Memorial University of Newfoundland
Department of Physics and Physical Oceanography
Physics 2053 Laboratory
Thermal Radiation: Stefan’s Law
Introduction
If an object is at temperature T , the energy radiated from its surface depends on the fourth
power of the absolute temperature, i.e.,
P = AeσT 4
(1)
This is known as Stefan’s law, where P is the power radiated by the object, A is the
surface area of the object and e is called the emissivity. The value of e depends on the
properties of the surface. σ is called the Stefan-Boltzmann constant and can be expressed
in terms of fundamental constants,
σ=
2π 5 k 4
= 5.669 × 10−8 W/m2 .K4
15c2 h3
We will investigate Stefan’s law using a tungsten filament which radiates energy due to the
electrical energy supplied to it.
Method
1. Connect the terminals of the lamp to the variable power supply. Increase the voltage
in suitable small steps from 0 V up to 12 V, recording the current each time. Do not
allow the filament voltage to exceed 13 V.
The lamp will get very bright and should be covered with a piece of card to avoid
damage to your eyes (and your neighbours’ !)
2. Since the power radiated by the filament depends on the electrical power supplied
(P ∼ IV ) and its temperature depends on resistance (T ∼ V /I), plotting a graph of
power versus resistance (or log(power) versus log(resistance)) will allow you to verify
the fourth power law.
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3. Plot your data on a suitable scale to verify the fourth power law predicted by Eq (1).
You will probably notice that the fourth power law is not obeyed at low currents. This
is because the filament loses most of its heat by conduction and convection at lower
temperatures, but at higher power heat loss by radiation dominates.
Determination of Temperature
For small changes in temperature, the resistance of the filament varies with temperature
according to
R = Rref {1 + α(T − Tref )}
(2)
where Tref is a reference temperature (usually room temperature) and Rref is the resistance
of the filament at Tref . α is the temperature coefficient of resistivity for the filament (α =
4.5 × 10−3 K−1 for tungsten). Thus for any measured resistance, R, the temperature of the
filament is given by
R − Rref
+ Tref
(3)
T =
αRref
Replot your power versus temperature data with temperature plotted along the x-axis. What
is the maximum temperature reached by the filament?
Inverse Square Law
The inverse-square law is very common in physics and states that the strength of a physical
quantity is inversely proportional to the square of the distance from the source of that
physical quantity. Typical examples are found in the study of light, gravitation and acoustics.
A radiation sensor measures the relative intensity of the incident thermal radiation. It
displays the measured intensity as a voltage when connected to a voltmeter. If you consider
the lamp to be the source of radiation, then the measured intensity will decrease as you move
the sensor away from it.
A shutter is provided by a spring clip which is opened and closed by sliding the shutter
ring forward and back. The shutter should be closed when you are not actively taking
measurements. This helps reduce temperature shifts in the thermopile reference junction
which can cause the sensor response to shift. The two posts extending from the front end
of the sensor protect the thermopile and also provide a reference for positioning the sensor
a repeatable distance from the lamp.
1. Place the lamp at one end of a meter stick and position the radiation sensor so that
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it is at the same height as the filament. You can assume that when the sensor is just
touching the bulb the filament-sensor distance is 2 cm.
2. Determine the ambient level of thermal radiation (lamp OFF). You will need to subtract this value from your measurements with the lamp on.
3. Set the power supply voltage to 12 V. [Do not let the voltage to the lamp exceed 13
V]. The bulb will be very bright and will need to be covered.
4. Record the sensor output voltage when the sensor is closest to the bulb and continue to
measure the sensor voltage as a function of distance as the sensor and bulb are moved
apart. Take as many readings as you can and plot a suitable graph to demonstrate the
inverse square relationship between radiation intensity and distance from the source.
Equipment Required
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Stefan light bulb and holder
Variable dc power supply.
Disgital meters for voltage and current
Thin cardboard to cover the light (eye protection)
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