HEAT AND EXPANSION EXPLAINED BY MR. AKINS

I have pleasure in introducing you to another interesting topic in Physics, as discussed in my last class when I appeared to you in person. Now, let us consider thermal expansion.

What Is Thermal Expansion?

If it wasn't for our understanding of thermal expansion, bridges would collapse, jars would remain unopened for years and we would have no way to measure the temperature. But on the bright side, a few less people would run out of gas next summer. Confused? All will make sense after today's lesson.

Thermal expansion is where materials expand while being heated, causing them to take up more space. Some materials expand more than others - metals, for example, tend to expand a lot. But this all happens due to the motion of tiny little molecules.

Temperature is the average kinetic energy of the molecules in a substance. So that means, if we heat something up, we are making the molecules move faster. Molecules that move faster tend to take up more space, and that's why materials expand when you heat them and contract when you cool them.

Examples of Thermal Expansion

Okay, so let's go through a few examples of thermal expansion. I said at the start of the lesson that bridges would collapse if we didn't understand thermal expansion, and that's true. Bridges have a feature called an expansion joint, containing little jagged teeth with a cap in-between. If the bridge material expands and the bridge gets longer, the teeth move closer together, and if it contracts, they move further apart. This allows the bridge to change in length without it, you know . . . collapsing in a chaotic mess of broken metal and falling cars.

Another example? Opening a tight jar; when you can't open a jar, what do you do? Well, there are a lot of tricks. Maybe you tap the lid of the jar against the counter to break the seal. Maybe you use one of those grippy rubbery things - that's a technical term. But one way you can open a tight jar is by running the lid under a hot tap. This causes the lid to expand. But wouldn't an expanding lid make it tighter?

To explain this, imagine heating up a doughnut-shaped piece of metal. Mm . . . doughnuts. Does the doughnut hole get larger or smaller? People sometimes think smaller, because they imagine the expanding doughnut filling the hole, but if the complete shape expands, the hole also gets larger. So if you heat up a jar lid, the gaps between the lid and the glass threads get larger, making it easier to open.

A thermometer also works by expansion. The liquid in a thermometer - which used to be mercury, but is now usually an alcohol of some kind - expands as it gets hotter, and the marks on the glass are calibrated to tell you the temperature based on how much the liquid's expanded.

Okay, one more example: the gas gauge on a car. People are much more likely to run out of gas in the summer than the winter. Why is that? Well, the gas in your car expands, like anything else, and changes the reading on your fuel gauge. In the summer, the gas takes up more space in the tank, and so when it reads empty, there's significantly less fuel left in the tank than in winter. Maybe you get an extra 35 miles after it hits empty in the winter, but that won't be the case in the heat of summer. So, be careful out there! Don't be the fool who has to walk three miles to the gas station because they don't know about thermal expansion.

Linear Expansivity

Most solids (and liquids*) expand when the temperature increases. According to the Kinetic Theory of Matter, the expansion is due to the increased amplitude of vibration of the particles. *see below for an important exception Consider a metal rod of original length, Lo Let the temperature change by ΔT, causing an increases in length, ΔL, as shown below. Experiments show that, for a wide range of temperatures, ΔL is directly proportional to ΔT. Now consider a rod of original length 2Lo (made of the same metal). Along the length of this rod there will be twice as many "layers" of atoms all increasing their amplitudes of vibration as the temperature increases.  We would therefore expect this rod to expand by 2ΔL, for the same increase in temperature. Experiments confirm this hypothesis. Summarizing the above: therefore which means that The constant is called the linear expansivity of the metal, given the symbol a (which is why I kept writing out "is proportional to"!). Definition: The linear expansivity of a substance is the fractional change in length of a sample of the substance per degree C change in temperature. units °C-1 (or K-1) Rearranging the above equation gives an expression for finding the length, L, of a sample of material, after a given temperature change, ΔT. The "Anomalous" Expansion of Water The important exception, mentioned above, is the case of water. Although most substances expand when the temperature increases and contract when the temperature decreases, water does the opposite but just between 0°C and 4°C in other words, just in the region where it is changing into ice. The shape of a water molecule is something like this: The next diagram shows a group of water molecules in a sample that we will imagine is at, say, 20°C (so, well away from its freezing point). The continual oscillation of the molecules prevents them from forming bonds and the substance is in the liquid state. However, if we decrease the temperature, the amplitude of the oscillations decreases and the molecules start to bond together in a more regular arrangement which takes up a bit more space, as shown here. The forces resulting from this expansion can be quite large. If water freezes inside sealed pipes in winter, the pipes can be damaged. Water freezing in cracks in roads sometimes damages the road surface as this expansion occurs. However, there is some good news here. Fish in ponds can survive in winter because the frozen water, being less dense, floats up to the surface and then prevents the whole pond from freezing (unless, of course, the temperature goes unusually low).

Now, let us consider how heat of different bodies are calculated. But before that, let me put you through some simple explanations on Thermal Energy.

The Heat Capacity of a Body

Consider the two pans shown below. The pans are of a similar type but different size.  Each pan is filled with water. They are placed on heaters having the same power. In which pan would the water boil first? (Don't worry, it's not a trick question...) Obviously, the smaller one. This is easily explained: The temperature of a body is a measure of the average kinetic energy of the particles of the body. If both bodies are supplied with energy at the same rate, then the one containing the greater number of particles will require longer to change the temperature by a given amount. To describe this situation, we say that the bigger pan of water has a greater heat capacity then the smaller one. Definition: The heat capacity of a body is the quantity of energy needed to cause its temperature to change by 1°C. Therefore, the units of heat capacity are J°C-1 or JK-1 (remember that the size of the degree is the same on the Celsius and Kelvin scales). The heat capacity of a body depends on: 1. the substances it is made of 2. the masses of the different substances in the body. The heat capacity of a body is clearly a useful figure to know, however, imagine that you were to sit down and write a list of the heat capacities of all the bodies you could think of... 't'  would be quite a long list, I think! More useful still would be a list from which the heat capacities of different bodies could be calculated. The Specific Heat Capacity of a Substance (c) Considering again the two pans of water. Suppose that the small pan holds 1kg of water and the larger one holds 3kg of water. It is reasonable to expect that to change the temperature of the 3kg of water, by a given amount, will require three times as much energy as to change the temperature of the 1kg of water. We are assuming that 1kg of water always needs the same quantity of energy to change its temperature by a given amount. We now define the specific heat capacity of a substance as follows: The specific heat capacity of a substance is the quantity of energy needed to change the temperature of 1kg of the substance by 1°C. So, the units of specific heat capacity are Jkg-1°C-1 or Jkg-1K-1 It is perfectly reasonable to imagine a fairly exhaustive list of specific heat capacities of different substances from which we can then calculate the heat capacity of any body we might find (assuming we also know the masses of the different substances, of course). From this definition we have the following useful equation to calculate the quantity of energy, Q, needed to change the temperature, ΔT, of a given mass, m, of a known substance: Comparing the Specific Heat Capacities of Different Substances To change the temperature of a body means to change the average kinetic energy of its particles. The particles of different substances have different masses. The number of particles in 1kg of a substance obviously depends on the mass of those particles. This explains why different substances have different specific heat capacities. For example, the mass of an atom of iron is about twice the mass of an atom of aluminium. So, 1kg of aluminium must contain about twice as many atoms as 1kg of iron. We would therefore expect the specific heat capacity of aluminium to be about twice that of iron. ciron 460Jkg-1°C-1 caluminium 908Jkg-1°C-1 ...I rest my case... NB The specific heat capacity of water is high compared with most other substances, cwater = (approximately) 4200Jkg-1°C-1, which means that water requires lots of energy to change its temperature. Remember this next time you take a shower... Should you have a question, contact your instructor on 08160001151  or comment on the comment link below.