This section follows on from the previous section 4.1.1.2 in that it is about energy changes in systems, but this time it is specifically about how energy changes in systems as a result of a change of Temperature.

As before, we can calculate the size of the energy change, so once again we have an equation to use and to learn.

Calculating Changes in Thermal Energy

To do this we use the following equation:

This equation tells us that if we increase the temperature of an object then its thermal energy store increases.

That is not really a surprise, is it?

Equally, the equation tells us that if the temperature of an object falls then its thermal store decreases.

It is more interesting to notice two other factors that will affect by how much the thermal store rises or falls, apart from the temperature change;
these are:
1. the mass of the object, m and
2. a quantity known as the specific heat capacity, c of the material or substance.

The first factor tells us that a large mass will hold onto its thermal energy for longer than a small mass of the same material.
For example, a bath full of hot water will retain its thermal energy for a lot longer than a spoon full of hot water; the larger mass of water contains more thermal energy.

The second factor tells us that the material or substance itself is also important.
Some materials will heat up quickly but not hold a lot of thermal energy and so will cool down quickly; these have a low specific heat capacity. Concrete, brick and metals are materials with low specific heat capacity, c.
Other materials take longer to heat up but hold a lot of heat energy and so cool down more slowly; these have a high specific heat capacity. Water is a good example of a material with a high specific heat capacity, c.

Why does the fish love the specific heat capacity of water?

Because it is high and so it will not heat up or cool down quickly.
In other words, its temperature tends to stay fairly constant. That is what the fish wants!

Here is the official definition of Specific Heat Capacity:

Let's do an example of a calculation using the equation:

Notice how large is the specific heat capacity of water; it is almost 4200 J/Kg °C.
This means that water will store a lot of thermal energy for just a small rise in temperature.
This makes water a good choice as a liquid to be used in central heating systems where a tank of water can be heated up, storing a lot of thermal energy, and then the water can be pumped around a house, through many rooms, slowly releasing its thermal energy as it does so.

We are also fortunate that the Earth's oceans are water, because their temperature fluctuates only by a small amount due to the very high specific heat capacity of the water. This, on the other hand, is why scientists warn that even a small change in their temperature is a sign of a dramatic change to the global climate.

As you can see, the same mass of lead stores far less thermal energy than the water when raised by the same temperature.
This will also mean that the lead (and other metals) will lose its energy and its temperature will fall much faster than the water. This makes metals useful as cooling fins around the back of fridges or behind room radiators.