Systems, Equilibrium and the Zeroth Law

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. When you have a fever, you keep a thermometer under your tongue, and you wait for a minute. But think about it. The thermometer can only show its own state, like how far its own liquid has risen. So how can it tell you your temperature? Strange, right? Hold on to that question. The answer is a law called the zeroth law of thermodynamics. On the way, we learn the basic words of this whole unit. Quick concept questions on them do come up in JEE, so let's begin.

0:34System and surroundings

So, the first word: system. The system is the part of the universe under study, whatever we choose to look at. For example, the gas inside a cylinder, okay? And the rest of the universe is called the surroundings. For our gas, that means the cylinder, the piston, the air in the room, everything else. Clear?

0:53Open, closed and isolated systems

Now, a system can exchange two things with its surroundings: energy and matter. First, an open system exchanges both. Think of a pan of water boiling without a lid: heat comes in from the flame, and steam goes out. Right? Next, closed. In daily life, closed means shut tight, nothing in and nothing out. So tell me: can heat get into a closed system? Yes, it can! In thermodynamics, a closed system exchanges energy, but not matter. Keep a sealed bottle of water in the sun: no water gets in or out, but energy flows in, and the water warms up. Got it? And the third kind is isolated: it exchanges neither energy nor matter. Now careful here, because students often mix up closed and isolated. Closed blocks only matter; isolated blocks both. Okay?

1:51The state of a system

Now, even a small cylinder of gas has a huge number of molecules, all moving around. So, to describe the gas, must we track every single molecule? No, not at all! The state of a system is fixed by macroscopic state variables. Macroscopic means large scale: properties of the system as a whole, like the pressure we read on a gauge, or the temperature we read on a thermometer. With me? Here are the main ones: small p for pressure, capital V for volume, capital T for temperature, and capital U for internal energy, the energy stored inside the system. We study internal energy properly in the next concept. Right?

2:36Intensive and extensive variables

Now, two very useful words. Take a bucket of water at forty degrees Celsius; the small circle and capital C on screen mean degrees Celsius. Pour half of it into another bucket. What is the temperature of each half? Still forty degrees, of course! Temperature does not depend on the amount of matter, so we call it intensive. Pressure, p, and density are intensive too. Clear? But the mass of each half is halved. So is the volume, capital V, and so is capital U, the internal energy. These depend on the amount of matter, so they are extensive. Okay? So here is a quick trick. Imagine cutting the system into two equal halves. If a variable keeps the same value, it is intensive; if its value is halved, it is extensive. Got it? Now, a small trap. Mix two buckets of water, each at forty degrees Celsius. Forty plus forty, so the mixture is at eighty degrees, right? No, no, careful here! The mixture is still at forty degrees Celsius. The mass and the volume double, but temperature is intensive, so it does not add up. With me?

3:48Thermal equilibrium and the zeroth law

Now, the second word in our title: equilibrium. Put a hot body and a cold body in contact. Heat flows from the hotter one to the colder one, until no net heat flows between them. Then they are in thermal equilibrium. Clear? Now take three systems, called capital A, capital B and capital C here. System A is in thermal equilibrium with C, and system B is also in thermal equilibrium with C, okay? But A and B have never touched each other. So if we now put them in contact, will heat flow from one to the other? No, it will not! The double arrow on screen means implies: A and B are already in thermal equilibrium with each other. This is the zeroth law of thermodynamics: if each of two systems is in thermal equilibrium with a third, they are in thermal equilibrium with each other. Clear? And this law makes temperature a well-defined property: systems in thermal equilibrium have the same temperature. So the zeroth law is the law that gives us the concept of temperature. Got it?

4:54Why a thermometer works

Now, back to our puzzle. The thermometer is simply the third system, C, and your body is one of the other two. So tell me: why must we wait for a minute before we read it? Yes, exactly! The thermometer needs time to come to thermal equilibrium with your body. Read it too early, and it is still at a different temperature from you. Right? Once they are in thermal equilibrium, they have the same temperature. So the thermometer shows its own temperature, and that is exactly your temperature! That is why a thermometer works, and our puzzle is solved. With me?

5:31Example 1: is a closed thermos flask an isolated system?

Alright, Example one. Read it with me: a thermos flask with hot tea, tightly closed, is an approximation to which kind of system? Open, closed or isolated? Pause the video and try it first. Done? Okay, let's check. The flask is tightly closed. So the answer is a closed system, right? Wait, let us not answer so fast. Tightly closed tells us only one thing: no matter goes in or out. No tea leaks out, and no air gets in. Okay? But a thermos flask is also made to stop heat. It exchanges almost no heat with its surroundings; that is why the tea stays hot for so long. Clear? So no matter crosses over, and almost no heat either. That means it is an isolated system, approximately. Only approximately, because a little heat does leak out: leave it for a whole day, and the tea goes cold. Very good!

6:31Example 2: intensive or extensive, molar heat capacity trap

Now a longer one. Classify as intensive or extensive: pressure, volume, temperature, internal energy, density, mass, and molar heat capacity. Seven quantities. Use the halving trick. Pause the video and try it first. Done? Okay, let's check. Cut the system in half: the pressure, the temperature and the density stay the same. So these three are intensive. Right? But the volume, the internal energy and the mass are all halved. So these three are extensive. Okay? Now the last one, molar heat capacity, and this is the trap. The bigger the sample, the more heat it takes to warm it up, so this one is extensive, right? Oh no, be careful with this one! Look at the word molar: it means per mole. Halve the sample, and its heat capacity is halved, but the number of moles is halved too. So the value per mole stays the same, and molar heat capacity is intensive. That makes four intensive and three extensive. Very good!

7:38Quick revision: system types, intensive, extensive, 0th law

So, quick revision. Open systems exchange energy and matter; closed ones, only energy; isolated ones, neither. Intensive variables, like p, T and density, do not depend on the amount of matter; extensive ones, like V, U and mass, do. And the zeroth law: two systems in thermal equilibrium with a third are in thermal equilibrium with each other, so they have the same temperature. Now go and try the practice problems on this page. All the best!