A rectangular film of liquid is extended from $(2 \mathrm{~cm} imes 3 \mathrm{~cm})$ to $(4 \mathr

Question

A rectangular film of liquid is extended from $(2 \mathrm{~cm} 	imes 3 \mathrm{~cm})$ to $(4 \mathrm{~cm} 	imes 3 \mathrm{~cm})$. If the work done is $3.6 	imes 10^{-4} \mathrm{~J}$, the value of the surface tension of the liquid is

Professor PC Thomas Classes · Answer

(d) : Work done is given by $W = T 	imes \Delta A$, where $\Delta A$ is the change in the total surface area. Since a film has two free surfaces, $\Delta A = 2 	imes (A_2 - A_1)$. Here, $A_1 = 2 	imes 3 = 6 \mathrm{~cm}^2$ and $A_2 = 4 	imes 3 = 12 \mathrm{~cm}^2$. Thus, $\Delta A = 2 	imes (12 - 6) = 12 \mathrm{~cm}^2 = 12 	imes 10^{-4} \mathrm{~m}^2$. We are given $W = 3.6 	imes 10^{-4} \mathrm{~J}$. Surface tension $T = \frac{W}{\Delta A} = \frac{3.6 	imes 10^{-4}}{12 	imes 10^{-4}} = 0.30 \mathrm{~N} \mathrm{~m}^{-1}$.