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Experiment No.-9 STEFAN’S LAW OBJECTIVE: To verify Stefan’s law by electrical method.
battery, y, D.C. Voltme Voltmeter ter,, D.C. ammete ammeter, r, Electr Electric ic bulb bulb (havin (having g APPARATUS: 6V batter tungsten filament) of 6V, 6W, Rheostat (100 ohm). FORMULA USED: Log10P= αLog10T + Log10C
Where, P = Total power emitted by a body at temperature T, α = power of T close to 4 T = temperature of a body C = some constant depending on the material and area of such a body. THEORY: For black bodies, Stefan’s law is E = σ (T4-T04), Where E is the net amount of radiation emitted per second per unit area by a body at temperature T and surrounded by another body at temperature T0. σ is called Stefan’s constant. A similar relation can also hold for bodies that are not black. In such case, we can write P = C (Tσ -T0σ), Where P is the total power emitted by a body at temperature T surrounded by another at temperature T0. σ is a power quite closed to 4 and C is some constant depending on the material and area of such a body. Further the relation can be put as P = C Tσ (1-T0σ/ Tσ), If T>> T0 (e.g., T = 1500K, and T0 ≈ 300K), we can write P = C Tσ Or Log10P = αLog10T + Log10C The graph between Log10P and Log10T should be a straight line whose slope gives α. Theref Therefore ore,, in order order to verify verify Stefan’ Stefan’ss law, law, we have have to measur measuree the followin following g two parameters: (i) (i) Powe Powerr radia radiate ted d P: We use use in this this exper experim imen entt tungs tungste ten n bulb bulb as the radi radiat atin ing g body and in the steady state the electrical power V.I should be equal to the radiation power P (neglecting power lost in the leads and through the gas in the bulb). (ii) (ii) Temp Temper erat atur uree of the the radia radiati ting ng body body,, T: In our our exper experim iment ent we we need need measu measure re the the temperature of tungsten filament. This is achieved by measuring the resistance of filament, R t, and then using the relation R t = R 0 (1+ αt + βt2) With α and β being known for tungsten, we can find temperature of the filament. One serious limitation arises in the measurement of R 0 (resistance of filament at 0°C or 273K, one can write R 0 or R 273 273). At very small current, V/I ratio will give filament
-2resistance as well as lead resistance. In order to calculate R 0 then we measure the resistance (R g) at the stage when the filament first starts glowing and temperature at this stage is approximately 800K. At this temperature contribution of lead resistance becomes smaller by a factor of 4 as compared with that at 273K. Therefore measurement of R g (=R 800) and using the computed factor, R 800/R 273, a more accurate value of R 273(=R 0) is found. PROCEDURE:
1. Make the connections as shown in the figure. In order to connect voltmeter across the bulb, the two wires are soldered to the base points of the bulb. 2. With different increasing and decreasing values of current, we adjust such that the bulb glows each time. Then for value of V and I, ratio V/I is found which gives R g. This is the filament resistance at 800K. From R t/R 0 vs. T graph, we note that R t/R 0 = R 800/R 273 = 3.9 Therefore R 800/3.9 = R 273 Or R g/3.9 = R 0 Graph R t/R 0 vs. T is to be provided to the student (see table3). 3. Now filament current I is increased from a value below glow stage to values high enough to get dazzling white light, measuring voltage V across bulb every time. From these V and I values, we deduce power P (=VI) and R t (=V/I). From R t using the value R 0 (or R g /3.9) or R 273K , we deduce the temperature T of the filament and obtain a graph in Log10P against Log10T. Observations: Current Increasing
Current Decreasing
S.No. Voltage V volts
Current I amp.
R g=V/I Ohms
Voltage V volts
Current I amp.
R g=V/I Ohms
1 2 3 4
Table 2. Determination of Power P: for different temperature T S.No. Pot. Current R t=V/I R t/R o Temp.From Log10T Diff. I amp. Ohms Table 3 or v from graph volts K Min. 10 values
Power Log10P P = V I Volts
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Table 3. For plotting Rt/Ro versus T graph Temp. in O0C 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
R t/R o 1.00 1.53 2.07 2.13 3.22 3.80 4.40 5.00 5.64 6.37 6.94 7.60 8.26 8.90 9.70 10.43
CALCULATIONS: Slope =AB/BC = α
RESULT: Plot the graph between log10P vs. log10T
SOURCE OF ERROR AND PRECAUTIONS:
1: Use the bulb having tungsten filament. 2: Increase the current in steps. 3: Note down the voltage reading after every change in current. 4: Choose the rheostat of appropriate range. 5: Connection should be tight.