Taking the temperature of the Sun
Student Brief
The surface of the Sun is hot. This experiment aims to find out how hot.
The heat from the sun radiates out into the solar system. By the time it gets
to us it has spread out into a sphere the size of the Earth’s orbit.
The idea of this experiment is that you can capture this spread out heat in a
cup of water.
If you know what part of the Sun’s spread out heat you have caught in your
cup you can calculate the total heat output of the Sun.
Once you have that piece of information it is possible to work out how hot the
surface of the Sun must be.
There’s quite a lot of maths needed to do the calculations but you are going to
use a computer spreadsheet to crunch the numbers for you.
You need to concentrate on getting a good set of measurements to plug into
the spreadsheet.
What will mess up your experiment?
Clouds reflect the Sun’s energy and will make it appear cooler – if it’s overcast
forget it!
The atmosphere will absorb the energy. People closer to the equator will see
the Sun through a thinner layer of heat absorbing atmosphere at mid day and
the Sun will appear hotter. (A measure of a stick’s shadow compensates for
this in the spreadsheet.)
The water could evaporate
Light could reflect off the water
Light could reflect off the cup
Heat could radiate/convect/conduct out of the cup
Heat could radiate/convect/conduct into the cup (from sources other than the
Sun – eg you hand)
The top of the cup will be at an angle to the Sun unless you are in the tropics.
(A measure of a stick’s shadow compensates for this in the spreadsheet.)
So, there are lots of factors to mess up the experiment but lots of opportunity
to try to design them out and probably lots to evaluate at the end too.
Created by M. Cripps, Neatherd High School, Norfolk, UK
Taking the Temperature of the Sun - Method
Equipment
Plastic cup, insulating material, sticky tape, cling film, thermometer,
measuring cylinder, stopwatch, 2 x metre rules, black ink, graph paper, results
sheet, access to a computer to use the spreadsheet
1.
2.
3.
4.
5.
Insulate the plastic cup on the outside (eg bubble wrap).
Measure the outdoor temperature.
Use water which is a couple of degrees below the outdoor temperature.
Accurately measure the amount of water needed to fill the cup ¾ full.
Add three drops of black ink to the water (so that it absorbs the
sunlight).
6. Put on a cling film top (to stop evaporation).
7. Push a thermometer through the cling film.
8. Place the cup outside in a sunny position.
9. Start the timer and take the temperature every minute.
10. Gently stir with the thermometer before taking each temperature.
11. Continue until it is several degrees above the outside temperature.
You also need to find out the angle of the Sun. Do this by holding the end of
a metre stick between your thumb and index finger and dangle it just above
the ground. Get someone else to use another metre stick to measure the
shadow length.
Created by M. Cripps, Neatherd High School, Norfolk, UK
Taking the Temperature of the Sun - Results sheet
Volume of water
Length of shadow
Weather conditions
Time (s)
0
60
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
1020
1080
1140
1200
cm3
mm
Clear/Average/Hazy
Temperature (oC)
Now plot a graph of temperature against time (in seconds)
Created by M. Cripps, Neatherd High School, Norfolk, UK
Look at the part of the graph that is a straight line both side of the outside
temperature and draw a line of best fit through it. Take the temperature rise
and time between two points on the graph and plug them into the
spreadsheet.
Unless you are on a mountain top in the tropics with the Sun directly
overhead, the sunlight will be partly absorbed by the atmosphere and striking
your cup top at an angle. Straight overhead is called the Zenith. You need to
find out the angle the Sun is off the Zenith. Plug your shadow stick
measurements into the Zenith Angle mini sheet. Mark the Zenith angle it
calculates on the transmission graph below. Draw a line up to the local
weather condition line. Now draw a horizontal line across to find out the
proportion of sunlight that should be getting into your cup. If you are using this
as a Word doc you can resize the box on the right to help take readings from
the graph.
Plug the figure into the main spread sheet or start crunching numbers
yourselves.
Some quantities in the calculation are shown in this diagram
Created by M. Cripps, Neatherd High School, Norfolk, UK
How the numbers are crunched
If you find maths scary don’t read this! It’s really only for those that
enjoy difficult maths.
First calculate the energy transfer rate by using the specific heat capacity
(how much energy 1g of something needs to heat up by 1oC) of water.
Luckily at our level of accuracy, 1g of water = 1cm3.
(oC/s) x 4.2(J/cm3/oC) x vol. water (cm3) = Watts
You now need to find the Effective Area of the cup.
First find the area of the top of the cup (A cup) using πr2 (in metres).
To compensate for the Zenith angle (θ) first find the angle using the length of
the stick (L) and the shadow (S).
tan(θ) =S
L
Now compensate by multiplying the area of the cup by the cosine of the
Zenith angle A = A cup . cos(θ)
Now you need to find out the amount of energy striking each square metre of
the Earth’s surface .
Divide the Watts absorbed by the cup by its effective area. You now have a
measurement in Watts/m2
You now need to compensate for the atmospheric absorption at your zenith
angle.
Read this off the supplied graph as described in the main method. Multiply
your Watts/m2 figure by this compensation factor
You have now calculated what is called the Solar Constant (E). This is a
measure of the number of watts striking one square metre of surface at a
distance of one astronomical unit (1.5 x1011m) from the Sun.
You now need too now find out the area of that one Astronomical Unit sphere
4πr2 where r =1.5 x1011m
= 2.83e+23
Now multiply the area of the Earth orbit sized sphere by your Solar constant
figure to find out the energy output of the Sun – its Luminosity.
2.83e+23 E = Luminosity
Created by M. Cripps, Neatherd High School, Norfolk, UK
It is at this point you will find out how far out you are as the figure is really
3.825 x 1023W
Now that you know how much total energy the Sun puts out, you can also
work out how much energy is given out by each square meter of the solar
photosphere (ESun). Since the radius of the Sun is about 7.0 x108m, we
divide the total energy output by its surface area:
ESun= Luminosity/4π(7.0 x108m)2
Next you need to convert the output to the temperature of the surface.
The Sun radiates energy according to the Stefan-Boltzmann law: the power
radiated per unit area (ESun) is proportional to the fourth power of its absolute
temperature T measured in degrees Kelvin:
ESun= σ T4
where σ (called the Stefan-Boltzmann constant) is known from experiments to
be 5.69E10-8 watts/(m2K4)
So
T = (ESun/ σ)1/4
You finally have the temperature of the Sun in oK
0o Kelvin = -273o Celsius (i.e. Absolute Zero temperature)
273o Kelvin = 0o Celsius
So to convert Kelvin to Celsius subtract 273
Check your answer with the spreadsheet
Diagrams and graphs courtesy of Sommers Bausch Observatory, Department
of Astrophysical & Planetary Sciences, University of Colorado
Created by M. Cripps, Neatherd High School, Norfolk, UK
Austrian Scientist first to
calculate the temperature of the Sun
Joseph Stephan 1835-1893
Ludwig Boltzman 1844-1906
The first person to take the temperature of the Sun was Joseph Stephan in
1884. He had done lots of experiments in his laboratory that showed that hot
objects gave off heat in a particular relationship to their temperature. His
student Ludwig Boltzman worked out the mathematics needed to calculate the
temperature. Stephan was then able to measure the approximate
temperature of the photosphere of the Sun as 5430°C, the first sensible
estimate.
Created by M. Cripps, Neatherd High School, Norfolk, UK