 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 đą
197
CBLEMS
2n1
absorbed by it and the work done by it in an infinitesimal quasi-static process in
which the dietance z is changed by an amount dz.
(6) Calculate the change im mean energy AE E(x) – E(0) of the film
when it is stretched at a constant temperature To from a length z = 0 to a
length z.
(c) Calculate the work W(0 - x) done on the film in order to stretch it at
this constant temperature from a length x =
O to a length r.
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