20 Thermal expansion
At the end of this chapter you should be
able to:
- appreciate that expansion and contraction
occurs with change of temperature - describe practical applications where
expansion and contraction must be allowed
for - understand the expansion and contraction
of water - define the coefficient of linear expansionα
- recognise typical values for the coefficient
of linear expansion - calculate the new lengthL 2 , after expan-
sion or contraction, using
L 2 =L 1 [1+α(t 2 −t 1 )]- define the coefficient of superficial expan-
sionβ - calculate the new surface areaA 2 ,after
expansion or contraction, using
A 2 =A 1 [1+β(t 2 −t 1 )]- appreciate thatβ≈ 2 α
- define the coefficient of cubic expansionγ
- recognise typical values for the coefficient
of cubic expansion - appreciate thatγ≈ 3 α
- calculate the new volumeV 2 , after expan-
sion or contraction, using
V 2 =V 1 [1+γ(t 2 −t 1 )]20.1 Introduction
When heat is applied to most materials,expansion
occurs in all directions. Conversely, if heat energy is
removed from a material (i.e. the material is cooled)
contraction occurs in all directions. The effects
of expansion and contraction each depend on the
change of temperatureof the material.20.2 Practical applications of thermal
expansion
Some practical applications where expansion and
contraction of solid materials must be allowed for
include:(i) Overhead electrical transmission lines are
hung so that they are slack in summer, other-
wise their contraction in winter may snap the
conductors or bring down pylons(ii) Gaps need to be left in lengths of rail-
way lines to prevent buckling in hot weather
(except where these are continuously welded)(iii) Ends of large bridges are often supported on
rollers to allow them to expand and contract
freely(iv) Fitting a metal collar to a shaft or a steel
tyre to a wheel is often achieved by first
heating the collar or tyre so that they expand,
fitting them in position, and then cooling
them so that the contraction holds them firmly
in place; this is known as a ‘shrink-fit’. By a
similar method hot rivets are used for joining
metal sheets.(v) The amount of expansion varies with differ-
ent materials. Figure 20.1(a) shows a bimetal-
lic strip at room temperature (i.e. two