A vessel filled with air under pressure `p_(0)` contains a soap bubble of diameter `d`. The air pressure have been reduced `n`-fold, and the bubble diameter increased `r`-fold is isothermally. Find the surface tension of the soap water solution.

Options

A. `T=(1)/(2)p_(0)d xx (1-(r^(3))/(n))/(r^(2)-1)`
B. `T=(1)/(8)p_(0)d xx (1-r^(3)/(n))/(r^(2)-1)`
C. `T=(1)/(4)p_(0)d xx(1-r^(3)/(n))/(r^(2)-1)`
D. `T=(1)/(6)p_(0)d xx (1-r^(3)/(n))/(r^(2)-1)`

Answer

B

Explanation

`P_(1)V_(1)=P_(2)V_(2)`
`impliesp_(0)(1-(r^(3))/(n))=(8T)/(d)(r^(2)-1)impliesT=(1)/(8)p_(0)d xx (1-(r^(3))/(n))/(r^(2)-1)`