Memorial University of Newfoundland
Department of Physics and Physical Oceanography
Physics 2053 Laboratory
Linear Expansion
Introduction
Most materials expand when heated as long as there is no phase change. In the case of a rod,
the change in length is proportional to its original length, L◦ , and the change in temperature,
∆T and we may write
∆L = αL◦ ∆T
where α is the coefficient of linear expansion for the material, defined as the fractional
change in length produced by a one degree change in temperature. The units of α are ◦ C−1 .
Note that α also depends on the temperature of the material. In this experiment you will
determine α for two metals.
Procedure
1. You are provided with three tubes - copper, aluminum and steel. Take one of these
and measure its length at room temperature. Check that the insulation fits snugly
around the tube. Place the tube in the base, with the stainless steel pin in the slotted
mount. The angle bracket should press against the spring dial gauge.
2. Attach the thermistor lug to the middle of the tube. Measure the resistance of the
thermistor (in kΩ) at room temperature.
3. Attach a tube from the steam generator to the end of the metal tube furthest from the
dial gauge. Raise the inlet end of the tube by 1-2 cm and place a beaker at the other
end to catch water. Turn the outer ring of the dial guage to establish a zero point and
turn on the water heater1 .
Safety Note: The metal tube will become very hot due to steam which
passes through it. Avoid touching the bare metal surface when in use.
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Note that one complete rotation of the indicator needle corresponds to a length change of 1 mm
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4. The indicator needle will move in a counterclockwise direction as the tube expands.
When the temperature has stabilized, record the resistance of the thermistor and note
how far the tube has expanded.
5. The relation between resistance (in kΩ) and temperature of the thermistor is given by
R = Ae−bT
where A = 269.8 ± 4 and b = 0.0404 ± 0.0003 and temperature is in degrees C. Use
your data to calculate α for your material.
A more careful determination of α
You should have noticed that once the water begins to boil, the tube heats up quickly so there
is no time to take a complete set of readings before it reaches its maximum temperature.
When the water heater is switched off, you can take a more careful set of readings as the
tube cools to room temperature.
1. Start with the tube at its maximum temperature, and note the dial gauge reading.
2. Switch off the water heater and take and many readings as you can of the length change
and resistance of the thermistor as the tube cools
3. Plot a graph of ∆L versus temperature, and use the slope to calculate α. What is
the experimental uncertainty in your determination of α? Discuss why is it possible
to measure the length L◦ with a metre rule, while the expansion is measured using a
dial gauge. By how much do you expect your value of α to be affected by errors in the
measurement of ∆L, L◦ ?
4. Repeat the procedure to determine α for one of the other two metals.
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