Object
To investigate the emissivity of different metal surfaces
To investigate the extent to which a tungsten light bulb filament emulates a black body when heated.
Apparatus
Tungsten lamp and current regulated power supply, two digital multimeters, Leslie's cube, radiometer, hotplate, glass slide, thermometer and beaker of water.
Theory
Stefan discovered that the power (P) or rate at which an object radiates its energy is proportional to its temperature (T) raised to the fourth power: P = s AeT^{4}, where P is in MKS units joules/second (watts), s is a constant equal to 5.6696x10^{-8}W/m^{2× }K^{4}, A is the surface area of the object in square meters, e is the emissivity constant, and T is the temperature measured in Kelvin. The emissivity, which can vary between zero and one depending on the properties of the object, is a measure of how "good" a radiator an object is. The ideal radiator, e = 1, is also an ideal absorber. Such an object is referred to as a "black body". In contrast, an emissivity of zero would correspond to an object which neither absorbs nor radiates energy.
The Leslie's Cube helps demonstrate the large differences in emissivity of the surface finish of metals. It is a container with four sides finished with different surfaces: black paint, white paint, polished brass, and roughened brass. Filling the Cube with water assures that all surfaces are the same temperature.
The electrical energy delivered to a tungsten filament bulb is predominately radiated as electromagnetic energy by the filament. By comparing the measured radiation from the bulb and calculated temperature of the filament, the performance of the filament as a blackbody and the Stefan-Boltzmann Law can be tested.
Procedure
1. Place the Leslie's Cube about 5cm from the front face of the radiometer to fill most of the collecting field.
2. Partially fill the Cube with hot water. Record the temperature of the water just prior to and after making measurements.
3. Darken the room and make sure no radiating objects are in the field of the radiometer. Set the radiometer on the #1 range. With the shutter closed, adjust the Zero. Open the shutter and note the reading. If it is over 0.2W/m^{2}, find the source of radiation and remove it. Now adjust the Zero, with the shutter open.
4. Measure and record the radiation from each surface.
5. Place a glass slide between the Cube and the radiometer and record the radiation that is transmitted.
6. Repeat Procedures #3 and #4 for three other temperatures evenly distributed between 50 °C and 100 °C.
Analysis and Questions
1. Rank the surfaces in order of increasing emissivity.
2. Plot the radiation from each source as a function of T on a log-log plot and find the slope for each surface. How well does each surface behave with regard to the Stefan-Boltzmann Law?
3. Compare the radiometer readings with and without the glass plate. What percentage of the radiation is absorbed or reflected by the glass? Is glass a better transmitter of infrared or visible light? What is the link between this behavior and the Greenhouse Effect. Also, does it explain why the inside of a car parked in the sun heats up so rapidly?
Procedure
1. Place the filament about 5cm from radiometer. The filament should be parallel with the front face of the radiometer.
2. Connect a digital voltmeter in parallel and an 0-300mA digital ammeter in series with the lamp and power supply. Draw a circuit diagram using circuit symbols. Make sure your connections are correct for each meter and that the main voltage and voltage fine adjust knobs on the power supply are turned fully counter-clockwise.
3. Darken the room and make sure no radiating objects are in the field of the radiometer. Do this by setting the radiometer on the #1 range. With the shutter closed, adjust the Zero. Open the shutter and note the reading. If it is over 0.2W/m^{2}, find the source of radiation and remove it. Now adjust the Zero, with the shutter open.
4. Increase the fine adjustments on the voltage and current to get a voltage reading of about 0.03V. Put the voltmeter on the 300mV scale. Record the voltage and current for a range of values between 10 and 50mA. You will need to use the fine adjustment knobs. These readings will be used, along with Ohm's law, to determine the cold resistance of the filament.
5.
Make the connections to read on the 10A maximum scale. Adjust the current
to read 1.5A.
Note: Don't let the current through or
voltage across the lamp exceed the lamp's maximum rating. For the bulb you
will use do not go over 1.6A!
6. Record the voltage, current and radiometer signal. Repeat this step at least ten times in small increments of voltage down to ~ 0.5V. Check the Zero frequently and adjust the radiometer scale as needed. Be careful as you change scales on the radiometer.
Analysis and Questions
1. The "cold" filament resistance can be found by a least-squares fit to the data from Procedure #4. The filament resistance for each reading from Procedure #6 can be calculated using Ohm's Law, R = V/I.
2. The resistance of a tungsten filament is approximately related to its temperature by the following relation:
R = R_{20} (1 + 0.0045(T-20))
where R_{20} is the resistance at 20 °C (the "cold" resistance) and T is expressed in °C. Find the temperatures for your data. You will need to solve the above equation for T.
3. Plot the log(measured radiation) as a function of log(T). Is this relationship linear over the entire range of measurements? If not, discuss the reasons for this non-linear behavior. What is the slope and y-intercept of the plot? What should each be if the filament is an ideal blackbody?
4. The Stefan-Boltzmann Law is exactly applicable for perfect blackbodies. Do your results indicate that the light bulb behaves as an ideal blackbody? If it does, over what temperature range? Discuss reasons for departure from blackbody behavior.
FOR FURTHER THOUGHT
How would you measure the spatial dependence of the total power radiated from a heated filament? What problems might you expect in making these measurements?