OCR Specification focus:
‘Absolute zero, 0 K, is the lowest temperature where a substance has minimum internal energy.’
At absolute zero, all molecular motion theoretically stops, representing the point of minimum internal energy. This concept underpins thermodynamics, kinetic theory, and the absolute temperature scale.
Understanding Absolute Zero
Absolute zero (0 K) is the lowest possible temperature, the point where a system has the least possible internal energy. It defines the zero point of the Kelvin scale, a thermodynamic temperature scale based on fundamental physical laws rather than arbitrary reference points. While it is physically unattainable, it provides a critical theoretical limit for understanding how temperature relates to molecular motion and energy.
The Concept of Temperature and Energy
Temperature measures the average kinetic energy of the particles in a system. As temperature decreases, particles move more slowly. At absolute zero, the kinetic energy of particles becomes minimal — they no longer have sufficient energy to vibrate or translate freely. This links the microscopic motion of particles directly to macroscopic temperature readings.
Absolute Zero: The lowest possible temperature, 0 K, at which a system has minimum internal energy and molecular motion is at its theoretical minimum.
Even at this temperature, quantum mechanics implies that some residual energy, known as zero-point energy, remains. This ensures that particles are never completely motionless, preserving the principles of quantum uncertainty.
Energy levels of a quantum harmonic oscillator, showing the ground state above the potential minimum and labelled “ZPE.” This illustrates that internal energy has a minimum at 0 K but not zero, owing to quantum effects. Extra detail beyond the syllabus: explicit eigenstate curves show where the ZPE arises. Source.
The Kelvin Scale and Its Importance
The Kelvin temperature scale is the absolute or thermodynamic temperature scale used in scientific work. It begins at absolute zero (0 K) and increases linearly with the average kinetic energy of particles. Unlike the Celsius scale, which is based on the freezing and boiling points of water, the Kelvin scale reflects fundamental physical properties.
EQUATION
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Relationship between Celsius and Kelvin (T) = θ + 273
T = Absolute temperature (kelvin, K)
θ = Temperature in degrees Celsius (°C)
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Absolute zero provides a universal reference point for measuring temperature in scientific contexts.
A plot of gas pressure versus temperature at constant volume for several gases, with linear extrapolations meeting at 0 K. This shows why an absolute temperature scale begins at absolute zero. Extra detail beyond the syllabus: it uses ideal-gas behaviour to illustrate the lower temperature bound. Source.
It avoids negative values, allowing thermodynamic laws to be expressed in a consistent, mathematically robust way.
Internal Energy and Its Minimum Value
Internal energy refers to the total microscopic energy contained within a substance, arising from both the random kinetic energy of its particles and the potential energy associated with intermolecular forces.
Internal Energy: The sum of the random kinetic and potential energies of all particles in a system.
At absolute zero, this internal energy reaches its minimum value because:
The kinetic energy component is effectively zero — molecular vibrations and motion cease.
The potential energy component reaches its lowest possible value for a stable arrangement of atoms or molecules.
No further energy can be removed from the system.
This minimum does not imply a total absence of energy, as the quantum mechanical zero-point energy ensures a residual baseline energy exists even at 0 K.
Theoretical Implications of Absolute Zero
Absolute zero has profound implications for thermodynamics and statistical mechanics. It defines the lower limit of the temperature scale and is linked to the Third Law of Thermodynamics, which states that as the temperature of a perfect crystal approaches absolute zero, its entropy approaches zero.
Third Law of Thermodynamics: The entropy of a perfect crystal is zero at absolute zero.
Key consequences include:
No spontaneous processes can occur at absolute zero because all energy exchanges cease.
Entropy, a measure of disorder, reaches its minimum possible value.
A temperature–entropy diagram showing S → 0 as T → 0 K for a perfect crystal, illustrating the Third Law of Thermodynamics. Extra detail beyond the syllabus: the figure includes labelled phase-transition steps (solid–solid, melting, boiling) showing typical entropy jumps. Source.
Thermal equilibrium becomes meaningless, as no further energy transfer is possible.
These ideas highlight why absolute zero represents not just a numerical limit but a fundamental boundary in physical reality.
Experimental Approaches to Near-Absolute Zero
Although absolute zero cannot be reached, scientists have developed methods to approach it closely. Techniques used to cool substances to fractions of a kelvin include:
Laser cooling — slowing atomic motion using the momentum transfer from photons.
Adiabatic demagnetisation — reducing temperature by decreasing the magnetic field acting on certain materials, thereby lowering their energy states.
Evaporative cooling — selectively removing high-energy atoms from a trapped gas, reducing the average energy of the remaining atoms.
Each method relies on reducing the kinetic energy of particles, illustrating the connection between energy and temperature.
These experiments confirm the predictions of the kinetic theory of matter, providing evidence that as temperature decreases, particle motion diminishes and internal energy approaches its theoretical minimum.
Energy, Motion and Quantum Considerations
Classical physics once suggested that particles would be completely motionless at absolute zero. However, quantum mechanics reveals that particles cannot have precisely zero energy or position simultaneously — a principle known as the Heisenberg uncertainty principle. Thus, even at 0 K, zero-point energy persists, preventing total stillness.
Zero-Point Energy: The lowest possible energy a quantum mechanical system can have, even at absolute zero.
This quantum behaviour explains phenomena such as superfluidity and Bose–Einstein condensation, observed in matter cooled extremely close to 0 K. These states reveal how matter behaves when thermal motion becomes negligible, governed instead by quantum statistics.
Summary of Key Points
Absolute zero (0 K) is the theoretical limit of the temperature scale and represents minimum internal energy.
It is the zero point of the Kelvin scale, essential for thermodynamic calculations.
Internal energy includes both kinetic and potential molecular energy; at 0 K, these reach their lowest possible values.
Quantum effects prevent complete stillness — particles retain zero-point energy.
The Third Law of Thermodynamics connects absolute zero with minimal entropy in perfect crystals.
Experimental cooling techniques can approach, but never achieve, absolute zero.
FAQ
Absolute zero cannot be reached because removing the final fraction of energy from a system would require an infinite number of cooling steps or an infinitely long time.
Each cooling method—such as laser cooling or adiabatic demagnetisation—approaches, but never attains, 0 K. This is due to diminishing energy transfer as particles lose motion.
At extremely low temperatures, quantum effects dominate and prevent all motion from stopping entirely, ensuring that zero-point energy always remains.
In most metals, electrical resistance decreases as temperature falls because lattice vibrations (phonons) reduce, allowing electrons to move more freely.
However, in some materials known as superconductors, resistance suddenly drops to zero below a critical temperature.
This occurs because electrons pair up into Cooper pairs, moving without scattering. Although superconductivity is linked to low temperatures, it does not mean absolute zero is reached—quantum effects still persist.
As a system cools towards absolute zero, the number of accessible microstates decreases dramatically.
According to the Third Law of Thermodynamics, the entropy of a perfect crystal becomes zero at 0 K, since the particles occupy a single, perfectly ordered state.
In real substances, impurities or structural irregularities prevent perfect order, meaning entropy never truly reaches zero, only an extremely low value.
Evidence for zero-point energy appears in several low-temperature phenomena:
Helium remaining liquid at 0 K under normal pressure — the residual motion prevents freezing.
Spectroscopic measurements show energy levels do not reach zero, even at the lowest temperatures.
Quantum harmonic oscillator models predict a finite ground-state energy that matches observed data.
These observations confirm that even at absolute zero, systems retain minimal quantum motion.
The kinetic model links temperature to the average kinetic energy of particles. As temperature falls:
Particle movement (vibration, rotation, translation) slows.
Collisions become less frequent and less energetic.
The system’s internal energy decreases accordingly.
At 0 K, motion is at its lowest possible level, and no energy can be removed. The model thus provides a direct physical interpretation of absolute zero as the limit of particle motion.
Practice Questions
Question 1 (2 marks)
Explain what is meant by absolute zero and state its value in kelvin.
Mark scheme:
1 mark for stating that absolute zero is the lowest possible temperature / point of minimum internal energy where molecular motion is minimal.
1 mark for stating the value 0 K (or equivalent to –273 °C).
Question 2 (5 marks)
Describe and explain, in terms of the motion and energy of particles, what happens to a substance as its temperature decreases towards absolute zero. In your answer, refer to both kinetic and potential energy, and explain why a small amount of energy still remains at 0 K.
Mark scheme:
1 mark: Recognises that as temperature decreases, average kinetic energy of particles decreases.
1 mark: States that particle motion slows (reduced vibration or translation).
1 mark: States that potential energy also decreases as intermolecular forces hold particles in their most stable arrangement.
1 mark: States that at 0 K the internal energy is minimal, as both kinetic and potential energies are at their lowest.
1 mark: Explains that quantum zero-point energy prevents particles from being completely motionless due to the Heisenberg uncertainty principle, so a small residual energy remains even at absolute zero.
