Brr, It's Cold Outside. What is temperature and how do we measure it?

Intuitively, temperature is a scale that describes how hot things are. According to thermodynamics and math, however, it is a bit more complicated. I will mention this definition in the comments section. We will go with the working definition: how much heat is in an object, or the amount of kinetic energy of particles in that object. When you see a weather forecast, you typically see temperature measured in Fahrenheit (°F). Water freezes at 32 °F and boils (at atmospheric pressure) at 212 °F. Another commonly used temperature scale is the Celsius scale (°C). In this system, water freezes at 0 °C and boils (at atmospheric pressure) at 100 °C. These are both relative temperature scales. You may have heard of absolute 0. Absolute 0 is the lowest energy possible, period. This isn't the 0 that your weatherman talks about. A more useful scale would begin at this temperature. Some examples of these scales include the Rankine (R) and Kelvin (K) scales, related to the Fahrenheit and Celsius scales, respectively. 459.67 R is equivalent to 0  R and 0 °F, with the same scale interval, and 273 K is equivalent to 0 °C, with the same scale interval.

How do we measure temperature? There are many ways. Many thermometers that you may have seen work by enclosing a liquid in a glass bulb and measuring the expansion of that liquid volume with temperature by seeing how far up a narrow tube the liquid volume extends. Such a liquid should expand significantly when heated. A pyrometer measures temperature (typically high-temperatures) by investigating the electromagnetic radiation (visible and invisible light) that is given off by all matter. This is called black-body radiation. This power given off by the material is absorbed by a material in the detector. Knowing the geometry of the setup, it is possible to relate the absorbed power to the object temperature by the following equation, where P_radiated is the power radiated, ε is a material constant called emissivity, σ_S is a constant, A is the radiating area, and T is temperature:

P_radiated=εσ_SAT⁴

This technique has the added bonus that you do not need anything to touch the thing that you are measuring.

Thermocouples can also measure temperature. A thermocouple has 2 wires made of different metals, attached together. One junction (where the 2 wires come together) is placed at the place that you want to measure the temperature and the other junction is placed at a known temperature. The voltage is measured (in series) at a point between the hot and cold ends. That voltage can be related to the temperature of the unknown junction. Try playing with this applet to see how the Seebeck coefficient and temperature affect the voltage measured. The Seebeck coefficient is a proportionality constant that relates the voltage developed across the wires to temperature. If you are having difficulty using this applet, download the player here.

Seebeck Effect in a Thermocouple from the Wolfram Demonstrations Project by Andrew Tuzhykov