Temperature scales and thermometers

Why temperature scales are needed

Temperature is a physical property, but to use it quantitatively we need a scale. A temperature scale assigns numbers to reproducible thermal states. Historically, scales were based on familiar reference points such as freezing and boiling water. Modern thermodynamics uses absolute temperature, measured in kelvins.

A useful temperature scale must be reproducible, monotonic, and connected to measurable physical behavior. As temperature changes, some property of a thermometer changes predictably.

Celsius and Fahrenheit

The Celsius scale sets the freezing point of water near $0^circ C$ and the boiling point near $100^circ C$ at standard atmospheric pressure. The Fahrenheit scale sets these points near $32^circ F$ and $212^circ F$.

The conversions are

T_F=rac{9}{5}T_C+32

and

T_C=rac{5}{9}(T_F-32)

These scales are convenient for everyday life, but they are not absolute scales. Zero Celsius and zero Fahrenheit do not mean zero thermal motion.

Kelvin scale

The Kelvin scale is the absolute temperature scale used in thermodynamics. It begins at absolute zero, the lowest possible temperature in the thermodynamic sense. The conversion between Celsius and Kelvin is

$T_K=T_C+273.15$

A temperature difference of $1 K$ is the same size as a difference of $1^circ C$. The Kelvin scale has no degree symbol; we write $300 K$, not $300^circ K$.

Many thermodynamic equations require absolute temperature. For example, the ideal gas law is

$PV=nRT$

where $T$ must be in kelvins.

Absolute zero

Absolute zero is

$0 K=-273.15^circ C$

At absolute zero, a system is in its lowest possible energy state. It is not correct to imagine classical particles simply frozen with exactly zero motion in all senses, because quantum mechanics allows zero-point energy. Still, absolute zero represents the lower bound of thermodynamic temperature.

No finite physical process can cool a system exactly to absolute zero, though laboratories can reach temperatures extremely close to it.

Thermometric properties

A thermometer uses a property that changes predictably with temperature. Liquid-in-glass thermometers use thermal expansion of a liquid. Gas thermometers use pressure or volume changes. Resistance thermometers use the temperature dependence of electrical resistance. Thermocouples use voltage generated by junctions of different metals.

A simple constant-volume gas thermometer relies on the relationship

$Ppropto T$

for an ideal gas at fixed amount and volume. This connection helped establish the absolute temperature scale.

Calibration

Thermometers must be calibrated against known reference points or standards. Calibration ensures that a thermometer reading corresponds to accepted temperatures. Without calibration, expansion, resistance, or pressure changes would be meaningless as numerical temperatures.

Different thermometers are useful in different ranges. Mercury thermometers are not suitable for extremely low temperatures. Infrared thermometers infer temperature from thermal radiation and depend on surface properties.

Temperature versus sensation

Human sensation is not a reliable thermometer. Metal feels colder than wood at the same room temperature because metal conducts heat away from your hand faster. The sensation depends on heat transfer rate, not temperature alone.

This distinction matters in thermodynamics: temperature determines equilibrium direction, while material properties determine how quickly energy transfers.

The big idea

Temperature scales turn thermal states into numbers. Celsius and Fahrenheit are everyday scales; Kelvin is the absolute thermodynamic scale required in fundamental equations. Thermometers work by using measurable properties that change with temperature, but accurate measurement requires calibration and thermal equilibrium.