Lab
Radiation of a Metal Cylinder
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In this lab we are going to investigate the properties of an incandescent solid. We will be using a variety of specific heat specimens at room temperature as our incandescent solids. They will radiate in the IR part of the spectrum.
Each group will be given a metal cylinder composed of either lead, copper, aluminum, or zinc. Each metal has its own unique emissivity constant listed in the table below. These values are based on the conditions of our specimens and are not standard for every sample of that metal.
metal
emissivity
aluminum
0.4
lead
0.6
copper
0.8
zinc
0.3
In our analysis we will be using the following relationships for incandescent solids:
Wien's Law
Stefan-Boltzmann Law
e
is the emissivity of the metal (0 <=
e
<= 1)
s
is Stefan's constant which equals 5.67 ×10
^{−8}
W/(m
^{2}
K
^{4}
)
We will also be using the relationships:
wave speed
photon energy E = hf
where h is Planck's constant and equals 6.63 x 10
^{-34}
Jsec
Since we are working with metal cylinders, you will also need to know how to calculate the surface area and volume of a cylinder
SA = 2
p
rL + 2
p
r
^{2}
V = (
p
r
^{2}
)L
^{ }
The volume of a sphere is V = 4/3(
p
r
^{3}
)
You will also need to remember how to calculate the mass density of a sample,
r
= M/V
Data Collection
Your metal sample is composed of what type of metal?
What is the mass of your cylinder in grams?
What is the height (length) of your cylinder in cm?
What is the diameter of your cylinder in cm?
What is the volume of your cylinder in cm
^{3}
?
What is the density of your cylinder in g/cm
^{3}
?
What is the total surface area of your cylinder in cm
^{2}
?
What is its surface area in m
^{2}
?
What is the room temperature in ºC?
What is the room temperature in Kelvin?
What is the emissivity of your cylinder's metal?
Data Analysis
Use the Stefan-Boltzmann Law to determine how much energy is radiated each second, power, by your cylinder (J/sec or watts).
Power =
es
AT
^{4}
Remember that all values must be in the MKS system. So your surface area must be in m
^{2}
and your temperature must be in Kelvin.
Use Wien's Law to calculate the peak wavelength of your cylinder's radiation (m)
In which part of the electromagnetic spectrum does this wavelength belong?
infrared
visible
ultraviolet
Using the fact that the speed of light is c = 3 x 10
^{8}
m/sec, determine the peak frequency of your cylinder's radiation in hz.
Determine the energy, in Joules, of a single photon emitted at the cylinder's peak frequency.
What is the total number of photons radiated
each second
by your cylinder?
Conclusions
In astronomy, the radiation energy density of a blackbody is given by the formula
u = aT
^{4}
where a = 7.5658 x 10
^{-16}
J/m
^{3}
/K
^{4}
This is a measure of the energy per unit volume emitted by a perfect blackbody based on its Kelvin temperature. This equation assumes that the photons carrying this energy are released isotropically (the same in all directions) and are traveling perpendicular to the emitting surface area. For our purpose, we can assume that we will let our generalized volume be spherical.
What would be the radiant energy density of a perfect blackbody in space if it were at the same temperature as your metal cylinder?
What is the volume of our perfect blackbody if it emits the same energy per second as our metal cylinder?
What would be the radius of our perfect blackbody radiator?
Which of
Jupiter's
moons
has a comparable radius to our perfect blackbody radiator?
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