Lesson summary
16.1.1 Internal Energy — AS PHYSICS 9702 notes: Define internal energy and relate it to temperature, changes of state and ideal gases.Internal energy U — the sum of the random distribution of kinetic and potential energies of the atoms or molecules of a system, measured in joules…
- Exclusions
- Kinetic part
- Potential part
- Exam wording
- Temperature rise
- Amount of substance
Section 1 of 9Definition of internal energy
Definition of internal energy
Internal energy U
- Internal energy U the sum of the random distribution of kinetic and potential energies of the atoms or molecules of a system, measured in joules
Exclusions
- Exclusions the kinetic energy of the object as a whole and the gravitational potential energy from its position
Kinetic part
- Kinetic part from the random motion of the particles, including translation, rotation and vibration
Potential part
- Potential part from the forces between the particles, which increases as they are pulled further apart against attraction
Exam wording
- Exam wording include the words random motion or random distribution
Section 2 of 9Temperature and internal energy
Temperature
- Temperature a measure of the average random kinetic energy of the particles
Temperature rise
- Temperature rise the mean kinetic energy and so the internal energy increases
Amount of substance
- 100 kg of water at 20 °C has 100 times the internal energy of 1 kg at 20 °C
Different states
- Different states water at 0 °C has more internal energy than ice at 0 °C, with the same mean kinetic energy but greater potential energy
Solids and liquids
- Solids and liquids molecules are bound by intermolecular forces, so they have both energies and vibrate more when heated
Real gas
- Real gas molecules have both forms of energy and move faster when heated
Section 3 of 9Changes of state
Constant temperature
- Constant temperature the mean kinetic energy of the particles does not change
Energy supplied
- Energy supplied it raises the potential energy as particles are separated against attraction
Melting
- Melting a modest rise in potential energy frees particles from fixed positions
Boiling
- Boiling a much larger rise separates them almost completely
Size of the change
- ΔU is approximately mL, plus a small amount of work against the atmosphere when the volume changes
Section 4 of 9Internal energy of an ideal gas
1No potential energy
- No potential energy there are no forces between molecules except in collisions, so internal energy is entirely random kinetic energy
2Monatomic gas
- U = (3/2)NkT = (3/2)nRT
3Depends on temperature only
- Depends on temperature only not on pressure or volume
4Change
- ΔU = (3/2)nRΔT, so if T is constant ΔU is zero even if p and V change greatly
5Proportionality
- ΔU ∝ ΔT, and U ∝ T with T in kelvin
6Polyatomic gases
- Polyatomic gases they also have rotational and vibrational contributions, but still depend on temperature alone
Section 5 of 9Ways to change internal energy
Increase
- Increase do work on the system or add thermal energy by heating
Decrease
- Decrease lose thermal energy to the surroundings or do work on the surroundings, such as a gas pushing a piston
Examples
- Examples rubbing hands raises U by work against friction, a radiator does it by heat transfer, and compressing air in a pump warms it
Language
- Language an object contains internal energy, not heat; heat is energy in transit
Section 6 of 9Comparing the three states
| State | Particle behaviour | Energy |
|---|---|---|
| Solid | Vibrate about fixed positions, held close by strong forces | Potential energy strongly negative, kinetic mostly vibrational |
| Liquid | Close but able to move past each other | Potential energy higher than in the solid |
| Gas | Far apart with tiny forces | Potential energy close to zero, internal energy essentially all kinetic |
Ranking
- Ranking at the same temperature and mass, internal energy is gas greater than liquid greater than solid, with the gaps being the latent heats
Graph of U against temperature
- Graph of U against temperature rising lines joined by steps at the melting and boiling points
- The steepness of each line is set by the specific heat capacity of that state
Section 7 of 9More from the specification
More from the specification
Internal Energy of an Ideal Gas
- The internal energy U of an ideal gas consists entirely of the random translational kinetic energy of its particles, with zero intermolecular potential energy.
Direct Proportionality to Thermodynamic Temperature
- For an ideal gas, total internal energy is directly proportional to thermodynamic temperature (U ∝ T); if the thermodynamic temperature triples, the internal energy also triples.
- (e.g. from 100 K to 300 K)
Temperature Units Consideration
- A common pitfall occurs when temperature is measured in degrees Celsius: if a temperature increases from 10 °C to 30 °C, the temperature value in Celsius triples,
- but because thermodynamic temperature changes from 283.15 K to 303.15 K, the thermodynamic temperature has not tripled and internal energy does not triple.
Thermodynamic temperature
- The absolute temperature in kelvin.
Directly proportional
- Two quantities increase together in a constant ratio, giving a straight line through the origin.
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Internal energy | the sum of the random distribution of kinetic and potential energies of the particles |
| Intermolecular potential energy | energy stored in the forces between particles, depending on their separation |
| Monatomic gas | a gas whose particles are single atoms with only translational energy |
| Heat | energy transferred because of a temperature difference |
| Latent heat | energy supplied or released in a change of state at constant temperature |
| Ideal gas | a gas with no intermolecular forces except in collisions |
Section 9 of 9Exam technique
1
Leaving out "random" in the definition — marks are lost without random motion or random distribution.
2
Saying an object contains heat — it contains internal energy.
3
Tripling U when Celsius temperature triples — use kelvin, since 50 °C to 150 °C is only a factor of 1.3.
4
Saying temperature rises during a change of state — the temperature stays constant while U increases.
Marked practiceQuizzes for this lesson
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- RNA: 5′ → 3′ 3′ → 5′.
- : AUG UAC .
- : UAA, UAG, UGA tRNA (Release Factor) .