Two spherical soap bubbles of radii `r_(1)` and `r_(2)` in vacuum combine under isothermal conditions. The resulting bubbles has a radius equal to

Explanation

When joined is isothermal condition change in temperature of system is zero, So change in internal change of the system is zero.
Let
Surface energy of 1st bubble `U_1= 8 pi R_1^2 S`
Surface energy of 2nd bubble `U_2=8 pi R_2^2 S`
Surface energy of new bubble `U=8 pi R^2 S`
But `8piR^2S=8piR_1^2S+8piR_2^2S`
`implies R^2=R_1^2+R_2^2`
Radius of new bubble R `=sqrt(R_1^2+R_2^2)`