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 quasistatic process
in which the distance
x
is changed by an amount
dx
.
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 Spring '12
 atkin
 Thermodynamics, Energy, Force, Work, Statistical Mechanics, Entropy, Reif

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