OCR Specification focus:
‘The thermodynamic scale defines absolute temperature independent of any substance’s properties.’
The absolute temperature scale is fundamental in physics, providing a universal measure of temperature that is independent of material properties. It underpins thermodynamics, energy transfer, and molecular motion studies.
Understanding the Absolute Temperature Scale
The Concept of Temperature
Temperature is a measure of the average kinetic energy of particles within a system. As the kinetic energy of particles increases, so does the temperature. Traditional scales such as Celsius (°C) and Fahrenheit (°F) are based on the behaviour of specific substances—water in particular. However, these scales are limited by their dependence on the physical properties of chosen materials.
The Thermodynamic or Absolute Scale
The thermodynamic scale—also called the absolute temperature scale—eliminates these limitations by defining temperature in a way that is independent of any specific material. It is a scale derived from fundamental physical laws rather than empirical reference points.
Absolute Temperature Scale: A temperature scale defined by the laws of thermodynamics, independent of the physical properties of any substance, with absolute zero as its lowest limit.
The scale starts from absolute zero, the theoretical temperature at which all molecular motion ceases. This makes it a universal reference for comparing temperatures across all physical systems.
Absolute Zero
Absolute zero (0 K) represents the point at which a system has minimum internal energy. At this temperature, the particles in a substance have no random motion—though in reality, absolute zero can never be reached, only approached. Absolute zero provides the natural zero point for the thermodynamic scale, ensuring there are no negative temperature values.
Absolute Zero: The lowest possible temperature, 0 K, where a system’s internal energy is at a minimum and molecular motion theoretically ceases.
Relationship Between the Kelvin and Celsius Scales
The kelvin (K) is the SI unit of temperature. It is directly linked to the Celsius scale but shifted such that 0 K corresponds to -273.15 °C. This relationship ensures continuity between scientific and everyday temperature measurements.
A labelled thermometer comparing Kelvin and Celsius scales. It marks absolute zero (0 K) and shows that both scales have identical increments but different zero points. The triple point of water (273.16 K, 0.01 °C) is also indicated; this historical reference is included but not required by the current definition. Source.
EQUATION
—-----------------------------------------------------------------
Temperature Conversion (T) = θ + 273.15
T = Temperature in kelvin (K)
θ = Temperature in degrees Celsius (°C)
—-----------------------------------------------------------------
Although the Celsius scale is useful for daily use, the Kelvin scale is preferred in scientific contexts because it aligns directly with the energy of particles, as described by the kinetic theory of gases and thermodynamics.
Why Independence from Substance Matters
The absolute scale’s defining feature—independence from substance—makes it universal. It is not based on specific material properties (such as the expansion of mercury or water’s phase changes) but on fundamental physical constants and thermodynamic laws.
This independence allows:
Accurate comparisons of temperature across different systems.
Application in theoretical physics and cosmology.
Consistent use in equations describing gas behaviour and energy transfer.
For instance, in the ideal gas law, the absolute temperature directly determines the energy of gas molecules, making the Kelvin scale indispensable.
The Thermodynamic Definition of Temperature
In thermodynamics, temperature is formally defined through heat transfer and entropy. It quantifies how energy moves between systems.
Thermodynamic Temperature: A measure of temperature based on the ratio of heat transfer to the change in entropy between two bodies in thermal equilibrium.
This definition forms the foundation of the absolute temperature scale, connecting it directly to the second law of thermodynamics, which governs energy exchange.
Establishing the Kelvin Scale
The modern Kelvin scale was defined in relation to absolute zero and the triple point of water—the temperature and pressure at which water can coexist in all three states: solid, liquid, and gas.
A phase diagram showing solid, liquid, and gas regions with the triple point at their intersection. This illustrates the thermodynamic state used historically to anchor temperature scales. The diagram is generic; it conveys the triple-point concept without water-specific pressures. Source.
Historically, this provided a reproducible reference point.
A triple-point of water (TPW) cell used for precision thermometer calibration at 273.16 K. Although the kelvin is now defined via a fixed Boltzmann constant, TPW cells remain important practical references. The apparatus detail is extra to the syllabus but clarifies how thermodynamic temperature is realised experimentally. Source.
However, in 2019, the Kelvin was redefined based on a fundamental constant of nature rather than the properties of water. The current definition fixes the Boltzmann constant (k) to a precise value, linking temperature directly to energy.
EQUATION
—-----------------------------------------------------------------
Boltzmann Relation (E) = kT
E = Average kinetic energy per particle (J)
k = Boltzmann constant = 1.380649 × 10⁻²³ J K⁻¹
T = Absolute temperature (K)
—-----------------------------------------------------------------
This relationship ensures that temperature measurement reflects the microscopic energy of particles, reinforcing the independence of the scale from material properties.
Importance of the Absolute Temperature Scale in Physics
The absolute scale is essential in many branches of physics, including:
Kinetic theory of gases: Relating particle motion and temperature.
Thermodynamics: Defining absolute zero and entropy changes.
Statistical mechanics: Describing energy distributions at different temperatures.
Astrophysics: Measuring temperatures of stars, cosmic background radiation, and other phenomena.
By using the Kelvin scale, scientists can express laws and equations universally, without reference to particular substances or empirical conditions.
Measurement and Practical Use
While thermometers measure temperature in Celsius or Fahrenheit, scientific instruments such as thermocouples and resistance thermometers are calibrated to the Kelvin scale. These instruments translate measurable quantities like voltage or resistance into temperature using absolute reference standards.
Key points:
Kelvin (K) is always used without the degree symbol.
Absolute zero is the baseline, ensuring no negative values.
It enables direct proportionality between temperature and energy.
The Universal Nature of the Kelvin Scale
The Kelvin scale applies across all physical phenomena, from cryogenics (near absolute zero) to plasma physics (millions of kelvins). Because it is grounded in physical law rather than human convention, it provides a consistent and universal standard for scientific measurement.
In summary, the absolute temperature scale—as defined by the thermodynamic laws—provides a fundamental, substance-independent framework for quantifying thermal energy across the universe. Its origin at absolute zero, linkage to the Boltzmann constant, and universal applicability make it one of the most significant concepts in physics.
FAQ
Absolute zero cannot be reached because it would require removing all thermal energy from a system, which violates the third law of thermodynamics. As temperature decreases, the energy that can be extracted from particles diminishes exponentially, and cooling methods such as gas expansion or laser cooling become less effective.
Approaching absolute zero is possible, but never fully attainable — laboratories have achieved temperatures within billionths of a kelvin above 0 K using advanced techniques, but molecular motion can never be completely stopped.
As temperature decreases toward absolute zero:
The average kinetic energy of particles falls dramatically.
Vibrational motion in solids reduces, with atoms oscillating about fixed points.
Quantum effects become significant — particles exhibit zero-point energy, a residual motion that persists even at 0 K.
This means that even at absolute zero, some microscopic motion remains due to the principles of quantum mechanics.
Historically, the absolute scale was developed from experiments with gases.
Scientists observed that the pressure of an ideal gas decreases linearly with temperature when volume is constant. Extrapolating this linear relationship to zero pressure predicted a temperature of –273.15 °C, corresponding to 0 K.
This discovery, primarily credited to Lord Kelvin, provided the foundation for defining the Kelvin scale before the introduction of quantum constants such as the Boltzmann constant.
The kelvin is not a relative scale like Celsius or Fahrenheit but an absolute scale with a fixed zero point.
Because the kelvin measures absolute thermal energy, it is treated as a base SI unit rather than a comparative temperature measure. Hence, we write “300 K” instead of “300 °K”.
This distinction emphasises that the kelvin represents a direct measure of thermodynamic temperature, not a difference from another reference point.
The Boltzmann constant (k) provides the bridge between macroscopic temperature and microscopic particle energy.
It states that the average kinetic energy of one particle in a gas is given by:
E = (3/2)kT
This means that a change in temperature corresponds directly to a change in the average energy of particles. The constant effectively connects the behaviour of individual atoms or molecules with the measurable temperature of bulk matter, reinforcing the universality of the absolute scale.
Practice Questions
Question 1 (2 marks)
State what is meant by the absolute temperature scale and explain why it is considered independent of the properties of any substance.
Mark Scheme:
1 mark: Identifies that the absolute temperature scale (thermodynamic scale) is based on the laws of thermodynamics, not on material properties.
1 mark: Explains that it is independent of any particular substance because it is defined using absolute zero and fundamental physical constants, rather than phase changes or expansion of materials.
Question 2 (5 marks)
The Kelvin scale is defined so that absolute zero is 0 K and the triple point of water is 273.16 K.
(a) Explain what is meant by absolute zero. (2 marks)
(b) Describe how the Kelvin scale is related to the Celsius scale and state one reason why the Kelvin scale is preferred in scientific measurements. (3 marks)
Mark Scheme:
(a)
1 mark: States that absolute zero is the lowest possible temperature.
1 mark: States that at absolute zero, particles have minimum internal energy or no random motion.
(b)
1 mark: States that the scales have the same size unit (1 K = 1 °C).
1 mark: States that 0 K corresponds to -273.15 °C or gives correct conversion relationship (T = θ + 273).
1 mark: States that the Kelvin scale is preferred because it is absolute, avoiding negative values and directly relating to particle energy in thermodynamic equations.
