Summary — What This Chapter Covers
- Internal energy is determined by the state of the system: the sum of a random distribution of molecular kinetic and potential energies.
- A rise in temperature means an increase in internal energy (the kinetic part increases).
- Work done when a gas changes volume at constant pressure: W = pΔV.
- First law: ΔU = q + W, where q is energy supplied by heating and W is work done ON the system.
1. Internal Energy
16.1
Kinetic plus potential, at random
The internal energy of a system is the sum of the random distribution of kinetic and potential energies of its molecules. It depends only on the state of the system (its pressure, volume, temperature and phase), not on how it reached that state.
The molecular kinetic energy is linked to temperature, so a rise in temperature means an increase in internal energy. The potential energy comes from intermolecular forces and changes when the separation of molecules changes, for example during melting or boiling, when the temperature is constant but internal energy still rises. In an ideal gas there are no intermolecular forces, so its internal energy is purely kinetic and depends only on T.
Practice Question
Ice at 0 °C melts into water at 0 °C. What happens to its internal energy, and to each component?
2. The First Law of Thermodynamics
16.2
ΔU = q + W
When a gas expands at constant pressure p by ΔV, it pushes the surroundings back and does work pΔV by the gas. When it is compressed, work pΔV is done on the gas. Be clear which one a question gives.
The first law is energy conservation: the increase in internal energy ΔU equals the energy transferred to the system by heating q plus the work done on the system W. In the 9702 convention every term is positive when energy goes into the gas. For expansion, W is negative.
First law and work
W = pΔV ΔU = q + W (q: heating of system; W: work done on system)
Worked Example
5
−3
3
−3
3
Memorise