STEFAN-BOLTZMAN LAMP
012-02889D
1 / 9 3
$1.00
Introduction
The Stefan-Boltzmann Lamp is a high temperature source of
thermal radiation. It can be used with a radiation detector,
such as PASCO's Model TD-8553 Radiation Sensor, to
investigate the Stefan-Boltzmann Law:
R
rad
=
σ
T
4
;
where R
rad
is the power per unit area radiated by an object,
and T is its temperature. This law can also be investigated
using a low temperature source such as PASCO's Model
TD-8554 Thermal Radiation Cube. However, the high
temperature of the Stefan-Boltzmann Lamp simplifies the
analysis because the fourth power of the ambient tempera-
ture is negligibly small compared to the fourth power of the
high temperature of the lamp filament.
When properly oriented, the filament of the Stefan-
Boltzmann Lamp provides a good approximation to a point
source of thermal radiation. It therefore works well for
investigations into the inverse square law.
Measuring the Filament Temperature
By adjusting the power into the lamp (13 Volts Maximum,
between 2 and 3 A or approximately 36 Watts), filament
temperatures up to approximately 3,000
°
C can be obtained.
The filament temperature is determined by carefully measur-
ing the voltage and current into the lamp. The voltage
divided by the current gives the resistance of the filament.
For small temperature changes, the temperature of the
tungsten filament can be calculated using
α
, the temperature
coefficient of resistivity for the filament:
Instruction Sheet
for the PASCO
Model TD-8555
T =
+
T
ref
R
-
R
ref
where,
T = Temperature
R = Resistance at temperature T
T
ref
= Reference temperature (usually room temp.)
R
ref
= Resistance at temperature T
ref
α
= Temperature coefficient of resistivity for the
filament
α
R
ref
Recommended Equipment
AC/DC LV Power Supply SF-9584 or equivalent capable of
13 V @ 3 A max.
Banana Connectors:
Connect to Power
Supply – 13 V MAX,
(2 A min, 3 A max)
For large temperature differences, however,
α
is not constant
and the above equation is not accurate.
For large temperature differences, therefore, determine
the temperature of the tungsten filament as follows:
1.
Accurately measure the resistance (R
ref
) of the tungsten
filament at room temperature (about 300
°
K). Accuracy
is important here. A small error in R
ref
will result in a
large error in your result for the filament temperature.
2.
When the filament is hot, measure the voltage and
current into the filament and divide the voltage by the
current to measure the resistance (R
T
).
3.
Divide R
T
by R
ref
to obtain the relative resistance
(R
T
/R
ref
).
4.
Using your measured value for the relative resistivity of
the filament at temperature T, use Table 2 on the
following page, or the associated graph, to determine the
temperature of the filament.
Model TD-8555
STEFAN-BOLTZMANN
LAMP
CAUTION
13 VDC MAX LAMP VOLTAGE
FOR MAXIMUM ACCURACY,
MEASURE VOLTAGE AT BINDING
POSTS.
USE NO. 1196 BULB
