Engineering: The challenge of temperature
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# 2.3 How things change with temperature

The temperature-dependent effects used in most thermometers have a fairly steady change over a good range of temperature (Figure 3a). By contrast, phase changes, of which melting and boiling are the common examples, happen at sharply critical temperatures (Figure 3c): at +1 °C your dahlias will survive, at −1 °C they are dead of frostbite.

Figure 3 Changes with temperature: (a) gradual, (b) accelerating, (c) sudden
Figure 3

Between these extremes of gradual and sudden change are temperature-sensitive phenomena which accelerate from insignificance to drama over a narrow but finite temperature range. Examples are the rates of many chemical reactions, and the electrical conductivity of semiconductors. Figure 3(b) illustrates one of these and, although it will not always be obvious whether to regard a particular change as 'gradual', 'accelerating' or 'sudden', we shall find the theoretical models for each category to be sharply distinct.

Notice that the horizontal axis in Figure 3 is temperature, not time. These graphs show how a material property depends on its temperature. There is nothing here about how quickly the temperature is changing. For instance, you could thaw ice by bringing the temperature up very slowly, and it would still all turn to water at 0 °C, and this would still be classed as a 'sudden' change, because it is how the property changes as you move along the temperature axis that is being described.

- Gradual changes are modelled in terms of the average thermal energy of the particles of the system. During a gradual change (of a property with temperature) doubling the change of temperature, say up ten degrees rather than up five degrees, will change the property by a factor of two or so (twice as big a change or half as small a change).

- Accelerating changes are modelled in terms of the fraction of the particles that have much higher than average thermal energy. During an accelerating change (of a property with temperature) the rate of change of the property varies with temperature.

- Sudden changes are modelled in terms of the balance between disorder generated by the vibration of atoms and order induced by inter-particle forces. During a sudden change (of a property with temperature) exceeding some critical temperature, Tcrit , is what triggers the change.

Because the models differ, our ideas about influencing and exploiting each sort of behaviour differ. We need to understand these behaviours because, within each category, there are 'opportunities' and 'challenges', from both the service and process points of view.

Before moving on to Section 3, have a go at Exercise 3 in the next section to reinforce your ideas on gradual, accelerating and sudden temperature changes.

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