If the surface tension (T) of a soap bubble depends upon excess of pressure radius 'r' of the bubble, then obtain an equation for the surface tension.

Explanation

Let `T prop p ^a r ^ b `
where ` [T] = ["Force/length"]= [ M ^ 1 L ^( 0 ) T^ ( -2) ]" " [ P] = ["Force/area"] = [M^ 1 L^ ( -1) T^( -2) ] `
` [r] = [L] `
Hence, ` [ M^ ( 1 ) L ^ 0T^ ( -2) ] = [M^ 1 L ^ ( -1) T ^( -2) ]^ a [ L ]^ b `
i.e., ` [ M^ 1 L ^0T^( -2) ] = [M^aL^(-a + b )T^( - 2a ) ] `
From the principle of homogeneity,
` a = 1 " " (1) `
` - a + b = 0 " " (2) `
` - 2a = - 2 " " (3) `
Using (1) in (2) we get
` -1 + b = 0 " " or b = 1 `
Therefore surface tension ` T = KPr" " or P = KT//r `