Lesson 1 of 6
Internal energy
I can describe internal energy as total random particle kinetic energy plus total potential energy between particles.Syllabus
Syllabus K323, 9(a). Describe internal energy as total random particle kinetic energy plus total potential energy between particles.
Make a guess. You are not marked.
A 2 kg block of iron and a 1 kg block of iron are both at 50 degrees C. Which has more internal energy?
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The 2 kg block, because it has twice as many particles.
At the same temperature the particles have the same average kinetic energy. The 2 kg block has twice as many particles, so its total internal energy is about twice as large.
Temperature describes an average property of the particles. Internal energy adds the motion and interaction energies of all the particles in the system.
A higher temperature corresponds to greater average random particle kinetic energy. Energy is measured in joules (J); a temperature reading in degrees Celsius is not a reading of the total energy stored.
Internal energy is an energy store made up of two particle contributions:
- The total kinetic energy associated with the random motion of the particles.
- The total potential energy between the particles, associated with their arrangement and interactions.
These are totals for the whole system, not the energy of one selected particle. The potential-energy contribution matters as well as the motion: changing the particles' arrangement can change internal energy without raising temperature.
Temperature is related to an average; internal energy is a total
Worked comparison
100 g and 200 g of the same liquid at 30°C
The two samples have the same average random kinetic energy per particle because they are the same substance at the same temperature.
The 200 g sample contains about twice as many particles. Adding their kinetic energies therefore gives about twice the total random kinetic energy, although the temperature has not doubled.
Internal energy also includes the total potential energy between those particles. Matching temperatures alone does not establish matching internal energies, and the temperature reading does not give a numerical value for either sample's internal energy.
For a fixed amount of one substance that stays in the same state, warming increases average random kinetic energy and increases internal energy. When comparing different samples, also consider the amount of material, the substance and its state. Temperature alone is not a complete energy comparison.
Keep motion of the whole body separate
A trolley moving across a room has a kinetic store associated with that overall motion. Its particles also move randomly and interact with one another; those contributions form its internal store.
Making the whole trolley move faster does not automatically mean its temperature has risen. Conversely, a stationary block can gain internal energy while its centre remains at rest.
Include both internal-energy contributions. "Total energy of moving particles" leaves out the potential energy between particles. "Average kinetic energy" describes the temperature relationship, not the full internal-energy store.
Check your understanding
Two samples of the same liquid, 100 g and 200 g, are both at 30 degrees C. Which statement correctly compares their particle energies?
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Same average kinetic energy per particle, but the 200 g sample has more in total.
The same substance at the same temperature has the same average random kinetic energy per particle. The 200 g sample has about twice as many particles, so its total random kinetic energy is about twice as large. The potential-energy contribution also belongs in a full internal-energy account.
Next, heat capacity relates an energy transfer to a temperature change. Changes of state show why internal energy can also change at constant temperature.