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Question
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
Solution
a) Let ABCD be an open rectangular frame of wire on which a wire PQ can slide without
friction
b) The frame held in horizontal position is dipped into soap solution and taken out so that
a soap film APQB is formed. Due to surface tension of soap solution, a force ‘F’ will act on the wire PQ which tends to pull it towards AB.
c) Magnitude of force due to surface tension is, F = 2Tl. [∵ T = F/l]
(A factor of 2 appears because soap film has two surfaces which are in contact with
wire.)
d) Let the wire PQ be pulled outwards through a small distance ‘dx’ to the position P'Q',
by applying an external force F′ equal and opposite to F. Work done by this force,
ΔW = F′dx = 2Tldx.
e) But, 2ldx = ΔA = increase in area of two surfaces of film
∴ ΔW = T ΔA
This work done is stored in the form of potential energy (surface energy).
∴ Surface energy, E = TΔA
∴ `E/(ΔA) = T`
Hence, surface tension = surface energy per unit area
f) Thus, surface tension is equal to the mechanical work done per unit surface area of the
liquid, which is also called as surface energy.
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