16.1 Internal energy
- Syllabus
- 9702–2028–2029
- Topic
- 16.1
- Level
- A2
Learning objectives
16.1.1Internal energy is determined by the state of the system and that it can be• understand that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated• With the molecules of a system16.1.2Relate a rise in temperature of an object to an increase in its internal• relate a rise in temperature of an object to an increase in its internal energy
Internal energy is the sum of random molecular kinetic and potential energies
The internal energy U of a system is the sum of the kinetic energies associated with the random motion of its molecules and the potential energies associated with their relative positions. U is determined by the state of the system.
| Included in internal energy | Not included |
|---|---|
| random translational, rotational and vibrational molecular kinetic energy | kinetic energy of the whole object moving |
| intermolecular potential energy from molecular separation/arrangement | gravitational potential energy of the whole object |
For fixed initial and final states, ΔU is fixed even if the transfer route differs. Heating and work describe energy crossing the system boundary; they are not energy contained as state quantities.
For an ideal gas, intermolecular forces are absent between collisions, so molecular potential energy is taken as zero. Its internal energy is therefore the total kinetic energy of random molecular motion.
Do not call internal energy “heat in the object”. Heating is a transfer process; internal energy is a microscopic energy store fixed by the system's state.
A rise in temperature increases an object's internal energy
temperaturerises→averagerandommolecularkineticenergyrises→totalmolecularkineticenergyrises→internalenergyUrises
Temperature indicates the average random kinetic energy of particles, not the total internal energy. Two objects at the same temperature can have different U because particle number, substance, phase and molecular potential energy can differ.
| Change | Molecular account | Internal energy |
|---|---|---|
| Temperature rises within one phase | average random KE rises | increases |
| Melting/boiling at constant temperature | average KE is unchanged; molecular separation and PE rise | increases |
| Elastic stretching at constant temperature | average KE is unchanged; molecular PE can rise | can increase |
For a fixed amount of ideal gas, molecular potential energy is zero, so U depends only on total random kinetic energy and therefore only on thermodynamic temperature. A decrease in U means a decrease in temperature.
A temperature rise guarantees an increase in internal energy, but the converse is not always true: internal energy can increase at constant temperature when molecular potential energy increases.