4. Thermal effects
Heating up P.18
Never heat up an aerosol. The pressure inside the can increases greatly when it is heated and may cause the can to burst.
Aerosol cans are tested for leaks once they have been filled. The cans are passed through a warm water bath. This heats the contents of the can, typically increasing the pressure to about 8 x 105 Pa (about 8 atmospheres). If there are any leaks or weak spots, these will reveal themselves with a trail of bubbles. There are sensors in the water bath that can detect the bubbles – they look for a difference in pressure between the top and bottom of the water. (Sometimes weak cans will explode in the water bath - it's better that they do so here under controlled conditions than when they have been sold.)

The cans spend at least 2 minutes in the water bath. They need to be in there for a couple of minutes because it takes time for the temperature inside to reach the temperature of the bath. There are two reasons for this:
  • the heat capacity of the can and its contents
  • the conductivity of the can and its contents.
What is heat capacity?
Heat capacity is a bit like thermal inertia (see box). It tells us how difficult it is to raise the temperature of something. We can define it as how much energy we have to provide to make its temperature go up by one degree Celsius.
For example, the heat capacity of 100 g of water (enough for a cup of tea) is 420 J °C-1. So it takes 420 joules to raise its temperature by 1 °C.

To take it from room temperature to boiling point is a rise of 80  °C.
So we would need: 80 x 420 J
33,600 J
or 34 KJ

Cup of tea for specific heat capacity
Picture 4.1. We have to heat 100 g of water to make a cup of tea. To make ten cups of tea, needs ten times as much heating.

The amount of heating we have to do is written as DQ or DQ. We can say that, for 100g of water:
DQ = 420 x q (q is the symbol for rise in temperature)
In general: DQ =  heat capacity x q
Being specific
The specific heat capacity of water is the heat capacity of 1 kg of water. The word ‘specific’ simply means ‘per kilogram’.

If we wanted to heat 1 kg of water (enough for ten cups of tea), it would take ten times as much energy as 100 g. So the heat capacity of 1 kg of water is 4,200 J  °C-1. In other words,
the specific heat capacity of water is:

cwater  4,200 J kg °C-1 [Notice that the units of specific heat capacity include per kg because that is what specific means. The usual symbol for specific heat capacity is c.]
Now let’s heat up 2kg of water (still heated through 80  °C). The amount of heating we need to do is:
DQ =  2 x 4200 x 80
672,000 J
In general, we can write:
DQ =  mass x specific heat capacity x rise in temperature
DQ =  m.c. q

Thermal inertia

Inertia is the resistance to change. It is particularly useful when thinking about forces and motion. It is a measure of how much a body (stationary or moving) does not want to accelerate. We can write Newton’s second law as:

Acceleration =  force

The force is what is trying to make the body accelerate (so it is on the top of the fraction). The mass is resisting the acceleration – pushing a bigger mass will give it a smaller acceleration. In this case, the mass is a measure of the body’s inertia.

Thermal inertia, is how much something resists having its temperature raised:

Temperature rise =  heating
heat capacity

The heating is trying to raise the temperature (on the top) and the heat capacity is resisting the change. The bigger the heat capacity, the more difficult it is to raise the temperature.

Question 14
Storage heaters use economy rate electricity to heat up some special bricks during the night. As these bricks cool down during the day, they heat up the room that they’re in; i.e. they have stored the energy.

a) Should the bricks have a high or low heat capacity?

Click shift/return to get a line break in your answer
b) Explain your answer.
c) Can you think of a mechanical equivalent of something that relies on inertia to store energy?

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Summary                                           Close
  • heat capacity is a measure of how much energy it takes to raise the temperature of an object
  • it's like thermal inertia - resistance to change in temperature
  • specific heat capacity is the heat capacity per kg
  • DQ = m.c. q