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Define surface energy and show that surface energy is equal to surface tension.


Surface energy is defined as the mechanical work required to increase the unit area of free surface under isothermal condition.


Surface energy is defined as the mechanical work required to increase

Take a wired rectangular frame whose three sides are rigid and one side AB is free to slide. Dip the frame in soap solution to form the film. The surface tension force acts on all the sides of the frame. Three sides of frame being fixed cannot displace but side AB is free to slide and 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 I. Since there are two free surfaces of liquid which touch the movable wire AB, due to surface tension total inward force on the wire is 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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How does the surface tension depend on temperature? 

Surface tension of the liquid decreases with increase in temperature, reaching a value of 0 at the critical temperature. 

This dependence of surface tension on temperature is given by the equation,

                       Tt = T0(1–αat)

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n identical drops of liquid of surface tension T each of radius r coalesce to form single drop. Find the energy released in the process.

Let R be the radius of big drop. Since on coalesce of droplets, the volume of liquid remains constant, therefore


Let R be the radius of big drop. Since on coalesce of droplets, the v
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The needle placed gently on the surface of clear water floats on it, what happens when some detergent is added to water?

Adding impurites to water decreases the surface tension of the liquid. So, when detergents are added into water, the surface tension decreases. Hence, vertical component of surface tension will not be able to support the needle and needle sinks.
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When a sewing needle is gently placed on the surface of water, it floats. Why?

When the needle is gently placed on the surface of water, it gets slightly depressed.


When the needle is gently placed on the surface of water, it gets sli

The force due to surface tension on depressed curved surface is inclined upwards, whose resultant is vertically upward, which balances the weight of needle. Hence the needle floats.
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