Internal energy (CIE A Level Physics)

• Internal energy, U is determined by the state of the system
  • Temperature
  • The random motion of molecules
  • The state of matter: gases have the highest internal energy, solids have the lowest
  • Intermolecular interactions between the particles 

• The molecules of all substances have both kinetic and potential energies
  • Kinetic energy is due to the speed of the molecules
  • Potential energy is due to the intermolecular forces between the molecules and varies with the separation of particles

• The internal energy of a substance is defined as:

The sum of the random distribution of kinetic and potential energies within a system of molecules

Internal energy of water molecules

All molecules in a substance possess both kinetic and potential energies

• The internal energy of a system can increase by:
  • Doing work on it
  • Adding thermal energy to it (heating it)

• The internal energy of a system can decrease by:
  • Losing thermal energy to its surroundings
  • The system doing work on its surroundings (e.g. a gas pushing a piston)

• The rise in temperature of an object is related to an increase in its internal energy
• Molecules in solids and liquids are close together and bound by intermolecular forces, so have kinetic and potential energy
  • Molecules in a solids and liquids are tightly packed, so begin to vibrate more when heated
• Molecules in a gas have no intermolecular forces so have no potential energy, only kinetic energy
  • When a container of gas molecules is heated, the molecules begin to move around faster, increasing their kinetic energy
• The change in internal energy of an ideal gas is proportional to the change in temperature, and can be written as:

ΔU ∝ ΔT

• Where:
  • ΔU = change in internal energy (J)
  • ΔT = change in temperature (K)

Molecular movement at low and high temperatures

As the container is heated up, the gas molecules move faster with higher kinetic energy and therefore higher internal energy