OCR Specification focus:
‘Internal energy equals the random kinetic plus potential energies of the system’s molecules.’
Internal energy describes the total microscopic energy stored within a system’s particles, combining both their motion and interactions. It underpins thermal behaviour, temperature changes, and phase transitions.
Understanding Internal Energy
Internal energy is a fundamental thermodynamic concept representing the total microscopic energy of all particles within a system. This includes both the energy due to motion of the particles (kinetic) and the energy due to their interactions or bonding (potential). It is a state function, meaning its value depends only on the system’s current state — not on the path taken to reach that state.
Internal Energy (U): The total of the random kinetic and potential energies of all molecules within a system.
In thermodynamics, internal energy provides the basis for understanding how energy is stored and transferred in physical systems, especially through heating, work, and changes of state.
Components of Internal Energy
Internal energy has two primary components that reflect different microscopic behaviours of matter.
Kinetic Energy of Molecules
The kinetic component arises from the random motion of particles in a substance. These motions include translation, rotation, and vibration, depending on the phase of matter:
Solids: Particles vibrate about fixed positions; energy is mostly vibrational kinetic energy.
Liquids: Particles move more freely, allowing translational and rotational motion in addition to vibration.
Gases: Particles move randomly at high speeds; kinetic energy dominates due to negligible intermolecular forces.
The average kinetic energy of molecules determines the temperature of a substance. An increase in temperature corresponds to a rise in molecular kinetic energy, raising internal energy.
Maxwell–Boltzmann distributions of molecular speeds for several temperatures; as temperature rises, the peak flattens and shifts to higher speeds, indicating greater average kinetic energy. This connects temperature directly to the kinetic portion of internal energy. Source.
Potential Energy of Molecules
The potential component arises from intermolecular forces and bond energies between particles. These forces depend on the distance between particles and the structure of the substance.
Graph of the Lennard-Jones potential showing steep short-range repulsion and longer-range attraction with a minimum at equilibrium separation. The well depth corresponds to the strength of intermolecular binding, i.e. the potential-energy contribution to internal energy. Extra detail beyond the syllabus: the specific 12–6 functional form is shown, a standard model for neutral atoms. Source.
In solids, strong attractive forces give a large negative potential energy since work must be done to separate particles.
In liquids, weaker forces result in a higher potential energy compared to solids.
In gases, particles are far apart with negligible forces, so potential energy is minimal.
Potential energy changes significantly during phase transitions, such as melting or boiling, even when temperature (and hence kinetic energy) remains constant.
Heating curve of water at 1 atm: sloped regions indicate temperature (kinetic energy) increase; horizontal plateaus show energy input changing potential energy as bonds are overcome during melting and boiling. Extra detail beyond the syllabus: labelled segments (A–F) and enthalpy terms may appear but can be omitted for simplicity. Source.
Relation Between Internal Energy and Temperature
For a fixed amount of a given substance, an increase in temperature means an increase in the average kinetic energy of the particles. Therefore:
EQUATION
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Average kinetic energy per particle (Eₖ) = (3/2)kT
Eₖ = Average kinetic energy of one molecule (J)
k = Boltzmann constant (1.38 × 10⁻²³ J K⁻¹)
T = Absolute temperature (K)
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This relationship demonstrates the link between temperature and the kinetic part of internal energy. However, internal energy itself includes both kinetic and potential contributions and therefore cannot be measured directly. Instead, changes in internal energy can be inferred through measurements of temperature, work, or heat transfer.
Factors Affecting Internal Energy
The internal energy of a system depends on several physical factors:
Temperature: Higher temperatures increase kinetic energy.
Phase of Matter: Different phases involve different potential energies due to intermolecular forces.
Mass and Composition: More particles (or greater mass) mean greater total energy content.
Intermolecular Forces: The strength and type of bonding influence potential energy.
These factors interact to define the total internal energy at any moment.
Changes in Internal Energy
When a system interacts with its surroundings, its internal energy can change through two key processes: heating and doing work.
Heating (Q): Transfer of energy due to a temperature difference, affecting mainly the kinetic component.
Work (W): Transfer of energy by macroscopic forces (for instance, compression or expansion in gases), affecting both kinetic and potential components.
EQUATION
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First Law of Thermodynamics: ΔU = Q + W
ΔU = Change in internal energy (J)
Q = Energy transferred as heat to the system (J)
W = Work done on the system (J)
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A positive ΔU indicates an increase in internal energy (system gains energy), while a negative ΔU indicates a decrease (system loses energy).
Internal Energy in Different States of Matter
Solids
Particles vibrate around fixed points with limited kinetic energy.
Strong intermolecular bonds lead to significant negative potential energy.
Total internal energy changes mostly through alterations in vibrational motion as the solid heats.
Liquids
Increased freedom of particle movement leads to higher kinetic energy.
Potential energy rises as intermolecular bonds weaken compared to solids.
Heating increases both kinetic and potential components.
Gases
Molecules move randomly at high speeds with minimal interactions.
Internal energy is dominated by kinetic energy.
Potential energy contributes negligibly except under high pressures or low temperatures.
Internal Energy and Phase Changes
During phase transitions, internal energy changes even though temperature may remain constant. For instance:
Melting: Heat energy increases potential energy as bonds weaken; temperature stays constant.
Boiling: Energy supplied overcomes intermolecular forces; kinetic energy remains steady, potential energy rises sharply.
Condensation/Freezing: Opposite processes where potential energy decreases as bonds form, releasing energy to surroundings.
These changes illustrate how internal energy encompasses both microscopic motion and interaction energy.
Measuring and Calculating Changes in Internal Energy
While absolute internal energy cannot be measured, changes in internal energy (ΔU) can be determined experimentally. This is often achieved by:
Measuring temperature change and calculating energy transferred using specific heat capacity.
Measuring work done on or by the system (e.g., in gas compression or expansion).
Accounting for latent heat during phase transitions.
Each of these approaches quantifies how the internal energy varies as energy is transferred to or from the system.
The Role of Internal Energy in Thermodynamics
Internal energy forms the foundation of thermodynamics, linking microscopic particle behaviour to macroscopic quantities such as temperature, pressure, and volume. It enables the explanation of:
Why heating increases temperature.
Why phase changes involve energy without temperature change.
How energy conservation applies to all physical processes through the First Law of Thermodynamics.
Understanding internal energy is therefore essential for explaining thermal phenomena, energy transfer, and the behaviour of matter across all states.
FAQ
Potential energy arises from electrostatic forces between charged particles—mainly attractions between oppositely charged ions or partial charges and repulsions between like charges.
In solids, these forces are strong and act over short distances, resulting in low (negative) potential energy. In gases, molecules are far apart, so potential energy is almost zero.
As particles move apart during melting or boiling, work is done against these forces, increasing potential energy even though temperature may not change.
Internal energy depends only on the current state of the system—defined by parameters such as temperature, pressure, and volume—not on how it reached that state.
For example, heating 1 kg of water from 20 °C to 30 °C gives the same change in internal energy whether heated slowly or rapidly.
Because of this, internal energy changes (ΔU) can be used in the First Law of Thermodynamics, where ΔU = Q + W depends only on the initial and final conditions.
When a substance is heated without a change of state, the energy supplied increases its internal energy, mainly through higher molecular kinetic energy.
The relationship is given by Q = mcΔT.
Here, Q represents the heat energy transferred, which equals the increase in internal energy (ΔU) if no work is done.
This shows that a material with a higher specific heat capacity requires more energy to produce the same temperature rise—indicating a greater increase in internal energy.
Yes. During processes such as condensation or freezing, temperature (and thus average kinetic energy) stays constant, but potential energy decreases as intermolecular bonds form.
The system releases energy to its surroundings, resulting in a decrease in internal energy. This explains why latent heat is released during phase changes that involve bond formation.
Internal energy consists of the microscopic energies of countless particles—both kinetic and potential—which cannot be measured individually.
Instead, only changes in internal energy (ΔU) can be determined experimentally through measurable quantities:
Temperature change, related to kinetic energy.
Work done on or by the system.
Heat transfer during heating or cooling.
Thus, we always refer to relative changes in internal energy between states, not an absolute value.
Practice Questions
Question 1 (2 marks)
Define internal energy and explain how it differs from the temperature of a substance.
Mark Scheme:
1 mark for correctly defining internal energy as the total of the random kinetic and potential energies of all the molecules in a system.
1 mark for clearly distinguishing it from temperature, stating that temperature measures the average kinetic energy of the particles, not the total energy.
Question 2 (5 marks)
A block of ice at 0 °C is placed in a container and allowed to melt completely into water at 0 °C.
Explain, in terms of changes to the internal energy of the system, what happens to the kinetic and potential energies of the molecules during this process.
Your answer should refer to the interactions between molecules and any energy transfers that occur.
Mark Scheme:
1 mark for recognising that the internal energy of the system increases as energy is supplied.
1 mark for stating that the temperature (and therefore the average kinetic energy of the molecules) remains constant during melting.
1 mark for explaining that the potential energy of the molecules increases because the intermolecular bonds are weakened or broken.
1 mark for describing that energy supplied as heat is used to overcome intermolecular forces rather than increase molecular motion.
1 mark for clearly linking the process to the definition of internal energy as the sum of kinetic and potential energies, noting that only the potential component changes during this phase transition.
