Question

A film of water is formed between two straight parallel wires each 10 cm long and at a separation of $0.5cm$. Calculate the work required to increase the distance between them by $1mm$. The surface tension of water =$72\times {10}^{-30}N/m$

Answer 1

Step 1:Given data:

Length of wires =$10cm=0.1m$

Separation between wires=$0.5cm=5\times {10}^{-3}m$

Distance to be increased between wires=1mm=$1\times {10}^{-3}$m

The surface tension of water=$72\times {10}^{-30}N/m$

Change in surface area = $\Delta S$

Surface Tension = $T$

Step 2: Formulae used

Change in surface area=Area of films $\times$no.of films

Work done=$\Delta S\times T$

Step 3:Solution

Work done by water to increase the separation= Change in surface area $\times$Surface Tension

Change in surface area=$\Delta$S=Area of films $\times$no.of films

$$\begin{gathered} =0.1\times 1\times {10}^{-3}\times 2 \\ =2\times {10}^{-4} \end{gathered}$$( Water has 2 films )

Work done=$\Delta$$S$$\times T$

=$$\begin{gathered} =2\times {10}^{-3}\times 72\times {10}^{-30} \\ =144\times {10}^{-7}J \\ =1.44\times {10}^{-2}J \end{gathered}$$

So, Work done to increase the separation between 2 parallel wires by $1mm$ is equal to $1.44\times {10}^{-2}J$