Under isothermal conditions, two soap bubbles of radii ' r₁ ' and ' r₂ ' combine to forms a single soap bubble of radius ' R '. The surface tension of soap solution is ( P = outside pressure)

Step-by-step solution

Pressure inside the first bubble = P + 4 ~T r ₁ Pressure inside the second bubble = P + 4 ~T r ₂ Using the formula PV = nR ( = absolute temp ) ( P + 4 ~T r ₁ ) 4 3 r ₁^3= n ₁ R ( R is molar gas constant) ( P + 4 ~T r ₂ ) 4 3 r ₂^3= n ₂ R and ( P + 4 ~T R ) 4 3 R ^3= ( n ₁+ n ₂ ) R ( P + 4 ~T R ) 4 3 R ^3= ( P + 4 ~T r ₁ ) 4 3 r ₁^3+ ( P + 4 ~T r ₂ ) 4 r ₂^3 3 ( P + 4 ~T R ) R ^3= ( P + 4 ~T r ₁ ) r ₁^3+ ( P + 4 ~T r ₂ ) r ₂^3 on solving: T = P ( R ^3- r ₁^3- r ₂^3 ) 4 ( r ₁^2+ r ₂^2- R ^2 )