Download Power loss from hot tungsten filament

Power loss from hot tungsten filament
S. R. PATHARE, R. D. LAHANE, S. S. SAWANT*, C. C. PATIL
Homi Bhabha Centre for Science Education (TIFR)
V. N. Purav Marg, Mankhurd. Mumbai 400 088.
[email protected]
*
Bhavan’s College, Munshi Nagar, Andheri (W), Mumbai – 400 058.
ABSTRACT
This is an edited version of the experiment set for the experimental
examination conducted at the orientation cum selection camp held at Homi
Bhabha Centre for Science Education (TIFR), Mumbai in May 2010. In
this experiment the modes of power loss from hot tungsten filaments in
electrical bulbs are studied are explored.
Introduction
There is a regular experiment in many Indian undergraduate colleges, where students are asked to
verify Stefan-Boltzmann law of radiation using an incandescent bulb. Generally it is assumed that
the electrical power supplied to the filament is lost in the form of radiation. In fact, there are three
modes of energy loss from a hot body: conduction, convection and radiation. But the assumption
may be based on an erroneous belief that heat loss from a body is basically due to radiation. The
observations leading to Newton’s Law of Cooling suggest that energy from a body which can be at a
temperature of about 100° C above the surroundings is mainly lost by conduction and convection
processes and radiation loss is almost negligible. The electrical bulbs are partially evacuated or are
filled by some inert gases. In both cases all the three processes of energy loss are to be considered.
This experiment tries to understand the contribution of these processes in heat loss from the tungsten
filament of a partially evacuated bulb.
Apparatus:
1) One partially evacuated bulb
2) Lamp holder mounted in a PVC cylinder
3) A 0-15 V/1A dc power supply
4) Two digital multimeters (DMMs)
5) A thermocouple (already inserted in the PVC cylinder) with digital thermometer
6) A yellow cloth for removing the hot bulb from the holder
7) Connecting wires
1 Circuit Diagram:
Fig.1 Circuit diagram
Description of apparatus:
1) Bulbs
Fig.2 Vacuum bulb (semicircular filament)
2) Bulb holder and thermocouple mounted in the PVC pipe:
Fig.3 PVC pipe consisting of bulb holder and Cr-Al thermocouple
3) DC power supply:
The 0-15V/1A dc power supply has coarse and fine controls for voltage and current adjustments. While
performing the experiment, set the current limit to its maximum value, i.e., fully rotate the current knob and
keep it on its maximum position. The fine knob for voltage control uses a 10 turn potentiometer.
4) Digital multi meters
Use the ‘V/Ω’ and ‘COM’ sockets of the DMM for voltage measurements. Use ‘2A’ and ‘COM’ sockets for
current measurements. Do not use the DMM for any resistance measurements in this experiment.
2 5) Cr-Al thermocouple with digital thermometer
Fig.4: Photograph of the thermometer with thermocouple
A digital thermometer with Cr-Al thermocouple as temperature sensor is given to measure the temperature of
the specimen rod. The thermocouple is placed in contact with the surface of the bulb using a cello tape. Note
the following points for thermometer operations:
a)
b)
c)
d)
Press “ON” button to start the thermometer and “OFF” to switch off the thermometer.
The thermometer is in “°C” mode and not in “°F” mode.
The thermometer has least count of “0.1 °C”.
Do not press any other button on the thermometer panel.
Accuracy:
Accuracy is specified for operating temperatures over the range specified below:
± (0.3% of reading + 1°C) for –50°C to 1000°C
Theory
A hot body left to cool in air loses heat both by conduction-convection and radiation. It is a well
observed fact that wind blowing over a hot body cools it faster and also lowers the temperature of its
surface. Lowering the surface temperatures increases the temperature gradient between its interior
and exterior leading to increase in conduction. At the same time the lowering of surface temperature
reduces the radiation loss from the body. This clearly shows that the cooling of bodies at
temperatures not far above that of surroundings is mostly due to conduction-convection process and
is accounted for by Newton’s Law of Cooling. . The heat loss due to radiation in this temperature
domain must be negligible. Newton’s law of cooling states that the rate of cooling of a body is
proportional to the difference between the temperature T of the body and T0 of the surroundings.
According to Stefan-Boltzmann law the net power loss in the form of radiation from a hot body at
absolute temperature T is proportional to T 4 − T04 . The rate of loss of energy by each mode would
depend on the proportionality constant appearing in the relevant law.
Let us write the relation for the rate of loss of thermal energy from a body as a sum of losses by the
two modes as,
3 (
P = a(T − T0 ) + b T 4 − T04
)
where a and b are some constants appearing in Newton’s Law of cooling and Stefan-Boltzmann’s
Law of Radiation for the given body respectively. There is possibility that the constant a may depend
on such parameters as the speeds of convection currents and pressure in the surrounding fluid. The
constant b depends upon the emissivity (ε) of the material of the hot body and the surface area (A) of
the hot body ( b = σ ε A ). Empirical studies have shown that emissivity of a material varies with
temperature.
When electrical power is supplied to the filament of the bulb, power supplied to the filament is equal
to VI where V is the voltage drop across the filament and I is the current through it. Equating the
supplied power with that dissipated by the filament we get
(
VI = a(T − T0 ) + b T 4 − T04
)
(1)
It is possible to determine the values of a and b by doing suitable experiments. We should expect
that at low temperatures Newton’s Law of Cooling should be accounting for almost all heat loss and
to a very good approximation we should find that VI = a(T-T0). So, by plotting a graph the value of
the constant a can be obtained. We are guided to restrict ourselves to that domain of T above which
the graph appears to deviate from straight line. It may also be noted that empirically the law is well
tested for temperature differences up to about 100°C.
If we assume that the law remains valid for all values of T we can calculate the fraction of power
dissipated by conduction–convection process for higher values of temperature. [There is no obvious
evidence to either support or oppose this assumption.] Subtraction of this fraction from the total
power supplied gives the power radiated in the form of electromagnetic radiation. A graph of
radiated power versus fourth power of T would give the value of b. But as mentioned earlier the
emissivity of the filament is a function of T. So, if we express the emissivity as ε = ε0Tx, where x is
some unknown number, we may write Eq.1 as
(
VI = a(T − T0 ) + b0 T 4+ x − T04+ x
)
(2)
where, b0 = σε0A.
To perform this experiment we need to know the temperatures of the filament at various values of
supplied electrical power. There can be various methods for estimating the temperatures of the
filament. Data regarding the resistivity of tungsten at temperatures starting from 300 K up to 3500 K
is available. Based on such data a relation between the ratio T/T0 and that of resistance R of the
filament at temperature T to its resistance R0 at T0 = 300 K can be written because the change in the
resistance is mainly due to change in resistivity. The temperature coefficient of linear expansion is of
the order of 10-5/K and so change in R due to changes in the dimensions of the filament is negligible.
Experiment:
Connect the circuit as shown in Fig.1.
4 The data can be collected by varying voltage and noting down the current for two different purposes:
1) to determine the resistance R0 of the filament at room temperature T0 and 2) to determine
resistance R of the filament at various higher values of temperature.
The uncertainties in the measurements of currents and voltages get propagated in the values of T. So,
to evaluate the uncertainties in your results you will have to enter the uncertainties in all your
readings of voltages and currents along with the readings of those quantities. Tabulate the measured
quantities and the evaluated uncertainties in them.
Assume that the uncertainty in the voltage readings of the DMM is 0.5% of reading + one
digit(= least count of the range selected) and for current readings it is 1% of the reading + one
digit(= least count of the range).
Part A: Determination of R0, the Resistance at Room Temperature T0 (assumed to be equal to
300 K)
To determine R0 using Ohm’s Law the power supplied to the filament must be so small that its
temperature remains practically unchanged. The choice of the range of readings depends upon the
lowest range of voltage and corresponding current measurements. See what the smallest voltage
range on your DMM is and select appropriate current range in the other DMM to measure the current
when the small voltage is applied across the filament. Take a good number of readings and plotting a
graph, determine the resistance R0 of the filament at T0. If the graph shows non-linearity above
certain values of V, use your judgment to select the proper range for this exercise. Report your value
of R0 with the uncertainty in the answer sheet.
Part B: Determination of R
The resistance of the filament is always given by the ratio V/I. Keep the circuit unchanged but
increase the voltage across the filament by larger steps so that you can get a good number of values
of R as you increase the voltage V from 0 to 15 V. To measure the temperature T0 of the bulb (which
acts as the surroundings) put the thermocouple in contact with it. Make a column in the table to enter
t0, the temperature of the glass bulb
While taking readings for R, you may take them in two sets. One set for values of V in the range 0200 mV and the other in the range 0-20 V. (The readings of 0-200 mV would be needed for part E
and the readings on 0-20 V for part F, G and H).
By carefully adjusting the applied voltage find the values of V and I for which the filament just
begins to show a reddish glow. Solids begin to glow with reddish light at a specific temperature
called Draper Point.
Calculate R.
Part C: Finding the Expression for the Absolute Temperature T
To determine the temperature of the filament at different values of R/R300, use the data giving the
values of temperatures T and corresponding values of R/R300.
5 You may assume that the resistivity and hence the resistance of the filament varies as Tm and obtain a
relation between R/R300 and T/300. Using the given data, plot a suitable graph to obtain the value of
m.
Substituting the value of m, write an expression for the absolute temperature T of the filament as a
function of R/R300. Calculate R300 for the filament resistance from your values of R0 and T0.
Calculate R/R300 and evaluate the uncertainties in the ratio R/R300.
Part D: Estimating Temperature T of the Filament from its Resistance R
Evaluate the temperature at various values of electrical power P (= VI) supplied to the filament using
that expression. Evaluate the uncertainty in the temperature thus determined.
Determine the temperature TD of Draper Point from your observations.
Make a table showing electrical power P, uncertainty ΔP, temperature T and uncertainty ΔT.
Part E: Determination of Constant a
Plot VI versus T for appropriate range of readings and determine the value of the constant a and the
uncertainty Δa in it.
Part F: Determining Temperature T1/2
Knowing the value of a, calculate the power dissipated by conduction-convection processes for all
values of T. Determine the value of T at which about half of the supplied power is radiated. Enter the
value of this temperature T1/2 with accompanying uncertainty in your answer sheet.
Part G: Radiated Power and its Relation with T
Make a table showing the radiated power Pr [= VI – a(T-T0)] and the corresponding temperature T for
values of T>T1/2. If the emissivity of tungsten filament varies appreciably with T, the radiated power
would be proportional to Tn –T0n, where n = 4 + x. For large values of T, T4+x >>T04+x and a suitable
graph can be plotted to estimate the value of x. Plot the required graph and enter the value of x with
its uncertainty in the answer-sheet.
Part H: Determination of b0 = σ ε0 A
Plot the required graph to obtain the value of b0 from its slope. Evaluate the uncertainty in its value.
Enter the values of a and b0 along with the accompanying uncertainties in the answer-sheet.
Typical values of dimensions of the filament are radius = 0.045 cm and the length = 6.5 cm. Stefan’s
constant = 5.67 × 10-8 W m-2 K-4. Determine the emissivity ε0 of tungsten filament. Evaluate the
uncertainty in the emissivity.
6 Data:
Table 1. Resistivity of tungsten as a function of temperature
R
T
Resistivity
R
T
Resistivity
R300K
/K
/μΩ·cm
R300K
/K
/μΩ·cm
1.0
300
5.65
10.63
2100
60.06
1.43
400
8.06
11.24
2200
63.48
1.87
500
10.56
11.84
2300
66.91
2.34
600
13.23
12.46
2400
70.39
2.85
700
16.09
13.08
2500
73.91
3.36
800
19.00
13.72
2600
77.49
3.88
900
21.94
14.34
2700
81.04
4.41
1000
24.93
14.99
2800
84.70
4.95
1100
27.94
15.63
2900
88.33
5.48
1200
30.98
16.29
3000
92.04
6.03
1300
34.08
16.95
3100
95.76
6.58
1400
37.19
17.62
3200
99.54
7.14
1500
40.36
18.28
3300
103.3
7.71
1600
43.55
18.97
3400
107.2
8.28
1700
46.78
19.66
3500
111.1
8.86
1800
50.05
20.35
3600
115.0
9.44
1900
53.35
10.03
2000
56.67
7 Typical Observations and Calculations:
Part A: Determination of R0, the Resistance at Room Temperature T0
Obs.
No.
1
2
3
4
5
6
7
8
9
10
V
/(mV)
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
I
/(mA)
0.750
1.525
2.27
3.07
3.74
4.52
5.25
6.03
6.76
7.48
10
V /mV
8
6
4
2
0
0
1
2
3
4
5
6
7
I /mA
R0 =1.338 ± 0.005 Ω
Part B: Determination of R
(i) 0 – 200 mV:
Obs.
No.
1
2
3
4
5
6
7
8
V
/(mV)
60.0
80.0
100.0
120.0
140.0
160.0
180.0
200
I
/(mA)
44.1
57.1
70.0
80.8
91.4
100.5
108.9
116.3
8 t0 /°C
35.9
36.0
36.1
36.3
36.3
36.3
36.3
36.2
R
/ (Ω)
1.361
1.401
1.429
1.485
1.532
1.592
1.653
1.720
8
(ii) 0 – 20 V
Obs.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
V
/(V)
0.50
1.50
2.00
2.50
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
I
/(mA)
160.9
238
275
308
338
394
445
491
534
574
613
649
684
716
748
779
t0 /°C
36.2
36.9
39.7
40.8
41.9
44.8
47.7
53.4
55.3
57.9
65.4
68.6
70.7
74.4
81.3
84.9
R
/(Ω)
3.11
6.30
7.27
8.12
8.88
10.15
11.24
12.22
13.11
13.94
14.68
15.41
16.08
16.76
17.38
17.97
Part C:
(i) Determining the relation between
R
T
and
:
R300
300
Obs.
No.
R300 K
T
300
1
2
3
4
5
6
7
8
9
10
11
12
1.00
2.34
3.88
5.48
7.14
8.86
10.63
12.46
14.34
16.29
18.28
20.35
1
2
3
4
5
6
7
8
9
10
11
12
R
⎛ R
ln⎜⎜
⎝ R300 K
0
0.850
1.356
1.701
1.966
2.182
2.364
2.523
2.663
2.791
2.906
3.013
9 ⎞
⎟⎟
⎠
⎛ T ⎞
ln⎜
⎟
⎝ 300 ⎠
0
0.693
1.099
1.386
1.609
1.792
1.946
2.079
2.197
2.303
2.398
2.485
2.5
ln(T/300K)
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
ln(R/R300K)
The value of the slope, m = 0.82
Relation for T as a function of
R
:
R300
⎛ R ⎞
⎟⎟
T = 300⎜⎜
R
⎝ 300 ⎠
10 0.82
Part D: (i) Estimating Temperature T of the filament from its Resistance R (0 – 200 mV)
Obs.
No.
V
/(mV)
ΔV
/(mV)
I
/(mA)
ΔI
/(mA)
t0 /°C
T0 /K
R
/(Ω)
ΔR
/(Ω)
R 300
1
2
3
4
5
6
7
80
100
120
140
160
180
200
0.5
0.6
0.7
0.8
0.9
1.0
2
57.1
70
80.8
91.4
100.5
108.9
116.3
0.7
0.8
0.9
1.0
1.1
1.2
1.3
36
36.1
36.3
36.3
36.3
36.3
36.2
309
309.1
309.3
309.3
309.3
309.3
309.2
1.401
1.429
1.485
1.532
1.592
1.653
1.720
0.011
0.011
0.011
0.011
0.011
0.012
0.015
1.046
1.066
1.108
1.143
1.188
1.234
1.283
R
⎛ R
Δ ⎜⎜
⎝ R 300
0.032
0.032
0.034
0.035
0.036
0.038
0.039
⎞
⎟⎟
⎠
T
/K
ΔT
/K
P
/×10-3W
ΔP
/W
(T- T0)
/K
Δ(T- T0)
/K
311.2
316.2
326.5
334.9
345.7
356.6
368.4
4.5
4.6
4.7
4.8
5.0
5.1
5.3
4.57
7.00
9.70
12.80
16.08
19.60
23.26
0.04
0.05
0.07
0.09
0.11
0.14
0.20
2.2
7.1
17.2
25.6
36.4
47.3
59.2
2.8
2.9
2.9
3.0
3.1
3.2
3.3
Part D: (ii) Estimating Temperature T of the filament from its Resistance R (0 – 20 V)
Obs.
No.
V
/(V)
ΔV
/(V)
I
/(mA)
ΔI
/(mA)
t0
/°C
T0 /K
R
/(Ω)
ΔR
/(Ω)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0.50
1.50
2.00
2.50
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
14.00
0.01
0.02
0.02
0.02
0.03
0.03
0.04
0.04
0.05
0.05
0.06
0.06
0.07
0.07
0.08
0.08
160.9
238
275
308
338
394
445
491
534
574
613
649
684
716
748
779
1.7
3
4
4
4
5
5
6
6
7
7
7
8
8
8
9
36.2
36.9
39.7
40.8
41.9
44.8
47.7
53.4
55.3
57.9
65.4
68.6
70.7
74.4
81.3
84.9
309.2
309.9
312.7
313.8
314.9
317.8
320.7
326.4
328.3
330.9
338.4
341.6
343.7
347.4
354.3
357.9
3.11
6.30
7.27
8.12
8.88
10.15
11.24
12.22
13.11
13.94
14.68
15.41
16.08
16.76
17.38
17.97
0.05
0.07
0.07
0.08
0.08
0.09
0.09
0.10
0.10
0.11
0.11
0.12
0.12
0.12
0.13
0.13
R 300
⎛ R ⎞
⎟⎟
Δ ⎜⎜
⎝ R 300 ⎠
T
/K
ΔT
/K
P
/W
ΔP
/W
(T- T0)
/K
Δ(T- T0)
/K
2.319
4.703
5.427
6.057
6.624
7.576
8.385
9.119
9.783
10.401
10.957
11.499
12.001
12.507
12.970
13.412
0.073
0.145
0.167
0.186
0.203
0.232
0.256
0.278
0.298
0.317
0.334
0.350
0.366
0.381
0.395
0.409
599.7
1073.6
1208.0
1322.3
1423.3
1589.8
1728.3
1852.0
1962.3
2063.9
2154.2
2241.6
2322.0
2402.3
2475.3
2544.5
8.9
15.6
17.6
19.2
20.6
23.0
25.0
26.8
28.3
29.8
31.1
32.3
33.5
34.7
35.7
36.7
0.0804
0.357
0.55
0.77
1.014
1.576
2.225
2.946
3.738
4.592
5.517
6.49
7.524
8.592
9.724
10.906
0.001262
0.003788
0.00537
0.00712
0.00902
0.013294
0.018121
0.023403
0.029138
0.035266
0.041851
0.048739
0.056018
0.063509
0.071414
0.07964
290.5
763.7
895.3
1008.5
1108.4
1272.0
1407.6
1525.6
1634.0
1733.0
1815.8
1900.0
1978.3
2054.9
2121.0
2186.6
5.3
9.1
10.2
11.1
12.0
13.3
14.5
15.5
16.4
17.2
18.0
18.7
19.4
20.0
20.6
21.2
R
Temperature TD of Draper Point = 800 ± 20 K
11 Part E: Determination of Constant a
0.025
0.015
-3
P /10 W
0.020
0.010
0.005
0
10
20
30
40
50
60
T - T /K
0
a ± Δa = (3.228 ±0.006) × 10-4 W/K
Part F: Determining Temperature, T1/2
Obs.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
P
/W
ΔP
/W
T
/K
ΔT
/K
(T – T0)
/K
a (T – T0)
/W
0.0805
0.357
0.55
0.77
1.014
1.576
2.225
2.946
3.738
4.592
5.517
6.49
7.524
8.592
9.724
10.906
0.001262
0.003788
0.00537
0.00712
0.00902
0.013294
0.018121
0.023403
0.029138
0.035266
0.041851
0.048739
0.056018
0.063509
0.071414
0.07964
599.7
1073.6
1208.0
1322.3
1423.3
1589.8
1728.3
1852.0
1962.3
2063.9
2154.2
2241.6
2322.0
2402.3
2475.3
2544.5
8.9
15.6
17.6
19.2
20.6
23.0
25.0
26.8
28.3
29.8
31.1
32.3
33.5
34.7
35.7
36.7
290.5
763.7
895.3
1008.5
1108.4
1272.0
1407.6
1525.6
1634.0
1733.0
1815.8
1900.0
1978.3
2054.9
2121.0
2186.6
0.094
0.247
0.289
0.326
0.358
0.411
0.454
0.492
0.527
0.559
0.586
0.613
0.639
0.663
0.685
0.706
T1/2 ± ΔT1/2 = 1141 ± 17 K
Part G: Radiated Power and its Relation with T
For T > T½ :
Obs.
No.
P
/W
Pr = P - a (T – T0)
/W
ΔPr
/W
T
/K
ln(Pr)
ln(T)
1
2
3
4
5
6
7
8
9
10
11
12
13
0.77
1.014
1.576
2.225
2.946
3.738
4.592
5.517
6.49
7.524
8.592
9.724
10.906
0.507
0.725
1.244
1.858
2.548
3.312
4.14
5.043
5.994
7.008
8.056
9.17
10.335
0.019
0.020
0.020
0.022
0.023
0.025
0.028
0.031
0.034
0.037
0.041
0.045
0.050
1322.3
1423.3
1589.8
1728.3
1852.0
1962.3
2063.9
2154.2
2241.6
2322.0
2402.3
2475.3
2544.5
‐0.679 ‐0.322 0.218 0.620 0.935
1.198 1.421 1.618 1.791
1.947 2.086 2.216 2.336
7.187
7.261
7.371
7.455
7.524
7.582
7.632
7.675
7.715
7.750
7.784
7.814
7.842
2.4
2.2
ln(Pr)
2.0
1.8
1.6
1.4
7.60
7.65
7.70
7.75
7.80
7.85
ln(T)
Slope = 4.3
x = 0.3
Part H: Determination of b0 = σ ε0 A
Obs.
No.
1
2
3
4
5
6
7
8
9
10
11
12
13
P /W
T4.3
0.507
0.725
1.244
1.858
2.548
3.312
4.14
5.043
5.994
7.008
8.056
9.17
10.335
2.6407E+13
3.6239E+13
5.8314E+13
8.3515E+13
1.1242E+14
1.4418E+14
1.7913E+14
2.1534E+14
2.5551E+14
2.9731E+14
3.4411E+14
3.9138E+14
4.4065E+14
0.025
0.015
-3
P /10 W
0.020
0.010
0.005
0
10
20
30
40
50
60
T - T /K
0
Calculation of emissivity, ε0:
b0 = (2.381 ± 0.006) × 10-13 W/K4.3
b0 = σAε 0 = 2.381 × 10 −13
A = 2πrl = 2 × 3.14 × 0.045 × 10 −2 × 6.5 × 10 −2 = 1.8369 × 10 −4 m 2
ε0 =
Uncertainty in ε0:
2.381 × 10 −13
= 0.0228
5.67 × 10 −8 × 1.8369 × 10 − 4
Δε0 = 0.0008
ε0 = 0.0228 ± 0.0008
Discussion:
The experiment involves a rigorous data analysis along with some good insights into the heat transfer
mechanisms. The value of a (3.228 × 10-4 W/K) and the value of b0 (2.381 × 10-13 W/K4) are different by
many orders of magnitude. This shows why near room temperature Newton’s law accounts for almost all the
energy loss. As the temperature of the filament increases, the loss by radiation increases faster than that by
conduction-convection because of the fourth power of absolute temperature appearing in the law. The two
modes appear to be of equal significance at an absolute temperature above 1100 K and at much higher
temperatures Stefan-Boltzmann law accounts for almost all the energy loss from the hot filament. The
emissivity of tungsten is shown to depend upon both wavelength and temperature. In this experiment both the
dependences are clubbed together with temperature. According to data in literature the value of ε for tungsten
lies somewhere between 0.2 and 0.4 at temperature of 2200 K. The value obtained in the experiment is 0.0228
× 22000.3≈ 0.23. The purpose of estimating the value of emissivity is to show that the data analysis based on
the theory gives realistic values for the constants confirming its correctness.
Acknowledgements:
We would like to thank Prof. D. A. Desai for his valuable guidance in the development of this experiment. We
would also like to thank all the students from the Olympiad camp for doing this experiment patiently. We also
wish to thank the students who helped us in standardizing the apparatus.
References:
Desai D. A., Ajit C. B., (2008), Laboratory Experiment with Tungsten Filament Lamp, Physics Education,
Vol.25, 1, pp.55-62.