A soap bubble in vacuum has a radius `3cm ` and another soap bubble in vacuum has radius `4cm`. If two bubbles coalesce under isothermal condition, then the radius of the new bubble will be:

Options

A. `7cm`
B. `5cm`
C. `2.3cm`
D. `4.5cm`

Answer

B

Explanation

The process is isothermal and the total pressure of air inside the bubble is same as excess of pressure is given by
`P=(4T)/(R )`
Where `T` is surface tension and `R` is radius. Also an isothermal process obeys Boyle's law hence, `PV=`constant ltbr. Let R be the radius of coalesce system then
`P_1V_1+P_2V_2=PV`
`((4T)/(R_1))((4)/(3)piR_1^3)+((4T)/(R_2))((4)/(3)piR_2^3)=((4T)/(R ))((4)/(3)piR^3)`
`impliesr_1^2+r_2^2=R`
Given `R_1=3cm` and `R_2=4cm`
`R=sqrt(3^2+4^2)`
`R=5cm`