Temperature

Quantity measuring the thermal state of a body and determining the direction of heat flow.

Conceptual context

Temperature is one of the most everyday quantities and, at the same time, one of the most difficult to define rigorously in physics. Everyone has an intuitive sense of what "hot" or "cold" means, but that subjective perception is not sufficient for physics. Temperature requires a quantitative definition, a reproducible scale, and a connection to the microscopic structure of matter.

Historically, the first temperature scales were operational: two reproducible reference points were chosen (ice melting, water boiling) and the interval was divided into equal parts. Celsius, Fahrenheit, and Réaumur took this approach and obtained scales with arbitrary zeros. The decisive conceptual advance came with nineteenth-century thermodynamics, when it was demonstrated that an absolute lower limit of temperature—absolute zero—existed and that it was possible to define a scale independent of the thermometric material.

This leaf focuses on three practical and essential aspects: the physical definition of temperature as a state quantity, the three most widely used scales (Celsius, Kelvin, and Fahrenheit) with their exact conversions, and the crucial distinction between absolute temperature $T$ and temperature change $\Delta T$—the most frequent thermodynamics error in secondary and upper secondary education.

🟢 Essential level

Temperature measures how hot or cold a body is. More precisely: it is the quantity that determines whether heat flows between two bodies in contact. If two bodies have the same temperature, no heat flows between them; if they have different temperatures, heat flows spontaneously from the hotter to the cooler.

To measure temperature we need a scale. Three are mainly used in science:

• Kelvin (K): the absolute SI scale. Its zero is absolute zero, the point of lowest possible thermal energy. There are never negative temperatures in kelvin. Water freezes at 273 K and boils at 373 K.

• Celsius (°C): the everyday scale in Europe and applied science. Zero corresponds to the water melting point and 100 °C to its boiling point. It can be negative. One Celsius degree has the same size as one kelvin.

• Fahrenheit (°F): predominant in the US. Water freezes at 32 °F and boils at 212 °F. The Fahrenheit degree is smaller than the Celsius degree.

All three scales measure the same physical quantity with different zeros and different degree sizes.

🔵 Formal level

Basic formulas

The exact relationship between Celsius and kelvin is:

Conversion between Celsius and kelvin

The offset of 273.15 reflects that the Celsius zero lies 273.15 kelvins above absolute zero. This relationship is an exact definition of the Bureau International des Poids et Mesures, not an approximation.

The relationship between Fahrenheit and Celsius is:

Conversion between Fahrenheit and Celsius

The factor 9/5 arises because the interval between the water reference points is divided into 180 parts in Fahrenheit and 100 parts in Celsius: 180/100 equals 9/5. The +32 term shifts the origin of the Fahrenheit scale.

Chaining the two previous relations converts directly between kelvin and Fahrenheit:

Conversion between kelvin and Fahrenheit

Order matters: first subtract 273.15 to get the Celsius reading, and only then apply the 9/5 factor and the +32 shift. This is the conversion needed when reading cryogenic tables or technical specifications published in Fahrenheit.

The temperature change in a process is defined as:

Temperature change

where positive $\Delta T$ indicates heating and negative $\Delta T$ indicates cooling. For temperature changes—unlike absolute temperatures—Celsius and kelvin give the same numerical value, because the 273.15 offset cancels out in the subtraction.

Real student questions

Why can I not use degrees Celsius in the ideal gas law? Because the ideal gas law requires absolute temperature in kelvin. $T_C$ can be zero or negative without the gas having zero thermal energy: at 0 °C (273 K) the gas has perfectly real kinetic energy. Substituting $T_C$ directly produces a physically absurd result —or even a negative volume— because the Celsius scale does not place zero at the point of zero thermal energy.

Why does a change of 1 °C equal a change of 1 K? Because both scales have the same degree size. The offset of 273.15 only affects the state value (temperature at a given instant), not the difference between two states. When two Celsius temperatures are subtracted, the 273.15 cancels and the result is the same as in kelvin.

Why does the Fahrenheit scale have 180 divisions between the water points? Because Fahrenheit chose 32 for the freezing point and 212 for the boiling point; the difference is 180. In Celsius, 0 and 100 were chosen, giving a difference of 100. The ratio 180/100 is 9/5, which is exactly the conversion factor between the two scales.

Is a negative temperature in kelvin possible? In classical thermodynamics and for equilibrium systems, no. The third law forbids reaching absolute zero and therefore negative kelvin temperatures do not exist in that framework. In quantum systems out of equilibrium with bounded energy levels (such as nuclear spins), temperature can be defined in a way that results in a "negative" kelvin value, but that is a very special regime outside the scope of classical physics.

Final synthesis

Temperature is the state quantity that determines thermal equilibrium between systems and the direction of heat flow. The three main scales—kelvin, Celsius, and Fahrenheit—measure the same physical reality with different zeros and degree sizes. $T$ is the only scale suitable for absolute thermodynamic laws; $T_C$ is equivalent to $T$ only for differences ($\Delta T$), not for absolute values. Scale conversion is an exact SI definition, with no additional physical hypotheses or validity limits beyond absolute zero.