Warming things up is an everyday occurrence

You pop a muffin in the microwave. You wrap your cold hands around a steaming mug of soup.

In each case three things happen:

• The temperature of the warmed object rises.
• The associated thermal store of energy fills a little.
• More energy is shared amongst the particles in the object being warmed, and they move around more.

All of these three aspects of warming up are linked and all happen together.

Warming in different ways

In two examples, the warming takes place in two different ways:

• By radiation (muffin in microwave) – the heating by radiation pathway.
• By conduction (cup warming hands, radiator warming socks) – the heating by particles pathway.

The last two need particles as a physical (particulate) link between the things doing the warming (the cup and the radiator) and the objects being warmed (the hands and the socks). Here the pathway from one store to another is warming by particles (see episode 03).

As the energy from the first thermal store (associated with the warm object) is shifted to the second thermal store, associated with the cooler object, one store is emptied and the other is filled. In the first example the muffin is warmed when electromagnetic radiation arrives, and this is an example of the warming by radiation pathway in action (see episode 03).

The connection between temperature and thermal energy

What is the relationship between the amount of energy in the thermal store of a warm object and the temperature of that object? In rather dated and unhelpful terms we might ask, what is the relationship between the heat energy in an object and its temperature?

To start off with, let's think about warming solids, taking care not to warm them so much that they melt and change from solid to liquid. As you warm the solid object, imagine that you keep a record of how much energy is shifted to the thermal store (no need to worry about how the energy is actually measured) and also that you measure the gradual rise in temperature of the object.

How do you expect the size of block, the quantity of energy shifted, and the temperature to be related?

Making hot chocolate

You might repeat this process, but this time thinking about warming a liquid. Imagine that you take 200 millilitre of milk from the fridge and pop in the microwave for 90 second at full power. The milk comes out just right for a hot chocolate.

You then take a further 300 ml of cold milk from the fridge to make another hot chocolate for a thirstier friend. You want to get the same drinking temperature for this greater amount of milk. It is clear that you need to put the milk in the microwave for longer to supply the extra energy for the extra liquid. In other words, the amount of energy you have to shift to achieve the same temperature depends on how much milk you have to warm.

Although not shown in this example, the quantity of energy also depends on how much you want to warm the milk. If you took the milk from a cooler fridge you would need to keep the milk in the microwave for longer to achieve the same final temperature.

Temperature and thermal energy store

Once the milk is heated up, the measured temperature does not depend on the amount of milk. For example, you might pour half of the warm milk into a separate cup. In each cup:

• The temperature of the milk is the same.
• The thermal energy stored in each cup is about half of the original (assuming not too much energy is shifted to the thermal store of the surroundings).

These observations can be linked to a particle model of the milk in each cup.

• The temperature is the same because on average the state of motion of the particles (how fast they are moving about) in both cups is the same.
• The thermal energy is halved because there is about half the number of particles moving around in each cup.

In general terms:

• The temperature of an object is related to the state of motion of its particles (the higher the temperature the faster moving are the particles).
• Temperature is termed an intensive quality since it does not depend upon the number of particles (or mass of substance) present.
• The energy in the thermal store of an object is related to the state of motion of its particles and the number of particles (a higher thermal energy follows from a larger number of faster moving particles).
• Thermal energy is an extensive quantity since it depends upon the number of particles (or mass of substance) present.

Conduction in solids: the particles do not change neighbours

Let's think about conduction in solids first. Here each particle vibrates but ends up going nowhere over the longer term. This is true of every particle, so each particle has fixed neighbours. In solids, only conduction is possible. Warm one end of a solid, and you get lots of vibration at one end, not so much at the other. The vibrations are transmitted from particle to particle, so gradually warming the whole solid object.

This is a good picture for what happens with electrical insulators, or non-metals. But metals, which can conduct electricity, also turn out to be better thermal conductors than non-metals. Why is this?

The clue is in the electrical conduction. Although the atoms are fixed, they share some of their electrons, and these are free to move within the metal. These electrons can shoot off from the hot end, with significant energy in their kinetic store. This energy is shared with the atoms at the cooler end, so warming these atoms more rapidly than if the sole mechanism was transfer of vibrations from atom to atom, as in the electrical insulators.

Overall, in solids the vibrations in one chunk of material are transmitted to the next but without any of the atoms having to move from one chunk to another.

Conduction and convection in liquids and gases, evaporation

For liquids and gases the picture is more complicated. Now the particles can change neighbours but it is still the case that more particle movement in one chunk can lead to more particle movement in the next, without the mass movement of the particles. However this transmission of movement in liquids and gases is not very effective. That is why air is such a good insulator. Your clothing relies on trapped pockets of air to keep you warm.

Where the particles are closer together, as in water, conduction is better precisely because it is easier for the random movements of the particles in one volume to affect the random movements of the particles in the next. But conduction in still not much better in water than it is in air. We rely on this in the design of wetsuits for diving that trap an insulating layer of water next to the skin.

Sometimes there is mass movement of particles, so whole volumes of fluid particles move, taking the energy in their thermal store on the journey. This is called convection, and the flow of such volumes results in convection currents.

Since convection relies on the floating and sinking of such volumes of fluid, the detailed discussion of convection is in the SPT: Motion topic.

The particles in liquids and gases are not all moving at the same speed. If you take some water in a glass, some particles move faster than others and therefore contribute more than an average amount to the thermal store of that water. Random collisions between the particles result in continuous redistribution of energy as particles speed up or slow down. If you selectively remove these faster particles, then the liquid cools. For liquids this process is called evaporation.

Evaporation occurs from liquids at all temperatures as particles escape from the body of the liquid. The fastest moving particles (with the greatest share of the energy in the thermal store) are those that have the greatest chance of escaping. As the fastest moving particles escape, the average speed of the remaining particles necessarily falls (remove the fastest particles and the average speed of those remaining must fall). The average energy per particle of the fluid therefore drops and so the temperature also falls. This fall in temperature is what keeps you cool when sweat evaporates from your skin.

Radiation

Radiation is quite different from both convection and conduction. Consider the case of warming by the Sun on a bright summer's day. As you feel the warmth of the Sun on your back, energy is shifted.

The radiation pathway does not rely on particles to allow warming to occur, but relies on electromagnetic radiation. We can be sure that warming is possible without particles just by remembering that there is a vacuum between the Earth and the Sun. In other words, there are no particles available to allow the warming to occur. The energy is shifted from the Sun to the Earth via electromagnetic radiation, and in this particular case the radiation acting is mainly infrared.

Electromagnetic radiation is best thought of as a stream of photons, or small packets of energy. Everything glows by emitting these photons – even the whole universe, with the afterglow of the Big Bang. Both the character and the number of photons emitted changes as the object gets warmer. If it gets hot enough, you can see the glow as it becomes red hot (or even white hot). In fact, you can often feel the stream of photons from an object at a lower temperature, even when you cannot see them.

Hold the back of your hand about 15 centimetre above a kitchen ring as it warms up. You can feel the warmth before you see the red glow. You feel infrared photons arriving at the back of your hand. A much more dangerous experiment would be to place your hand under the grill (we most certainly are not recommending this). Then you could be sure that moving warm particles plays little part (air is a very poor conductor) in the warming process since your hand would be below the heating element.

Everything glows

Because everything glows, emitting electromagnetic radiation, it follows that cooler objects also emit a stream of photons. So if two objects are placed close to each other in a vacuum (no energy shifted by the heating by particles pathway), each will warm the other by radiation. However the net flow of photons is from the hotter to the cooler, so the temperature of the cooler one rises and the temperature of the warmer one falls.

The energy in the thermal store is related to the temperature

The energy in the thermal store is not the same as the temperature of an object. But the temperature of an object can determine the rate at which energy accumulates in a thermal store. This rate of accumulation is the power in the different pathways.