OCR Specification focus:
‘Temperatures are measured and reported in degrees Celsius and in kelvin for absolute values.’
Temperature measurement underpins all thermal physics, linking microscopic molecular motion to macroscopic readings. Understanding Celsius and kelvin scales allows scientists to quantify heat and energy precisely and consistently.
Measuring Temperature in °C and K
Temperature quantifies how hot or cold an object is, corresponding to the average kinetic energy of particles in a substance. In physics, accurate temperature measurement ensures that energy changes, phase transitions, and thermodynamic processes can be described mathematically and experimentally. The Celsius and kelvin scales are the two standard temperature units used in A-Level Physics, with the Celsius scale suited to everyday contexts and the kelvin scale used in scientific and thermodynamic calculations.
The Concept of Temperature Measurement
All temperature measurement is based on comparing an unknown temperature to a known reference point using a calibrated scale. Early thermometers used physical properties that change predictably with temperature, such as the expansion of mercury, alcohol, or the resistance of a metal wire. Modern digital thermometers may use semiconductors, thermocouples, or infrared sensors, yet all rely on establishing a consistent relationship between a measurable quantity and temperature.
Temperature provides a means of expressing thermal energy distribution.
It allows scientists to compare thermal states of different systems.
A uniform scale ensures consistent results across all experiments.
The Celsius Scale (°C)
The Celsius scale is the most familiar scale in everyday use. It is a relative temperature scale, meaning it is based on fixed reference points rather than fundamental thermodynamic principles.
Celsius scale: A temperature scale defined by assigning 0 °C to the melting point of pure ice and 100 °C to the boiling point of pure water, both at standard atmospheric pressure (1 atm).
Between these fixed points, the scale is divided into 100 equal intervals, each representing one degree Celsius (°C). Thus, it is often referred to as a centigrade scale, though “Celsius” is the correct modern term.
While this scale is practical for meteorology, engineering, and daily life, it depends on the physical properties of water, which vary slightly with pressure and impurities. Hence, it is not ideal as a universal or absolute scientific measure.
The Kelvin Scale (K)
In physics, the kelvin scale is used because it is based on absolute temperature, independent of the properties of any specific substance. It originates from the thermodynamic temperature scale, which defines temperature through the behaviour of an ideal gas and the laws of thermodynamics.
Kelvin scale: The absolute thermodynamic temperature scale that begins at absolute zero, where a system has minimum internal energy and molecular motion ceases.
Absolute zero (0 K) represents the theoretical point of zero thermal energy, at which no further heat energy can be removed from a substance. The kelvin is defined by the Boltzmann constant (k), linking microscopic molecular energy to macroscopic temperature, making it a fundamental SI base unit.
The size of one kelvin is identical to one degree Celsius.
Absolute zero is equal to −273.15 °C.
A comparative axis marks absolute zero (0 K, −273.15 °C) and the freezing/boiling points of water in kelvin and Celsius. The graphic visually confirms the equal interval size of °C and K. (This figure also includes Fahrenheit, which is beyond the syllabus scope but helps situate the two required scales.) Source.
The kelvin scale provides direct correspondence between molecular energy and temperature.
Comparing the Celsius and Kelvin Scales
Both scales use identical interval sizes, so temperature differences are the same whether expressed in °C or K.
Side-by-side thermometers illustrate that one kelvin is the same size as one degree Celsius, with distinct zero points. Absolute zero appears at 0 K (−273.15 °C), and water’s phase points are aligned across both scales. This visual directly supports reporting and converting temperatures between °C and K. Source.
This allows direct conversion between the two using a simple linear relationship.
EQUATION
—-----------------------------------------------------------------
Temperature Conversion (T) = θ + 273
T = Absolute temperature in kelvin (K)
θ = Temperature in degrees Celsius (°C)
—-----------------------------------------------------------------
This means that a temperature increase of 10 °C is equal to an increase of 10 K. However, it is essential to note that the numerical zero points are different: 0 °C is not the absence of thermal energy, whereas 0 K represents absolute zero, the fundamental lower limit of temperature.
Importance of Using Kelvin in Physics
The kelvin scale allows thermodynamic equations and kinetic theory relationships to be expressed consistently. Because it begins at absolute zero, it directly relates temperature to particle energy. For example:
In the ideal gas law, pV=nRTpV = nRTpV=nRT, temperature must always be in kelvin.
In kinetic theory, the average kinetic energy of gas molecules is proportional to temperature in kelvin.
Phase change calculations, such as those involving specific latent heat or internal energy, rely on absolute temperature values for accuracy.
By using kelvin, scientists avoid negative temperatures and maintain proportionality between temperature and molecular energy.
Measurement Instruments and Calibration
Temperature measurement relies on instruments whose measurable properties vary with thermal energy. The accuracy of any device depends on calibration, which aligns the instrument’s response with known standards.
Common measurement instruments:
Liquid-in-glass thermometers: Use thermal expansion of mercury or coloured alcohol.
A laboratory thermometer with dual scales (K and °C) shows how a single instrument can report temperatures directly in either unit. This reinforces that kelvin is used for absolute values while Celsius is common in laboratory contexts. The large, clear markings support accurate reading and logging. Source.
Thermocouples: Generate a voltage dependent on the temperature difference between two metals.
Resistance thermometers (RTDs): Depend on the resistance change of metals such as platinum with temperature.
Thermistors: Use temperature-sensitive semiconductors for precise digital readings.
Calibration process:
Identify fixed reference points (e.g., ice point and steam point).
Measure instrument output at these points.
Mark equal divisions corresponding to the chosen scale (°C or K).
Accurate calibration ensures reliability and allows conversion between scales to be meaningful in experimental contexts.
Applications in Physics and Everyday Use
Kelvin (K):
Used in all scientific equations and thermodynamic laws.
Applied in fields like astrophysics, cryogenics, and gas dynamics.
Ideal for describing absolute energy changes and molecular motion.
Celsius (°C):
Used in laboratory work where comparison with everyday temperatures is practical.
Common in environmental, medical, and meteorological measurements.
Understanding both scales allows smooth transition between theoretical and experimental applications, ensuring that students and researchers communicate results with precision and consistency.
Summary of Key Points
Celsius (°C) is a relative scale based on water’s phase change points.
Kelvin (K) is an absolute thermodynamic scale starting from absolute zero.
The conversion between the two is linear, with T = θ + 273.
The kelvin is an SI base unit, essential for accurate physical laws.
All scientific temperature measurements must use kelvin to preserve proportional relationships with energy.
Through mastering these concepts, students gain the foundational understanding needed to interpret and calculate thermal phenomena across all areas of physics.
FAQ
The kelvin scale is based on absolute zero, a fundamental thermodynamic limit, making it independent of any particular substance’s properties. This ensures that temperature differences directly correspond to proportional changes in internal or kinetic energy.
Celsius, in contrast, is defined relative to water’s phase points, which vary slightly with pressure and impurities. Using kelvin allows equations in thermodynamics and kinetic theory to remain universally valid and consistent.
In classical thermodynamics, absolute zero (0 K) is the theoretical lowest temperature — particles cannot have less kinetic energy than this.
However, in specific quantum systems, scientists can achieve negative temperatures on an inverted energy scale, where particles occupy higher energy states more frequently than lower ones. These are not “colder” than absolute zero but represent systems with unusual population distributions, such as certain laser-cooled atomic gases.
A dual-scale thermometer is calibrated using fixed reference points and a linear relationship between °C and K.
Calibration steps:
Set 0 °C at the melting point of ice.
Set 100 °C at the boiling point of water (both at 1 atm).
Mark equal divisions between these points.
Label a secondary kelvin scale by adding 273 to each °C mark, ensuring consistent spacing.
This produces a thermometer that can measure and report both absolute and relative temperatures accurately.
Both scales are linear and use identical interval sizes, meaning that one degree Celsius is equal to one kelvin in magnitude.
The only difference lies in their zero points:
0 °C corresponds to the melting point of ice.
0 K represents absolute zero.
Because the scales progress in equal steps, a change of +10 °C corresponds exactly to +10 K. This consistency is why conversions between them involve only a fixed offset of 273.
Modern thermometers often use electronic sensors that convert physical changes into electrical signals.
Common types include:
Thermistors: Semiconductor materials whose resistance decreases predictably as temperature increases.
Resistance Temperature Detectors (RTDs): Metals such as platinum with precisely calibrated resistance–temperature relationships.
Thermocouples: Produce a voltage difference between two joined metals proportional to temperature.
These sensors provide fast, accurate, and wide-ranging temperature measurements suitable for both laboratory and industrial use.
Practice Questions
Question 1 (2 marks)
Explain the difference between temperature measured in degrees Celsius (°C) and temperature measured in kelvin (K).
Mark scheme:
1 mark: States that the Celsius scale is a relative scale based on the melting and boiling points of water (0 °C and 100 °C).
1 mark: States that the kelvin scale is an absolute scale starting at absolute zero (0 K), where particles have minimum internal energy.
Question 2 (5 marks)
A physics student records the temperature of a gas sample as 27 °C.
(a) Convert this temperature to kelvin. (1 mark)
(b) Explain why, when performing thermodynamic calculations such as those involving the ideal gas law, the temperature must be expressed in kelvin rather than in degrees Celsius. (4 marks)
Mark scheme:
(a)
1 mark: Correct calculation using T = θ + 273 → 27 + 273 = 300 K.
(b)
1 mark: States that the kelvin scale is an absolute temperature scale beginning at absolute zero.
1 mark: Explains that absolute zero represents zero kinetic energy or the point where molecular motion ceases.
1 mark: Notes that temperature in kelvin is directly proportional to the average kinetic energy of the molecules.
1 mark: Concludes that using °C would not give proportional or meaningful results in thermodynamic equations because the Celsius scale can include negative values.
