Experiments for B. Tech. 1st Year Physics Laboratory
Stefan’s Constant
AIM :
To determine the Stefan’s constant using vacuum tube Diode
EZ- 81
Apparatus Used :
Diode EZ-81, Ammeter, Voltmeter, Current source.
In the experiment we use a commercially available vacuum
diode EZ-81 which has a cylindrical cathode made of nickle.
Closely fitted inside the cathode sleeve is the tungsten heater
filament. On the outer surface of the Nickle sleeve, a coating of
BaO and SrO mixture is formed from which thermionic
emission takes place.
Formula Used :
Power (P) radiated by a hot surface depends on the temperature (T) of the surface according to
the relation:
P =A∗𝑇
Where A is a constant which depends upon the properties of the material used as follows:
A = ε*S*𝜎
Where ε is emissivity of the material of the cathode
S is surface area of cathode and
𝜎 is the Stefan’s constant
n the exponent of temperature has a value of 4 theoretically. Here we shall determine n
experimentally to calculate 𝜎.
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Experiments for B. Tech. 1st Year Physics Laboratory
Stefan’s Constant
Theory:
If the power losses due to conduction and convection are neglected then power (P) radiated by a hot
surface definitely depends on the temperature of the surface according to the relation:
P∝𝑇
(where T is the temperature of the body in Kelvin )
P = A ∗ 𝑇 …………………………….…(1)
Or,
log P = log A + n log T
.………..…..(2)
A = ε*S*𝜎
…………….……….….(3)
Where ε , the emissivity of the material of cathode, is less than unity because it is not a black body.
S is surface area of cathode = 2𝜋𝑟𝑙 (r is the radius of cylindrical cathode & 𝑙 the length of
cathode).
𝜎 is Stefan’s constant which is independent of the material used.
Cathode is heated by passing electric current through the tungsten heater filament .Temperature of the
filament can be determined using known resistance (R), temperature(T) relationship for tungsten. Since
the cathode sleeve and the heater filament are in close physical contact, we can take the temperature of
the cathode to be the same as that of the filament.
Thus the operating temperature of the filament can be determined from measurement of the electrical
resistance of the filament. Power radiated and hence resistance can be found out as:
P = Vf*If watts
RT =
ohms
Once the resistance is calculated it is convenient to use a graph drawn T vs (RT/R300) for determination
of filament temperature . This graph can be drawn using data of Table 1 available for ready reference for
a tungsten filament.
Table 1
RT /R300 vs T for Tungsten ; R300= 0.6 ohms for Tungsten
S. No.
RT /R300
To K
1.
2.
3.
4.
5.
1
4
6
8
10
300
920
1300
1645
1990
Applying Stefan’s law to the heated cylindrical cathode we can determine Stefan’s constant from the
knowledge of the surface area and the emissivity of the cathode which is less than unity in this case,
because the radiation is not from an ideal black body.
Method :
1. Put the voltmeter range switch at 1.2 V or 1.0 V position and the voltage control knob ( Marked
control VF) at minimum i.e. at the extreme left position.
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Experiments for B. Tech. 1st Year Physics Laboratory
Stefan’s Constant
2. Connect the set-up to the main’s and switch ‘ON’.
3. Apply some filament voltage Vf say 0.2, 0.4 , 0.6, 0.8, 1.0, 1.5, 2.0 ..... 5 V to the filament and
measure the corresponding filament current If in the ammeter displayed during steady-state
condition.
NOTE: For steady state condition the time difference between each reading of V f should be about 20
to 30 sec. minimum.
Observations:
Given constants for Vacuum tube diode EZ-81
1. R300
= 0.6Ω
2. Emissivity (ε)
= 0.24
3. Radius (r) of cathode
= 0.12*10-2 m
4. Length (l) of cathode
= 3.12*10-2 m
5. Surface (S) area of cathode = 2.42*10-4 m2
S.No
1.
2.
3.
4.
5.
6
7.
Table - 2
Filament
Voltage Vf
Current If
(volts)
(Amp)
0.2
0.4
0.6
0.8
1.0
1.5
..
12.
13.
RT = Vf/ If
(ohms)
P= Vf* If
(watts)
RT/R300
=RT/0.6
ToK
(from.graph1)
Log T
Log P
4.5
5.0
Calculation
1. Calculate P and RT for each value of Vf .
2. Plot a graph between ToK and RT/R300 with the help of table 1 as shown in graph 1. And join the
points as a smooth curve.
3. Calculate RT/0.6 (As R300 = 0.6 for EZ - 81) and then measure the value of ToK for each
calculated values of RT/0.6 from graph (1).
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Experiments for B. Tech. 1st Year Physics Laboratory
Stefan’s Constant
4. Calculate log T and log P and Plot a straight line graph between log P and log T (graph 2) .
Calculate the slope ‘n’as n 
 log P
 log T
5. Read X intercept directly. Calculate Y intercept as Yintercept = slope * Xintercept
6. Now by equating Yintercept = Log A [equation (2)].
& calculate the value of Stefan’s constant equation (3).
Graph (1)
Graph (2)
Result:
1. The experimentally determined value of Stefan’s constant = Wm-2k-4.
2. The standard value of Stefan’s constant
= 5.67 x 10 -8 Wm-2k-4
3. From graph log P vs log T for the vacuum diode EZ – 81, the slope of the straight line graph is
found to be ….. (≈ 4) thus verifying Stefan’s law within experimental errors.
Precautions:
1. Readings of Vf and If should be taken only when steady state is obtained.
2. While plotting the graph between log P and log T values at higher temperature should be
considered because the power losses in this region are negligible and so in fig (2) the straight line
is drawn through such points.
3. The slope of the curve should be determined as accurately as possible, by using a large triangle.
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Experiments for B. Tech. 1st Year Physics Laboratory
Stefan’s Constant
GRAPH - 1
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