Internal energy and energy transfers

Energy is stored inside a system by the particles — atoms and molecules — that make up the system. This is called internal energy.

Internal energy is the total kinetic energy and potential energy of all the particles that make up a system.

Both halves matter. The kinetic part is the energy of the particles' movement, and it is what temperature measures. The potential part is the energy stored because of the separation of the particles, and it is what changes when a substance melts or boils.

Heating changes the energy stored within the system by increasing the energy of the particles that make up the system. This either raises the temperature of the system, or produces a change of state — and which of the two happens is the whole of the rest of this sub-topic.

If the temperature of the system increases, the increase in temperature depends on the mass of the substance heated, the type of material, and the energy input to the system.

The following equation applies:

change in thermal energy = mass × specific heat capacity × temperature change ∆E = m c ∆θ

change in thermal energy, ∆E, in joules, J; mass, m, in kilograms, kg; specific heat capacity, c, in joules per kilogram per degree Celsius, J/kg °C; temperature change, ∆θ, in degrees Celsius, °C.

This equation is given on the Physics equation sheet. The specific heat capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius.

This equation and specific heat capacity also appear under energy changes in systems, along with the practical for measuring it.

The energy needed for a substance to change state is called latent heat. When a change of state occurs, the energy supplied changes the energy stored — the internal energy — but not the temperature.

That is the fact everything here turns on. During melting or boiling the thermometer reading does not move, even though energy is still being supplied. The energy is going into the potential part of the internal energy, breaking the forces holding the particles together, rather than into the kinetic part which temperature measures.

The specific latent heat of a substance is the amount of energy required to change the state of one kilogram of the substance with no change in temperature.

energy for a change of state = mass × specific latent heat E = m L

energy, E, in joules, J; mass, m, in kilograms, kg; specific latent heat, L, in joules per kilogram, J/kg. This equation is given on the Physics equation sheet.

You should be able to distinguish between specific heat capacity and specific latent heat. The distinction decides which equation to use:

• Specific heat capacity is about a temperature change with no change of state. Use ∆E = m c ∆θ. • Specific latent heat is about a change of state with no change in temperature. Use E = m L.

If a question has a temperature in it, you need the first. If it says melting, freezing, boiling or condensing at a fixed temperature, you need the second.

You should be able to interpret heating and cooling graphs that include changes of state.

These graphs plot temperature against time while energy is supplied or removed at a steady rate, and they have a characteristic shape: sloping sections separated by flat ones.

Two things can be read off directly. The temperature of a flat section is the melting point or the boiling point of the substance. The length of a flat section tells you how much energy the change of state required — the longer the flat section, the greater the latent heat, since energy is being supplied at a steady rate throughout.

A cooling graph is the same shape upside down, with flat sections where the substance freezes and condenses at the same temperatures.