Download resistivity variation and temperature of a tungsten filament

Lab Experiments 301
KamalJeeth Instrumentation and Service Unit
Experiment-352
A
RESISTIVITY VARIATION AND
TEMPERATURE OF A TUNGSTEN
FILAMENT
Jeethendra Kumar P K and Ajeya PadmaJeeth
KamalJeeth Instrumentation & Service Unit, No 610, Tata Nagar Benaguluru-560 092. INDIA.
Email: [email protected]
Abstract
Using the tungsten filament torch bulb and a regulated power supply, variation of
filament resistance is studied for different values of current. The resistivity of the
tungsten filament is calculated and its temperature is estimated using two different
equations.
Introduction
There are a number of methods for estimating the temperature of the filament used in
incandescent lamps [1, 2]. Incandescent light bulbs, in addition to providing illumination, are
useful in physics experiments [3]. In the present work we have used filament of a torch bulb
operating at 6V. For a given voltage applied across the filament of the lamp, a steady state is
reached when the current (I) passing through the filament is stabilized. In the steady state, it
is expected that the electrical power input to the lamp is equal to the power lost by the
filament through conductive, convective, and radiative processes. In the steady state
௏మ
ோ
= ‫ ܭ‬ሺܶ − ܶ௢ ሻ+ ∈ ߪ‫ܣ‬௦ (T4-To4)
…1
where
V is voltage applied across the filament
R is its resistance
T is the temperature
To is room temperature
ε is the emissivity of the filament
As is surface area of the filament
σ is Stefan-Boltzmann constant
K is a constant whose value depends on conductive and convective property of the material
of the filament.
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Lab Experiments 302
KamalJeeth Instrumentation and Service Unit
For higher filament temperatures (say above 1000K), it is reasonable to assume that T4>>T40.
Moreover, for low wattage bulbs [2], such as those used in the present work, the studies
published in literature indicate that convection and conduction losses are negligible. Hence
Equation-1 may be rewritten as
V2=εσ AsT4R
௏మ
ோ஺ೞ
…2
= εσT4
…3
This equation is the well known Stefan-Boltzmann equation indicating that energy radiation
per unit area is given by fourth power of temperature of the filament.
Resistivity of a metal wire
The resistance (R) of a wire of uniform radius is given by
௅
…4
R =ρ஺௖
where L is the length of the wire
Ac is cross sectional area of the wire and
ρ is resistivity
The length and cross sectional area are dimensional parameters that vary with temperature,
hence the value of ρ also varies with temperature. The temperature dependence of resistivity
of the tungsten filament on absolute temperature is well known. Consequently, if the
resistivity of the filament is known, its temperature can be determined. The temperature
dependence of resistance of a wire is given by
RT = RO
ఘ೅
…5
ఘೀ
where RT = resistance of the wire at the temperature T ( in Kelvin)
RO = Resistance of the wire at 300K (room temperature)
ρT is resistivity at the temperature T ( in Kelvin)
ρO is the resistivity of the tungsten filament(=5.65µΩ.cm) at room temperature.
This is based on the fact that both Ac and L are constant at relatively low temperatures
(<2000K) [6]. However, the percentage variations in length and cross sectional area are
estimated to be around 2% for a temperature of 3000K. Hence Equation-5 is more
appropriate to describe the temperature dependence of resistance of a wire.
Determination of temperature from resistivity
The resistivity-temperature relation for a tungsten bulb filament is well known and the data
can be fitted by the least square method to a quadratic equation of the form
Y = C2X2+C1X+Co
...6
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Lab Experiments 303
KamalJeeth Instrumentation and Service Unit
Fitting this equation to given data of temperature and resistivity of tungsten filament wire
(Figure-3), one can solve for temperature T as
T = -0.0498ρ2+35.84ρ +129.1
…7
where T is in Kelvin and ρ is in µΩcm.
A similar analysis [5] provided by gives another temperature calculation equation for
tungsten filament bulb as
T = 3.05X108Xρ0.83
…8
In this equation T is in Kelvin and ρ is in Ω݉.
Equations-7 and 8 are used to estimate filament temperature by knowing resistivity in this
experiment.
Apparatus used
The experimental set-up consists of a 5V regulated power supply, digital voltmeter with 0200mV/0-20V dual range, and digital current meter with 0-2000µA/0-2A dual range. Figure1 shows the experimental set-up used.
Figure-1: Experimental set-up for measurement of resistivity variation of a tungsten
filament
Experimental procedure
The experiment consists of two parts. In the first part, the resistance of the cold filament is
determined by passing a small current through the filament. In the second part, resistance of
the heated filament is determined by passing a large current so that the bulb glows. The
temperature of the filament is then calculated using Equations-7 and 8.
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1. The given bulb is fitted in the socket and the circuit connections are made as shown in
Figure-2.
R
I
5V
Torch
filament
V
Figure-2: Circuit connections for measuring resistance of the filament
2. Two sets of series resistors are provided in the set-up. R is taken as 1KΩ, 2KΩ, and
3KΩ etc. and the resistance of the filament at room temperature (cold resistance) is
measured by connecting the resistors in series with the bulb one by one. In this case
the bulb does not glow because of low current. Hence the filament remains cold and
therefore its resistance is constant. The current meter is switched to read in the µA
range and the voltmeter is switched to read in the mV range.
3. The voltage and current flowing through the filament are noted
Voltage (VO) = 1.3mV
Current (IO) = 1620µA
Filament resistance = 1.3mV/1620µA=0.802Ω
4. The trial is repeated by choosing the next resistor in series and readings obtained are
tabulated in Table-1.
5. To determine resistance of the filament at different temperatures, the power (current
and voltage) is varied so that the bulb glows. This is done by connecting resistors of
low value in series with the bulb. To do this another set of resistors 1Ω, 2Ω…,8Ω ,10
Ω, 20 Ω, ...80 Ω are provided.
6. The resistor of 1Ω is selected as R in the circuit in Figure-2, and the current flowing
through the filament and voltage across the filament is noted. In this case the bulb
glows.
Current flowing through the bulb (IT) = 464mA
Voltage across the bulb (VT) = 4.13V
∴ Resistance of the filament (RT) = 4.13/0.464=8.90Ω
7. The trial is repeated by varying the current flowing through and voltage applied
.
across the filament. The readings obtained are tabulated in Table-2
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Lab Experiments 305
KamalJeeth Instrumentation and Service Unit
Voltage
(mV)
1.3
1.0
0.8
0.7
0.6
0.5
Average
Voltage
(V)
4.13
3.75
3.47
3.25
3.01
2.80
2.60
2.42
2.26
2.09
1.04
0.49
0.18
0.117
0.091
0.075
Table-1
Resistance of the cold
filament (Ω)
0.802
0.817
0.813
0.851
0.849
0.807
RO=0.823Ω
Resistance of the Cold filament
Current
(µA)
1.620
1.223
0.983
0.822
0.702
0.619
Table-2
Current Resistance of the filament
(mA)
RT (Ω)
464
8.900
432
8.681
414
8.380
400
8.125
386
7.799
371
7.547
358
7.262
345
7.014
331
6.827
318
6.572
229
4.541
176
2.784
141
1.276
115
1.017
96
0.947
82
0.914
Hot resistance of the filament
8. Resistivity of the filament at different temperatures is calculated by rearranging
Equation-5 and presented in Table-3.
ோ
଼.ଽ଴
ߩ் =ρO ோ ೅ = 5.65µ ଴.଼ଶଷ = 61.09μΩ/ܿ݉
ೀ
9. The resistivity and filament temperature are related through Equations-7 and 8. Hence
the values of temperature of the filament, calculated using Equations-7 and 8, are
presented in Table-3 along with their corresponding standard values available in
literature.
T = -0.0498ρ2+35.84ρ +129.1= -0.0498x (61.09)2 +35.84 X61.09+129.1
T = -185.85+2189+129.1=2132.25
The readings obtained are tabulated in Table-3. Similarly the temperature is calculated
using Equation-8
Vol-11, No-4, Dec.-2011
Lab Experiments 306
KamalJeeth Instrumentation and Service Unit
= 3.05X108Xρ0.83
Resistance
(Ω)
= 3.05 X108X (0.6109x10-6)0.83=3.05X108X6.955=2121.5K
Table-3
Temperature estimated (K)
Equation-6 Equation-7 Standard value
[4]
61.09
2132
2121
2150
59.60
2088
2078
2099
57.53
2036
2018
2030
55.78
1973
1967
1960
53.54
1905
1901
1905
51.81
1852
1850
1850
49.85
1792
1792
1800
48.15
1739
1740
1730
46.86
1699
1702
1700
45.11
1644
1649
1660
31.17
1198
1214
1200
19.11
796
808
805
8.759
439
423
450
6.981
377
350
400
6.501
362
330
380
6.274
352
320
360
Resistance of the hot filament
Resistivity
µΩ/ࢉ࢓
8.900
8.681
8.380
8.125
7.799
7.547
7.262
7.014
6.827
6.572
4.541
2.784
1.276
1.017
0.947
0.914
10. A graph is drawn taking resistivity on the X-axis and temperature on the Y-axis, as
shown in Figure-3. The temperature of the filament estimated from two different
equations is found to agree well with the standard value of resistivity of a tungsten
filament which indicates the accuracy of the measurements and the equations (7 & 8).
Equation-7
Equation-8
Standard value
Filament Temperature (K)
2500
2000
1500
1000
500
0
0
10
20
30
40
50
60
70
Resistivity (µΩcm)
Figure-3: Resistivity variation of the tungsten filament with temperature
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Lab Experiments 307
KamalJeeth Instrumentation and Service Unit
Results
Filament temperature for the maximum glow condition = 2150K (standard value)
Temperature obtained using Equation-7=2132K
Temperature obtained using Equation-8= 2121K
Inferences
The tungsten filament temperature estimated using Equation-7 and Equation-8 agree well
with the standard value as shown in Figure-3. This shows that the measurements and
equations derived are quite accurate. One can, therefore, use these two equations to
determine the filament temperature.
The resistivity of tungsten filament varied from 61µΩcm to 6.27µΩcm for temperature
variation 2150K to 360K.
References
[1]
Agrawal D C and Menon V J, Lifetime and temperature of incandescent lamps, Phys.
Education, Vol. 33, 1998, Page-55.
[2]
Clauss D A, Ralich R M and Ramsier R D, Imtiaz Ahmad, Sidra Khalid and E
Khawaja, Hysteresis in light bulb: connecting electricity and thermodynamics with
simple experiment and simulations, European Journal of Physics, Vol.-22, 2001,
Page-385.
[3]
Edmonds I R, Stefan-Boltzman law in laboratory, American Journal of Physics, Vol.36, 1968, Page-845.
[4]
Weast, Robert (Editors), CRC Handbook of Chemistry and Physics, 53rd Edition.
[5]
Imtiaz Ahmed, Sidra Khalid and Ehsan E Khawaja, Filament temperature of low
power incandesecent lamps: Stefan-Boltzman law, http:// www.journal.lapen.org.nix
[6]
Austin R Carter, Department of Physics, The College of Wooster, Stefan-Boltzman
Law, 2004.
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