Question

Physics
Derive the Relationship b/w Surface tension and surface Energy.
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Answer 1

Answer:

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Explanation:

Assuming that a soap film is distributed over the area surrounded by a frame ABCD which is U-shaped and a PQ crosspiece, which can move easily over the frame. Let T be the soap solution's surface tension and l, the wire PQ's length in contact with the soap film. Along with the wire, the film has 2 surfaces. The film exerts a force on the wire PQ and tends to contract. The total wire force is 2Tl2Tl, since this surface exerts a TlTl force. Assume the PQ wire is pulled to P′Q' at a dx distance very slowly. The work was done by and external force against the force due to film is-

⇒⇒W = applied force ×× displacement

Since the value of force is given as F=2TlF=2Tl.

Therefore-

⇒W=Fdx⇒W=2Tldx⇒W=Fdx⇒W=2Tldx

The film's surface area increases due to the dx displacement. With two surfaces, the increase in its surface area will be-

⇒A=2ldx⇒A=2ldx

Hence, the work done per unit area will be-

⇒WA=2Tldx2ldx=T⇒WA=2Tldx2ldx=T

This work is stored as potential energy in the unit surface. The surface energy is this potential energy.

The above relation shows that the surface energy is equal to its surface tension per unit area of a liquid.

Answer 2

Answer:

Since the value of force is given as F=2Tl. This work is stored as potential energy in the unit surface. The surface energy is this potential energy. The above relation shows that the surface energy is equal to its surface tension per unit area of a liquid.