Question

The surface tension of a soap solution is $0.035N/m$. the energy needed to increase the radius of the bubble from $4$ cm to $6$ cm is

• A. $1.75\times {10}^{-3}J$
• B. ${1.510}^{-2}J$
• C. ${310}^{-3}J$
• D. ${1.510}^{-4}J$

Answer 1

The correct option is A $1.75\times {10}^{-3}J$

There are two free surface available in bubble.

Change in surface area $\Delta A=2(4\pi R_f^2-4\pi R_i^2)$

Energy needed to change radius from 4 to 6 is

$W=T\Delta A=T\times 2(4\pi R_f^2-4\pi R_i^2)$

$W=.035\times 2\times 4\pi \left(\right(6\times {10}^{-2}{)}^2-(4\times {10}^{-2}{)}^2)$

$W=1.75\times {10}^{-3}J$