Define surface energy and show that surface energy is equal to surface tension. from Physics Mechanical Properties of Fluids Class 11 Manipur Board
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Define surface energy and show that surface energy is equal to surface tension.

The amount of mechanical work required to increase the unit area of a free surface under the isothermal condition is known as surface energy. 

To show: Surface energy is equal to surface tension

i) Take a wired rectangular frame whose three sides are rigid and one side AB is free to slide.

ii) Dip the frame in a soap solution to form the film.

iii) The surface tension force acts on all the sides of the frame.

iv) Side AB is free to slide and the other three sides being fixed cannot displace. Due to surface tension force slides in left direction and free surface tries to contract.

Let surface tension of soap solution be T and length of movable rod AB be l.

There are two free surfaces of liquid which touch the movable wire AB.

The surface tension of total inward force on the wire = 2Tl.

If frame AB is displaced by distance x in right direction, then work done against surface tension to increase the surface area is,
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Increase in surface area of film is
 
                    straight ell straight x plus straight ell straight x equals 2 straight ell straight x

therefore space space space space space Surface space energy

           equals space fraction numerator Work space done space to space space increase space the space area over denominator Increase space in space area end fraction

    
space space space space space space space space space equals fraction numerator 2 straight T straight ell straight x over denominator 2 straight ell straight x end fraction equals straight T

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