Temperature conversion between degrees Celsius (°C) and kelvin (K) is fundamental in thermal physics, linking everyday temperature measurement to the absolute thermodynamic scale used in scientific calculations.

The Concept of Temperature Scales

The Celsius Scale

The Celsius temperature scale is a relative scale based on two fixed points:

• The melting point of ice at 0 °C.

• The boiling point of water at 100 °C under standard atmospheric pressure (1 atm).

These reference points make Celsius convenient for everyday and laboratory use, aligning with common environmental temperatures. However, Celsius does not start from an absolute zero value—it merely divides the interval between the two reference points into 100 equal units.

The Kelvin (Absolute) Scale

The kelvin is the SI unit of thermodynamic temperature, forming the absolute temperature scale. It begins at absolute zero, the lowest possible temperature at which the internal energy of a system is at a minimum, and molecular motion theoretically ceases.

The Kelvin scale is not defined by arbitrary physical points but by fundamental constants. Since 2019, the kelvin has been defined using the Boltzmann constant (k), ensuring its independence from specific materials or physical conditions.

Relationship Between Celsius and Kelvin

The Linear Conversion

The Celsius and Kelvin scales are linearly related, meaning the size of one degree Celsius equals one kelvin in magnitude. Only their zero points differ.

A labelled thermometer comparing the Celsius and Kelvin scales. It marks absolute zero (0 K = −273.15 °C) and shows that equal increments on both scales are the same size. The figure also includes historical water points (extra detail beyond the OCR conversion requirement). Source.

The conversion between the two scales is expressed by the following equation:

EQUATION
—-----------------------------------------------------------------
Temperature Conversion
T(K) = θ(°C) + 273
T = Temperature on the Kelvin scale (K)
θ = Temperature on the Celsius scale (°C)
—-----------------------------------------------------------------

This relationship shows that the Kelvin scale is simply offset by 273 from the Celsius scale. For instance, 0 °C corresponds to approximately 273 K, while 100 °C equals about 373 K.

Why the Offset Exists

The offset originates from the positioning of absolute zero at −273 °C on the Celsius scale. Historically, early experiments with gases (notably by Lord Kelvin) revealed that pressure decreases linearly with temperature and would theoretically reach zero at −273 °C. By shifting this zero point upward, the Kelvin scale establishes a non-negative temperature scale beginning at zero, simplifying physical relationships in thermodynamics.

A constant-volume gas-thermometer plot of pressure versus temperature for several gases. Linear trends extrapolate to zero pressure at −273.15 °C (0 K), motivating an absolute temperature scale. Clean axes and labels make the underlying proportionality clear. Source.

Importance of Using Kelvin in Physics

Thermodynamic Calculations

In thermodynamics and kinetic theory, temperature must always be expressed in kelvin because many physical laws depend on absolute temperature rather than relative temperature.

Key laws requiring temperature in kelvin include:

• The Ideal Gas Law

• Stefan–Boltzmann Law

• Kinetic Energy–Temperature Relationship

When using Celsius, these laws would yield incorrect results because 0 °C does not represent the absence of thermal energy.

Example of Relevance

For instance, the kinetic energy of gas particles is directly proportional to temperature in kelvin. Doubling the Kelvin temperature doubles the average molecular energy. However, if Celsius were used, the proportionality would not hold true due to its arbitrary zero point.

Practical Aspects of Conversion

Measurement and Reporting

In laboratory settings, temperatures are often measured in degrees Celsius using thermometers or electronic sensors, but converted to kelvin for use in calculations. This maintains consistency with SI units and ensures clarity when applying formulae.

University figure comparing Kelvin, Celsius, and Fahrenheit. It clearly marks absolute zero (0 K) and shows that Δ1 K = Δ1 °C; the Fahrenheit scale is included for context (extra detail not required by the OCR subsubtopic). Labels are succinct and the layout is uncluttered. Source.

Process for Conversion:

• Identify the measured temperature in Celsius.

• Add 273 to obtain the temperature in kelvin.

• For approximate calculations, 273 is often used, but the more accurate value 273.15 K is used for precision work.

Example Reference Points

While no worked examples are to be included, it is useful to remember typical correspondences:

• 0 °C → 273 K

• 25 °C → 298 K

• 100 °C → 373 K

These simple conversions reinforce that kelvin and Celsius share identical intervals, differing only in their starting points.

Significance in Experimental Physics

Preventing Negative Values

Expressing temperature in kelvin avoids negative values, which simplifies calculations in physical equations. For example, in gas laws, a negative absolute temperature would be non-physical since volume and pressure cannot become negative.

Consistency Across Systems

Kelvin provides a universal standard recognised in all branches of physics and engineering. Whether analysing molecular energy, blackbody radiation, or thermal expansion, expressing temperature in kelvin ensures that energy-related quantities remain consistent.

Historical Development of the Absolute Scale

The idea of an absolute temperature scale emerged from the study of gases. William Thomson (Lord Kelvin) proposed a scale where zero temperature corresponded to zero energy. His work linked the behaviour of gases with fundamental thermodynamic limits and led to the equation linking Celsius and Kelvin.

The scale was later standardised as part of the International System of Units (SI), ensuring compatibility with other scientific measurements.

Common Misconceptions

Misunderstanding of “Degrees” in Kelvin

Students often mistakenly refer to “degrees kelvin”. The correct unit is simply kelvin (K), not degrees kelvin. The Kelvin scale measures absolute temperature, not a degree-based relative measure like Celsius.

Confusion with Temperature Differences

While the conversion equation adds 273 for absolute temperatures, the difference between temperatures is the same in both scales. For example:

• A change from 20 °C to 30 °C equals a 10 °C rise, which is also a 10 K increase.

  • This is because both scales have identical step sizes.

Key Takeaways

• Celsius (°C) is a relative scale based on water’s phase changes.

• Kelvin (K) is the absolute thermodynamic scale beginning at 0 K, corresponding to −273 °C.

• The conversion between Celsius and Kelvin is linear, following T(K) = θ(°C) + 273.

• Kelvin is used in scientific equations because it directly reflects molecular energy and avoids negative values.

• Both scales share identical temperature intervals, ensuring easy comparison and consistency in measurements.