understand that a physical property that varies with temperature may be used for the measurement of temperature and state examples of such properties, including the density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m

Temperature Scales

Temperature is a measure of the average kinetic energy of the particles in a substance. Different temperature scales have been devised for practical and historical reasons. In physics we usually work with the Kelvin scale because it is absolute (i.e. it starts at absolute zero, the point at which molecular motion ceases).

Common Temperature Scales

Using Physical Properties to Measure Temperature

A physical property that changes in a predictable way with temperature can serve as a thermometer. The essential idea is to calibrate the property against a known temperature scale, then use the measured value of the property to infer the temperature.

Key Requirements for a Good Thermometric Property

• Monotonic variation with temperature (always increases or always decreases).
• Reproducible and easily measurable.
• Linear or at least well‑characterised relationship over the range of interest.
• Minimal dependence on other variables (e.g., pressure, composition).

Examples of Temperature‑Dependent Properties

1. Density of a liquid – Most liquids expand on heating, so their density \$\rho\$ decreases with temperature. For water near 4 °C the relationship can be approximated by

   \$\rho(T) \approx \rho0\left[1 - \beta (T - T0)\right]\$

   where \$\beta\$ is the volumetric expansion coefficient.

2. Volume of a gas at constant pressure – According to Charles’s law,

   \$\frac{V}{T} = \text{constant (at constant }p\text{)}\$

   Hence measuring the volume \$V\$ of a known amount of gas gives the temperature \$T\$.

3. Electrical resistance of a metal – For many metals the resistance \$R\$ varies linearly with temperature:

   \$R = R0\,[1 + \alpha (T - T0)]\$

   where \$\alpha\$ is the temperature coefficient of resistance.

4. Electromotive force (e.m.f.) of a thermocouple – A thermocouple consists of two dissimilar metals joined at one end. The e.m.f. \$E\$ generated is a function of the temperature difference \$\Delta T\$ between the junctions:

   \$E = S\,\Delta T\$

   where \$S\$ is the Seebeck coefficient (often varies slightly with temperature, requiring calibration).

Calibration and Use

To use any of the above properties as a thermometer, follow these steps:

1. Choose a reference temperature scale (usually the Kelvin or Celsius scale).
2. Measure the property at several known temperatures to obtain calibration data.
3. Fit the data to an appropriate functional form (linear, polynomial, etc.).
4. Use the fitted equation to convert future measurements of the property into temperature values.

Practical Example: Thermocouple Thermometer

A common laboratory thermocouple uses a copper‑constantan pair. The e.m.f. produced is measured with a sensitive voltmeter and then converted to temperature using the calibrated \$E\$–\$T\$ relationship.

Summary

• Temperature scales provide a numerical way to express thermal state; Kelvin is the absolute scale used in physics.
• Any physical property that varies reliably with temperature can be employed as a thermometer.
• Typical properties include liquid density, gas volume (at constant pressure), metal resistance, and thermocouple e.m.f.
• Accurate temperature measurement requires careful calibration of the chosen property against a standard scale.