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# If T is the surface tension of the soap solution the amount on work done blowing a soap bubble from a diametre D to 2d is

8 Points
11 years ago

Let r be the instantaneous radius of the bubble in the process of enlargement and let the radius increases to r+dr. Then increase in surface area  ds = 4*pi*(r+dr)^2 - 4*pi*r^2 = 8*pi*rdr (neglecting 4*pi*(dr)^2 which is small)

Now work done in increase of this surface area dw = T*ds (T surface tension of soap solution)

As tehre are two free surfaces of soap bubble so net work done dw = 16*pi*T*rdr

therefore net work done in increasing diameter D to 2d is  W = 16*pi*T ∫D/2 d r dr = 8*pi*T*(d^ 2 - (D^2)/4)