Question

Why equation for excess pressure inside soap bubble and air bubble is different?

Answer 1

The work done by excess pressure in displacing the surface is

dW = force × displacement

     = (excess pressure x Surface area × displacement of surface)

   = (p × 4 × 22/7 × R^2 ) × dR ........... (i)
increase in the potential energy is

dU = surface extension × increase in the area of free surface
= T [ 2 { 4 × 22/7 } [( R + dR^2 )^2 - 4× 22/7× R^2]
= T [ 2( 4×22/7{ 2rdR})


From (1) and (2), we get,

p× 4×22/7×r^2 × dR = T ( [ 2( 4×22/7{ 2rdR})

therefore , p = 4T/r

Hope it helps u
: )