9702 · 14.1Thermal equilibrium

Thermal energy flows hot to cold

0:00Make a cup of tea and forget about it. Come back an hour later and it's cold. Take a can of drink out of the fridge and leave it on the table, and an hour later it's warm. One went down in temperature, the other went up, and both ended up in the same place: the temperature of the room. Nobody told them to stop there. So why does the tea stop cooling at room temperature, and not keep going until it freezes?

0:23In this video we'll answer that. We'll see which way thermal energy flows and why, what it means for two things to be in thermal equilibrium, and why that idea is the whole reason a thermometer works. You already know that all matter is made of particles that are constantly moving. In a gas they fly around, in a liquid they slide past each other, and in a solid they vibrate about fixed positions.

0:48For now, you only need one link between that picture and temperature: the higher the temperature of an object, the faster, on average, its particles are moving or vibrating. You'll make that link precise later in the series, when we get to the kinetic theory of gases. Now put a hot object and a cold object in contact. Say, a hot metal block pressed against a cold one. At the boundary, fast-vibrating particles from the hot block bump into slow-vibrating particles in the cold block.

1:17In a typical collision, the faster particle loses some energy and the slower one gains some. Collision after collision, energy is passed across the boundary. So the hot block cools, and the cold block warms. This is the first big idea. Thermal energy is transferred from a region of higher temperature to a region of lower temperature. It never happens the other way round on its own. And notice the word "region".

1:44This doesn't only apply to two separate objects. If one end of a metal rod is in a flame, energy flows along the rod from the hot end towards the cold end. Inside a single object, energy still moves from hotter parts to cooler parts.

Reaching thermal equilibrium

1:59Let's go back to our two metal blocks. As energy flows, the hot block's temperature falls and the cold block's temperature rises. The temperature difference between them gets smaller and smaller. Eventually, the two blocks reach the same temperature. At that point, there's no longer a higher-temperature region and a lower-temperature region. So there's no net transfer of thermal energy between them. When that happens, we say the two blocks are in thermal equilibrium.

2:26Here's the precise idea. Regions that are at the same temperature are in thermal equilibrium, which means there is no net transfer of thermal energy between them. That's why the tea stops at room temperature. Once it's at the same temperature as the room, it's in thermal equilibrium with its surroundings, and there's no net flow of energy out of it any more. The word net is the one that's easiest to skip over.

2:50So pay close attention to it. In thermal equilibrium, the particles haven't stopped moving, and they haven't stopped colliding across the boundary. Energy is still being passed from the left block to the right block, and from the right block to the left block, all the time. What's special about equilibrium is that these two flows are exactly balanced. On average, as much energy goes one way as comes back the other way.

3:13So the overall, or net, transfer is zero, and neither temperature changes.

Thermometers and equilibrium

3:19Now here's where this becomes really useful. How does a thermometer actually tell you the temperature of something? A thermometer can only ever measure its own temperature. When you put it into a liquid, energy flows between the thermometer and the liquid until the two are at the same temperature. Once they're in thermal equilibrium, the thermometer's temperature equals the liquid's temperature. So the reading on the thermometer is also the temperature of the liquid.

3:45That's also why you have to wait before reading a thermometer. If you read it straight away, it hasn't reached thermal equilibrium yet, and it's still showing a temperature somewhere between its starting value and the true value. You wait until the reading stops changing. And thermal equilibrium lets a thermometer compare things that never touch each other. Suppose you put a thermometer in beaker A and it settles at 40 degrees Celsius.

4:09You put it in beaker B and it also settles at 40 degrees Celsius. The thermometer was in thermal equilibrium with A, and with B. So A and B are at the same temperature, and if you pour them together, there will be no net energy transfer between them. In general: if two objects are each in thermal equilibrium with a third object, they're in thermal equilibrium with each other.

4:31This is sometimes called the zeroth law of thermodynamics, and it's what lets you trust that equal thermometer readings mean equal temperatures. Let's reason through a question step by step. A block of copper at 90 degrees Celsius is dropped into an insulated beaker of water at 20 degrees Celsius. Describe what happens, and state what is true when the system reaches thermal equilibrium. Step one: compare temperatures. The copper is at a higher temperature than the water, so thermal energy is transferred from the copper to the water.

5:05Step two: follow the temperatures. As energy leaves the copper, its temperature falls. As the water gains energy, its temperature rises. Step three: find the end point. The transfer continues until the copper and the water are at the same temperature. That final temperature must lie somewhere between 20 and 90 degrees Celsius. It can't go above 90, and it can't go below 20, because energy only flows while there's a temperature difference, and it always flows from hotter to colder.

5:36Step four: describe equilibrium. At the end, the copper and the water are at the same temperature, and there is no net transfer of thermal energy between them. Working out the exact final temperature needs specific heat capacity, which comes later in this chapter.

Common mistakes and exam answers

5:53Mistake one: thinking "cold" flows into things. When you hold an ice cube, cold isn't flowing into your hand. Energy is flowing out of your hand into the ice, because your hand is at the higher temperature. Mistake two: thinking energy flows from the object with more energy to the object with less. The direction is set by temperature, not by the amount of energy stored. A warm bath at 40 degrees stores far more energy than a small cup of tea at 80 degrees, simply because it contains so much more water.

6:26Now stand the cup of tea in the bath. Energy flows from the tea into the bath, because the tea is at the higher temperature. Mistake three: thinking that objects that feel different must be at different temperatures. Touch a metal table leg and a wooden table top in the same room. The metal feels colder. But both have been in the room for hours, so both are in thermal equilibrium with the room, and they're at the same temperature.

6:51The metal feels colder because it conducts energy away from your hand much faster than the wood does. Your hand senses how quickly it's losing energy, not the temperature of the object. Mistake four: saying that in thermal equilibrium "no energy is transferred". Energy is still being exchanged in both directions. The correct statement is that there is no net transfer of thermal energy. Questions on this sub-topic are short, but they reward precise wording.

7:20"Two objects are in thermal equilibrium. State what is meant by this." A good answer has two parts. First, the two objects are at the same temperature. Second, there is no net transfer of thermal energy between them. Leaving out the word "net" is the most common way to lose the mark. You might also be asked why a thermometer needs time before it gives a correct reading. The answer: it must reach thermal equilibrium with the object, so that it's at the same temperature as the object.

7:50Only then does its reading equal the object's temperature. Let's pull it together. Thermal energy is transferred from a region of higher temperature to a region of lower temperature, whether that's between two objects or between different parts of the same object. As energy flows, the temperature difference shrinks, until the regions reach the same temperature. Regions at the same temperature are in thermal equilibrium. There is no net transfer of thermal energy between them, even though energy is still being exchanged in both directions.

8:22A thermometer works because it reaches thermal equilibrium with whatever it's measuring, so its own temperature, which is what it reads, becomes the temperature of that object. In the next video, we'll look at what a thermometer actually measures, how temperature scales are built, and why there's a lowest possible temperature.