Engineering: The challenge of temperature
Engineering: The challenge of temperature

This free course is available to start right now. Review the full course description and key learning outcomes and create an account and enrol if you want a free statement of participation.

Free course

Engineering: The challenge of temperature

3 Gradual temperature effects

3.1 Modelling properties

This section provides a model for properties interpreted in terms of the average thermal energy of all the constituent atoms of a material. Since absolute temperature T is a measure of average atomic kinetic energy, we shall expect to be looking at properties that change gradually with T, roughly proportionally, over a wide range. In terms of the classification introduced in Figure 3, we shall be looking at changes like Figure 3(a). The experimental descriptions of such changes usually use power series, setting the property X, for example the length of a specimen, as a function of a change in temperature, ΔT (here the Greek capital letter delta, Δ, is used to express a change in the quantity that follows it):

Often the constant β is small enough that ΔX is almost proportional to ΔT. Then α is called the linear temperature coefficient of the property (expansion, resistance or whatever) and we can express the change in X as:

In particular, I want to discuss details of the thermal expansion of solids, but the temperature dependence of the electrical resistance of metals, the thermal conductivity of solids and the Young's modulus of many materials also vary in a gradual way.

Exercise 4

The length of a steel rod is precisely measured to be 1.000000 m at 300 K. When heated to 350 K it is measured again and found to be 1.000550 m. Assuming the change to be linear, calculate the coefficient α.

Answer

The change in length of the steel rod is

The change in temperature is

T207_2

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has nearly 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to university level study, find out more about the types of qualifications we offer, including our entry level Access courses and Certificates.

Not ready for University study then browse over 900 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus