Surface Tension and Surface Energy

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle to start. Eight tiny drops of water touch, and join into one bigger drop. Nobody heats them. Nothing rubs them. And yet, a little heat is given out. Where does that energy come from? The answer lives in the surface of the water. Today: surface tension and surface energy. Questions on this come up often in JEE, so let's begin.

0:28Why the surface pulls inward

So, let us start with the molecules. Deep inside a liquid, a molecule has other molecules all around it. Now take a molecule right at the surface. Where are its neighbours? On one side only! Yes, exactly! Below it, there is liquid. Above it, there is no liquid at all. With me? So the surface molecule has extra potential energy, and it is pulled inward, into the liquid. Because of this, the whole surface behaves like a stretched membrane, like the tight rubber skin of a balloon. Remember this picture. Everything today comes from it. Clear?

1:06Surface tension: force per unit length

Now, how do we measure this pull? Imagine a line of length capital L drawn in the surface. The surface on one side pulls on the other side with a force capital F, okay? Surface tension, capital T, equals F over L: the force per unit length. Unit: newton per metre. On screen, capital N is newton, and m to the power minus one means per metre. Careful: in this chapter, capital T is surface tension, not temperature. Got it? Now think. Which way does this force point? Straight up, out of the liquid? Or along the surface? Along the surface! Correct! The force acts in the surface, perpendicular to the line you drew, like a stretched sheet pulling sideways. Right? Quick question. You know the dimensions of force. Divide them by length. What do you get? M T to the power minus two! Very good! The square brackets mean dimensions. Force is MLT to the power minus two; divide by length, capital L, and M T to the power minus two is left. Careful: inside these brackets, capital M is mass and capital T is time, not surface tension. Okay?

2:23Surface energy: the same idea, as work

Now, the same idea, seen as energy. Every surface molecule carries extra potential energy, so more surface means more energy. Surface energy is the work needed to create unit area of new surface. So if the area grows by delta A, the work done is W equals T times delta A, okay? Delta, the little triangle, is the Greek capital letter that means change in. With me? Now, surface energy is in joule per square metre: capital J over m squared on screen. Surface tension is in newton per metre. Are these really different units? No, they are the same! One joule is one newton metre. So we get newton metre over metre squared; one metre cancels, and newton per metre is left. So surface tension is exactly the surface energy per unit area: two ways of looking at one thing. Right?

3:19Films, bubbles and drops: count the surfaces

Now, the most common trap in this topic. Dip a wire frame in soap solution, and you get a thin soap film. Tell me, how many surfaces does this film have? Two! Yes, exactly! The film has a front surface and a back surface, and both of them pull. Clear? So, if one side of the frame is a sliding wire of length capital L, each surface pulls on it with T times L, right? The force on the slider is F equals two T L, okay? In the same way, when the film's area grows by delta A, new surface forms on both sides, so the work is two T times delta A as well. Got it? Now, a soap bubble, and a drop of water. How many surfaces does each one have? The soap bubble has two, inside and outside, because it is a thin film. But a drop is liquid all the way through, so it has just one surface. Forget this factor of two, and your answer is half the correct value. Don't fall for it! With me?

4:21What changes surface tension

Alright, what changes surface tension? First, temperature. As the temperature rises, surface tension falls, and it becomes zero at the critical temperature. The double arrow you see means so, or implies. Okay? Next, what we dissolve in the water. Soaps and detergents lower the surface tension. But highly soluble salts raise it, only slightly. Clear? Now, back to our puzzle. When small drops merge into one bigger drop, what happens to the total surface area? Up, or down? It falls! Correct! Less surface means less surface energy. So energy equal to T times delta A is released, as heat. That is where the heat in our puzzle comes from! In example two, we will calculate it. Got it?

5:10Example 1: force on the sliding wire of a soap film

Now, Example one. Here, a soap film, with surface tension zero point zero three newton per metre, is held on a wire frame with a sliding wire, ten centimetres long. Find the force needed to hold the slider. Pause the video, and try it first. Done? Okay, let's check. Force equals T times L, zero point zero three times zero point one. Three times ten to the power minus three newton, right? No, no, careful! It is a soap film, so it has two surfaces. The force is F equals two T L, okay? And change to S I units first. Ten centimetres is zero point one metre. Right? So, F equals two times zero point zero three times zero point one. Six times ten to the power minus three newton. Six, not three! The film pulls with both its faces. Clear?

6:09Example 2: energy released when 8 water drops merge

Now, Example two, and this one is our puzzle. Eight water drops, each of radius one millimetre, merge into one drop. The surface tension is zero point zero seven five newton per metre. Find the energy released. Pause the video and try it. Hint: find the new radius first. Done? Let's see. Eight drops of radius one millimetre join together. So the new radius is eight millimetres, right? Oh no, careful! Radii do not add. Volumes do. The volume is kept the same: the big drop's volume, four thirds pi capital R cubed, equals eight times four thirds pi small r cubed. Capital R is the new radius, small r the old one, and pi is the Greek letter. So capital R cubed is eight r cubed, and capital R is two r: two millimetres. Clear? Now the areas. Each drop has one surface, remember? Before: eight drops, each four pi r squared. After: four pi times two r, whole squared, that is four times four pi r squared. Okay? So the area lost, delta A, is four pi times, eight r squared minus four r squared: sixteen pi r squared. Right? Now S I units. One millimetre is ten to the power minus three metre, so r squared is ten to the power minus six square metres. With me? Energy released equals T times delta A: zero point zero seven five, times sixteen pi, times ten to the power minus six. Zero point zero seven five times sixteen is one point two. One point two pi times ten to the power minus six is approximately three point eight times ten to the power minus six joule. The wavy equals sign means approximately. That tiny energy is the heat from our puzzle. Puzzle solved! Got it?

8:03Quick revision: T as F over L, surface energy, two surfaces

So, quick revision. Surface tension, capital T, is force per unit length, and it equals surface energy per unit area, with dimensions M T to the power minus two. Count the surfaces: a soap film and a soap bubble have two, a drop has one. Temperature up, surface tension down. And when drops merge, energy T times delta A is released as heat. Now go and try the practice problems on this page. All the best!