Thermal expansion describes how the size of materials changes with increasing temperature. There are three main types of thermal expansion: 1. Linear expansion is the increase in length per unit length for each degree rise in temperature. 2. Area expansion can be calculated from linear expansion. 3. Volume expansion also relates to linear expansion, with volume expansion being three times the linear expansion rate. Water is an anomaly as it contracts in volume from 0 to 4 degrees C before expanding normally at higher temperatures.

1. PHYSICS
THERMAL EXPANSION
Short revision series

2. Thermal expansion in solids
 Linear expansivity of a solid (α): Increase in
lenght per unit lenght for one degree rise in
temperature.
α = l2 – l1 K-1
l1(θ2 – θ1)
 Eg : a solid metal of lenght 100m is heated
from 600 C to 1000 C, the new lenght
measured after heating is 101m. What is the
linear expansivity?

3. α = 101 – 100
100(100 - 60)
= 1
4000
= 0.00025K-1

4. Area expansivity
β = A2 – A1
A1 (θ2 – θ1)
This can be rearranged to calculate change in
area
(A2 – A1) = βA1 (θ2 – θ1) = βA1θ
Or calculate final lenght A2
A2 = βA1θ – A1 = A1 (1 + βθ)

5. Volume (cubic) expansion of
solids
γ = V2 – V1
V1 (θ2 – θ1)
V2 – V1 = γ V1 θ
V2 = V1 ( 1 + γθ)
 Remember β = 2α; γ = 3α
 So when you are given only linear expnsivity
to solve questions involving area and volume
expansion, use the logic above.

6.  For this eqn (A2 – A1) = βA1 (θ2 – θ1) = βA1θ we
can substitute β
(A2 – A1) = 2αA1 (θ2 – θ1) = 2αA1
 V2 – V1 = γ V1 θ
V2 – V1 = 3α V1 θ
 Eg: A piece of material with an initial area of
20m2 is heated through 500 C. Find the
change in area. Find cubic expansivity of the
material. {take linear expansivity = 10x10-5K-1}

7.  a) β = 2α
β = 2 x 10x10-5 = 20x10-5
(A2 – A1) = βA1θ
= 20 x 20x10-5 x 50 = 20,000 x 10-5 = 0.20m2
OR
(A2 – A1) = 2αA1θ
= 2 x 10 x10-5 x 20 x 50 = 0.20m2

8.  Cubic expansivity = 3α
= 3 x 10 x10-5 = 30 x 10-5
= 0.30 x 10 -3 K-1

9. Liquid expansion
 Liquids do not have lenghts and surface
area, so only volume expansion applies to
liquids
 Real (Absolute) cubic expansivity of a liquid
is the increase in volume per unit volume
per unit rise in temperature.
 Apparent cubic expansivity is increase in
volume per unit volume per unit rise in
temperature when the liquid is heated in an
expansible vessel.

10.  Real is normally greater than apparent
because in apparent the container also
expands and that must be considered.
 Real expansivity = apparent expansivity +
cubic expansivity
γr = γa + γ

11. Anomalous expansion of water
 Water does not expand continously with
temperature rise.
 From 00 C to 40 C, water tends to contract or
rather the volume decreases until it reaches
40 C.
 From 40 C to 1000 C it expands normally as
most liquids.

12. END