Radiation Energy
Last modified: July 14, 2015
Abstract
Radiation is everywhere on our planet: solar radiation that makes our bodies warm,
radiation heaters, radiation from antennas for communication. In this module, we
will learn how this radiation works by studying objects that have similar radiation
patterns as the sun. We will then make use of what we know about the sun's
radiation to make a device that efficiently converts solar energy into electrical
energy that can be used for generating electricity.
Preparatory Problems:
Adapted from the MIT Junior Laboratory guide "Blackbody Radiation and the StefanBoltzmann Law"i
1. What is a ‘blackbody’, and what is the Stefan-Boltzmann law?
2. The resistivity of tungsten at 300 K is 5.65 μΩ-cm. Compute the resistance of
tungsten wire 0.001 cm in diameter and 1 cm long.
3. Suppose a voltmeter with an internal resistance of 10^6 ohms registers 1 mV
when it is connected across a 1-Ω precision resistor in series with a pilot light to
measure the current through the filament, as illustrated in Figure 1. What is the
exact current in the filament?
4. Suppose the error in a measured value of P is 2%, and the error in the
corresponding measured value of T is 1%. What is the error in the calculated
quantity PT−4?
5. In this experiment you will measure V2 as a function of V1. For each pair of
voltage values you will compute a value of T according to Equation (2). On the
basis of the Stefan-Boltzmann law, predict the shape of a plot of the quantity
V1V2/T4 against V1.
6. Calculate the power of light emitted from the sun, and the intensity of light once
it hits the Earth.
Safety:
It is important that you do not look directly at the sun, or at an object that is
reflecting light from the sun. Our eyes are extremely sensitive organelles, and even
direct exposure for xx seconds to the high power light that our sun can cause
blindness.
Blackbody radiation:
Adapted from the MIT Junior Laboratory guide "Blackbody Radiation and the StefanBoltzmann Law"
In this experiment, you will be studying radiation from a tungsten filament light
bulb and comparing it to a blackbody. You will determine the law that relates the
power dissipated by the light bulb to the temperature of the bulb. Additionally, you
will determine the Stefan-Boltzmann constant that relates those two quantities.
Introduction
Many objects that radiate light are blackbodies, meaning that they absorb all colors
of light. The name "blackbody" comes from the fact that the object doesn't reflect
any light, similar to the color black. However, the sun is an example of a blackbody,
and it doesn't look black. In fact, all stars are examples of blackbodies, and none of
them look black. This is because, when a blackbody is in thermal equilibrium with
its surroundings, it will actually emit light, giving it a color.
A special characteristic of blackbodies is that the amount of each color of light it
emits only depends on the temperature of the object, and not on its shape. An
example of the amount of light emitted by a blackbody at each frequency is shown in
Figure xx.
We see the amount of light peaks at some frequency, and the peak is what gives the
blackbody its shape. So for a yellow-colored sun, the shape of the graph is peaked at
about 500 nm, whereas for a blue-colored sun (which is much hotter), the graph is
peaked at about 300 nm.
Blackbodies became an interesting thing to study in the early 1900s, because Figure
xx could not be explained by classical physics. Only in 19xx did Max Planck realize
that the figure could be explained if you assumed that light was exchanged between
matter and the electromagnetic field in units of hv, where h was a new constant
(later called Planck's constant), and v was the frequency of the light. Before Planck
discovered this, there was a lot of work done on blackbodies, and one of those was
Joseph Stefan's observation that the total power radiated by the blackbody
depended on the temperature to the 4th power:
P = sigma * A * T^4
(1)
where sigma is Boltzmann's constant 1.381 × 10-23 W-m-2-K-4, T is the absolute
temperature in Kelvin, and A is the surface area of the object in meters^2.
Other objects, like light bulb filaments, also act similar to blackbodies. In this
experiment, we will make electrical measurements of a tungsten filament in a light
bulb to determine the quantity P/T4 from just above room temperature to over 3000
K. We will thereby test how well tungsten mimics the behavior of an ideal
blackbody.
Experiment
Setup
The setup is shown in Figure xx and consists of a tungsten filament flashlight light
bulb, 2 multimeters, a low resistance resistor, and a power supply. We will use the
power supply to apply different voltages to the light bulb (which will change the
power dissipated by the filament). Simultaneously, we will be using one multimeter
to monitor the current through the light bulb and one multimeter to monitor the
voltage drop across the light bulb; the two quantities together will tell us the power
dissipated. After the experiment, you will be cracking open the light bulb to
determine the surface area of the filament.
Unfortunately, we cannot directly monitor the current through the light bulb with a
multimeter, because the range of currents that is needed is larger than the range of
the multimeter. Instead, we will use a current shunt, where a small resistance is
connected in series with the lightbulb, and we will measure the voltage drop across
the resistor to determine the current through the light bulb. (see Preparatory
problem 3) (Should I explain more here and make it more explicit? xx)
To measure the temperature of the filament, we can actually use the resistance of
the light bulb. We know that the resistance of a filament of cross sectional area A
and length L is directory proportional to the resistivity R = ρL/A. If L/A is constant,
then we can use the resistance as a direct measure of the resistivity. For a relation
between the resistivity and temperature of tungsten, we can look in The Handbook
of Physics and Chemistryii. A fit to the handbook data gives:
T = a0 + a1ρ + a2 ρ2 + a3 ρ3
(2)
where T is the temperature in Kelvin, a0 = 103.898, a1 = 214.93, a2 = -2.9944, and a3
= 0.043. To find the resistivity without knowing L/A, we can use the relation R/R300
= ρ/ ρ300, where R300 is the resistance at room temperature (which we will measure),
and ρ300 is the resistivity at room temperature (which we will look up in the
Handbook of Physics and Chemistry). Once we know the resistivity, then we can
calculate the temperature using Equation (2).
write procedure and data analysis
Solar cells
In this experiment, you will be making a solar cell that converts solar energy into
electrical energy. You will be characterizing the solar cell's efficiency in various
different ways by using the blackbody radiation curve of the sun and the total power
radiated from the sun.
Introduction
Background to solar panels and their use in Rwanda.
Components of a solar cell
Making the solar cell
We will be making a solar cell by using cuprous oxide as a semiconductor, copper as
a counter electrode, and salted waver as an electrolyte.
More serious chemistry
http://topdiysolarpanels.com/how-to-build-your-own-solar-cells/
Making solar cells with household items (hibiscus tea, powdered sugar, coffee filter,
ethanol, conducting glass, iodine)
http://www.wired.co.uk/magazine/archive/2010/03/how-to/how-to-make-yourown-solar-cell
Less serious solar cell (seems like photoelectric effect)
http://scitoys.com/scitoys/scitoys/echem/echem3.html#flatpanel
Can also check out Practical Education Network's solar energy modules. (most about
using solar panels and solar cells, as opposed to making them)
Physics with solar cells: Measuring IV curve
http://www.ijsoweb.org/qna/expt-2011-phy.pdf
Or measuring efficiency of solar cell at different wavelengths, then using
blackbody radiation curve to normalize to find absolute efficiency
Or measuring effect of tilt angle on efficiency
Calculate the efficiency of the solar cell, by knowing what the total power
radiated from the sun is.
Blackbody Radiation: The Stefan-Boltzmann Law, Junior Physics Lab, MIT
Department of Physics, 2003.
ii Handbook of Physics and Chemistry
i