Internal Energy

In GCSE, you probably did an experiment where you took some ice, heated it steadily with an electric heater and measured the temperature as time passed. You should have got these results:

Even though you heated constantly, the temperature only rose sometimes. So where was the heat going when the temperature wasn’t rising?

Answer – it was being used to change the state of the water.

Remember in the energy topic we said that the energy of an atom was made up of two components – E_k and E_p. Well:

The E_k component relates to the temperature of the substance

The E_p component relates to the state of the substance.

So during times of increase of temperature (e.g. a, c and d from the graph) the heat energy supplied is going into the E_k component of the internal energy.

And during changes of state (e.g. b and d) it’s going to E_p. Because E_k isn’t changing during these times, the temperature remains the same.

Specific Heat Capacity

If you look back at the graph, the straight line sections suggest that to change the temperature of water by 1^oC takes a certain amount of energy whether the rise is from 1 to 2^oC or from 90 to 91^oC. This is true! The amount of energy required is called the Specific Heat Capacity.

The definition of Specific Heat Capacity is:

“The amount of energy required to raise the temperature of 1 kg (a unit mass) of the substance by 1^oC (a unit temperature rise)”

Symbol: c  Unit: Jkg^-1K^-1

where

is the heat energy added (or removed)

m is the mass of the substance you are heating (or cooling)

is the change in temperature.

Note – the value of ‘c’ for ice isn’t the same as that for water or for steam. However, the value of ‘c’ is the same if you are cooling rather than heating the substance. In other words you get as much heat back out of thee substance when you cool it as you put in when you heated it.

Specific Latent Heat

It takes a certain amount of energy to change the state of 1kg of water from solid to liquid. This amount of energy is called the Specific Latent Heat, l_f, of water

The definition:
“The amount of energy per kg (unit mass) required to change ice to water.”
Units: Jkg^-1

where:

is the heat energy added
m is the mass of the substance involved.

There is no temperature term involved in this equation as it all takes place at the same temperature.

Note that there are two occasions when you change state and both of these require different amounts of energy (as different things are happening to the atoms during the state changes). So there are two symbols.

l_f – latent heat of fusion – solid to liquid and back.

l_v – latent heat of vaporisation – liquid to gas and back.

You can actually have l_s – latent heat of sublimation – solid to gas and back. But you don’t often come across that.

So back to the graph.

a, c and e – Heat energy goes to change the E_k component. Specific heat capacity equations apply.

b and d – Heat energy goes to change the E_p component. Specific latent heat equations apply.