Description
Coefficient of Linear Expansion
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Coefficient of Linear Expansion
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1.
Objective:
The purpose of this experiment is to understand the mechanism of thermal expansion of
different materials and to measure the coefficient of linear expansion of some sample
materials. We will also look at some applications of thermal expansion.
2.
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Equipment:
Aluminum, steel, copper and brass rods
Linear expansion apparatus
Steam generator
Meter rule
Thermometer
3.
Theory:
The linear expansion of a material in the form of a rod is directly proportional to its
original length and the increase in temperature.
L L
This statement can be written using an equality sign as:
L = L
where is a constant for the given material and is called its coefficient of linear
expansion. Here L is the original length of the rod and is the increase in temperature.
L
….(i)
L
When L is m and in K, the unit of is K-1. Coefficient of linear expansion of a material
is a measure of the increase in length per unit length per Kelvin rise of temperature. The
following table lists the actual values of for the four materials you use.
=
Material
Aluminum
Brass
Copper
Steel
(K-1)
2.4 x 10-5
1.88 x 10-5
1.68 x 10-5
1.34 x 10-5
4.
Method:
Pour enough water into the steam generator and keep it on the hot plate to boil.
Measure the initial length of the metal rod and record it as L m
Measure the initial temperature of the rod and record it as 1oC.
Insert the rod in the steam jacket and after positioning it properly so that one end of it is
firmly in contact with the fixed end. Turn the micrometer screw until its tip touches the
free end of the rod. Take the reading of the micrometer screw at this position record it
as R1. Now work the screw back to allow space for the rod to expand. Connect the
steam outlet from the steam generator to the inlet of the jacket using a rubber tube.
Position the outlet of the steam jacket so that condensed water from the jacket can be
removed easily. Insert a thermometer in the steam jacket. When the steam begins to
flow, allow about five minutes for the rod to attain the temperature of the steam and
expand. Measure the temperature shown by the thermometer and record it as 2. Work
the screw back until its tip just touches the free end of the rod. Take the reading of the
micrometer now and record it as R2.
5.
Calculations:
1. For each metal rod record L, 1, R1, R2 and 2.
2. The increase in length of the rod = R2 – R1 = L
3. The increase in temperature of the rod = 2 – 1 =
4. Calculate using equation (i) above.
5. Use the actual value of and obtain the percent error in your experiment.
6. Repeat the procedure for the other three rods.
Notice that there is no graph for this lab.
Present your data and calculation steps for each material neatly and in detail.
6.
1.
Questions:
A concrete highway is built of slabs 15 m long. If the coefficient of linear
expansion for concrete is 1.2 x 10-5 K-1, how wide should the expansion gaps be
between the slabs to prevent buckling of the slabs when temperature changes
from (-20oC in the winter to 48oc in the summer?
2.
An ordinary glass of volume V is filled to the brim with water at 100oC. How
much water could be added to the glass if the temperature is lowered to 20oC?
Assume that the coefficient of volume expansion for glass is 2.7 10-5 K-1 and for
water it is 2.1 10-4 K-1. Express your answer as a fraction of the initial volume V
of the glass.
V
Use the definition for coefficient of volume expansion = −
to show that
V
the change in density of a substance when temperature changes by is
given by = -. What is the fractional change in the density of mercury
when temperature changes for 30oC to -10oC. The density of mercury at 30oC is
13600 kgm-3.
3.
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