Picture a beaker of boiling water. You want to measure its temperature, so you pick up a thermometer that is lying on the bench. The thermometer reads ${20^ \circ }C$. You place the thermometer in the water and the reading goes up … ${30^ \circ }C,\,{40^ \circ }C,\,{50^ \circ }C\,$. This tells you that the thermometer is getting hotter; energy is being transferred from the water to the thermometer.

Eventually, the thermometer reading reaches ${100^ \circ }C$ and it stops rising. Because the reading is steady, you can deduce that energy is no longer being transferred to the thermometer and so its scale tells you the temperature of the water.
This simple, everyday activity illustrates several points:
- We are used to the idea that a thermometer shows the temperature of something with which it is in contact. In fact, it tells you its own temperature.
As the reading on the scale was rising, it wasn’t showing the temperature of the water. It was showing that the temperature of the thermometer was rising.
- Energy is transferred from a hotter object to a cooler one. The temperature of the water was greater than the temperature of the thermometer, so energy transferred from one to the other.
- When two objects are at the same temperature, there is no transfer of energy between them. That is what happened when the thermometer reached the same temperature as the water, so it was safe to say that the reading on the thermometer was the same as the temperature of the water.
From this, you can see that temperature tells us about the direction in which energy flows. If two objects are placed in contact (so that energy can flow between them), it will flow from the hotter to the cooler.
Energy flowing from a region of higher temperature to a region of lower temperature is called thermal energy. (Here, we are not concerned with the mechanism by which the energy is transferred. It may be by conduction, convection or radiation.)
When two objects are at the same temperature, they are in thermal equilibrium with each other. There will be no net transfer of thermal energy between them when they are in contact with each other – see Figure 19.11.

The thermodynamic (Kelvin) scale

The Celsius scale of temperature is a familiar, everyday scale of temperature. It was originally based on the properties of water with the melting point of pure ice as ${0^ \circ }C$ and the boiling point of pure water as ${100^ \circ }C$.
There is nothing special about these two temperatures. In fact, both the melting point and boiling point change if the pressure changes or if the water is impure. The thermodynamic scale, also known as the Kelvin scale, is a better scale in that one of its fixed points, absolute zero, is very important.
It is not possible to have a temperature lower than $0 K$. Sometimes it is suggested that, at this temperature, matter has no energy left in it. This is not strictly true; it is more correct to say that, for any matter at absolute zero, it is impossible to remove any more energy from it. Hence, absolute zero is the temperature at which all substances have the minimum internal energy. (The kinetic energy of the atoms or molecules is zero and their electrical potential energy is minimum.)
We use different symbols to represent temperatures on these two scales: $\theta $ for the Celsius scale, and T for the thermodynamic (Kelvin) scale. To convert between the two scales, we use these relationships:

$\begin{array}{l}
\theta \,(in\,{0^ \circ }C) = T\,(in\,K)\, - 273.15\\
\theta \,(in\,K) = T\,(in\,{0^ \circ }C)\, - 273.15
\end{array}$

For most practical purposes, we round off the conversion factor to 273 as shown in the conversion chart (Figure 19.12).

The thermodynamic scale of temperature is designed to overcome a problem with scales of temperature, such as the Celsius scale, which depends on the melting point and boiling point of pure water. To measure a temperature on this scale, you might use a liquid-in-glass thermometer. However, the expansion of a liquid may be non-linear. This means that if you compare the readings from two different types of liquidin-glass thermometer, for example a mercury thermometer and an alcohol thermometer, you can only be sure that they will agree at the two fixed points on the Celsius scale. At other temperatures, their readings may differ.

The thermodynamic scale is said to be an absolute scale as it is not defined in terms of a property of any particular substance. It is based on the idea that the average kinetic energy of the particles of a substance increases with temperature. The average kinetic energy is the same for all substances at a particular thermodynamic temperature; it does not depend on the material itself. In fact, as you will see in Chapter 20, the average kinetic energy of a gas molecule is proportional to the thermodynamic temperature. So, if we can measure the average kinetic energy of the particles of a substance, we can deduce the temperature of that substance.
The thermodynamic scale has two fixed points:
- absolute zero, which is defined as $0 K$
- the triple point of water; the temperature at which ice, water and water vapour can co-exist, which is defined as $273.16 K$ (equal to $0.01{\,^ \circ }C$).
So the gap between absolute zero and the triple point of water is divided into 273.16 equal divisions.
Each division is $1 K$. The scale is defined in this slightly odd way so that the scale divisions on the thermodynamic scale are equal in size to the divisions on the Celsius scale, making conversions between the two scales relatively easy.
A change in temperature of $1 K$ is thus equal to a change in temperature of $1{\,^ \circ }C$.