Two spherical soap bubbles of radius `r_1` and `r_2` coalesce under isothermal conditions. What is the resultant radius?

Explanation

Under isothermal conditions, the total energy (work done in blowing) remains constant.
Work done = Energy stored x = `8piR^2T`
`therefore 8pir_1^2T + 8pir_2^2T = 8piR^2T`
`r_1^2 + r_2^2 = R^2 therefore R = (r_1^2 + r_2^2)^(1/2)`