State Functions and Kinds of Property

Transcript

0:00Introduction

Hello everyone! Two friends climb the same hill, from the same base camp to the same summit. One takes a short, steep path. The other takes a long, gentle one. At the top, who has gained more height? And who has walked more? One of these answers depends on the path, and the other does not care about the path at all. That difference is today's lesson: state functions and path functions, and then extensive and intensive properties. In JEE, quick questions on these come up often. So, let's begin.

0:36State functions: only the present state matters

So, back to our two climbers. Same base camp, same summit. Who gained more height? Same for both, yes, exactly! Height gained depends only on where you start and where you stop. And that is exactly what a state function is: it depends only on the present state of the system, not on how the system got there. Okay? So, which quantities behave like this? Capital P, pressure. Capital V, volume. Capital T, temperature. Capital U, the internal energy. Capital H, enthalpy. Capital S, entropy. And capital G, the Gibbs energy. Learn these seven well. Right? So, the change in a state function depends only on the initial state and the final state. The route in between does not matter. Clear? Now think. Our climber goes up to the summit, and then comes back down to the base camp. Net height gained on the full trip? Zero, correct! Same in thermodynamics: when a system goes round a cycle and comes back to its starting state, every state function has zero change. The little triangle on screen is the capital Greek letter delta, and it means change in. So round a cycle, delta U, delta H and delta T are all zero. Got it?

1:57Path functions: heat and work

Now the other answer: the distance walked. The gentle path is much longer, right? So distance depends on the route. Anything that depends on the route taken is called a path function. With me? And in thermodynamics, the two famous path functions are heat and work: small q for heat, and small w for work. Go between the same two states by different routes, and in general, q and w will be different. Okay? Now here is a beautiful question. Heat depends on the path. Work depends on the path. So their sum, q plus w, must also depend on the path, right? No, no, careful! Their sum, q plus w, equals delta U, the change in internal energy. And U is a state function, so delta U is fixed by the initial and final states alone. Heat and work change from route to route, but their sum stays the same. Remember this line; Example two is built on it. Clear?

2:58Extensive and intensive properties

Alright, now a second way to sort properties. Take a bucket of water, and pour out half of it. What changes: the mass of the water, or its temperature? The mass, yes! It becomes half, but the temperature stays the same. So, properties like mass depend on the amount of matter. We call them extensive. And they are additive: put two portions together, and you add their values. Okay? Here are the extensive ones: mass and volume, then U, H, S and G, our internal energy, enthalpy, entropy and Gibbs energy, then heat capacity, and the number of moles. Double the matter, and each one doubles. Right? And temperature? It did not care about the amount at all. Such properties are called intensive. They do not depend on the amount of matter. Clear? The list: T, temperature, and P, pressure. Then density, concentration, refractive index, viscosity, and surface tension. And the last one, e m f, the electromotive force of a cell. These stay the same for any amount of matter. Got it?

4:06Topper's trick: a ratio of two extensives

Now, a lovely trick. Mass is extensive. Volume is extensive. So density, which is made from mass and volume, must be extensive too, right? No, no, wait! Double the matter, and the mass doubles, but the volume doubles too. So their ratio does not change at all. The ratio of two extensive properties is intensive. That's the trick. Okay? Density equals m over V, mass over volume; the fraction bar means divided by. And molar volume equals V over n, volume over small n, the number of moles. Both are intensive. With me? And this gives a quick rule. Molar means per mole, and specific means per unit mass. So every molar or specific quantity is a ratio like this, and it is intensive. Right? Now, the classic trap. Heat capacity is extensive. But molar heat capacity and specific heat are intensive, because they are the heat capacity divided by the amount, or by the mass. Similar names, different groups. Don't mix them up! Clear?

5:12Example 1: classify 8 properties as extensive or intensive

Okay, time for Example one. Classify each of these as extensive or intensive: mass, density, heat capacity, specific heat, molarity, enthalpy, viscosity, and the e m f of a cell. Pause the video, and try it first. Done? Okay, let's check. Heat capacity and specific heat. They sound like twins, so they go in the same group, right? Oh no, careful! That is the trap we just saw. Heat capacity goes here, but specific heat does not. Extensive: mass, heat capacity, and enthalpy. Three properties that grow when the amount of matter grows. Okay? Everything else is intensive: density, specific heat, molarity, viscosity, and the e m f of the cell. Five of them. Right? And how do you catch density, specific heat and molarity so quickly? Each one is a ratio of two extensive properties: mass over volume, heat capacity over mass, and moles of solute over volume of solution. So, intensive. As simple as that!

6:22Example 2: heat absorbed on path II, with Delta U fixed

Now Example two, a little harder. Here, a system goes from state A to state B by path one, absorbing fifty joules of heat, while twenty joules of work is done by it. By path two, it does thirty five joules of work. The capital J on screen means joules, and the paths are written with the Roman numerals one and two. How much heat does it absorb along path two? Pause the video, and try it. Done? Okay, let's check. Same start, same end. So the heat absorbed along path two is fifty joules again, right? No, no, careful! Heat is a path function, so it can change with the route. Now the sign convention of this course. Heat absorbed by the system is positive, so along path one, q is plus fifty joules. Work done by the system is negative, so w is minus twenty joules. With me? Now, delta U equals q plus w. Fifty minus twenty: thirty joules. Okay? Now path two. The heat and the work both change. But what stays exactly the same? Delta U, exactly! U is a state function, so delta U depends only on state A and state B, nothing else. So along path two, delta U is thirty joules too. Just like the height of our summit! Got it? So, along path two, the system does thirty five joules of work, so w is minus thirty five. Thirty equals q minus thirty five. The arrow on screen means which gives: q equals sixty five joules! More work done by the system, so more heat absorbed, and delta U stays at thirty. That's it!

8:08Quick revision: state vs path functions, kinds of property

So, quick revision. One: a state function depends only on the state, and its change round a cycle is zero. Two: heat q and work w are path functions, but q plus w equals delta U, which is fixed by the two states. Three: extensive properties depend on the amount, intensive ones do not, and extensive over extensive is intensive. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!