Ask an Expert: Help with the StefanBoltzmann Equation
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 Posts: 4
 Joined: Mon Dec 30, 2019 4:59 pm
 Occupation: Student
Help with the StefanBoltzmann Equation
Hi all,
I am planning on doing the project "Absorption of Radiant Energy by Different Colors" from this website. However, I don't really understand how to use the StefanBoltzmann Equation/Law in the project.
I am most confused on steps 712. How do I calculate the energy flow and the energy carried by the visible and infrared photons from the data? What type of graph should I use for the graphs required?
A little background: I'm an 8th grade student doing this project for the school science fair. A dumbingdown of sorts regarding the math portion of this project would be helpful and greatly appreciated.
Thanks so much! A quick response would be nice.
I am planning on doing the project "Absorption of Radiant Energy by Different Colors" from this website. However, I don't really understand how to use the StefanBoltzmann Equation/Law in the project.
I am most confused on steps 712. How do I calculate the energy flow and the energy carried by the visible and infrared photons from the data? What type of graph should I use for the graphs required?
A little background: I'm an 8th grade student doing this project for the school science fair. A dumbingdown of sorts regarding the math portion of this project would be helpful and greatly appreciated.
Thanks so much! A quick response would be nice.
Re: Help with the StefanBoltzmann Equation
Hi thehappinessfund,
I'm assuming that you're working on the project described here:
https://www.sciencebuddies.org/science ... ioncolors
You can calculate the power radiated from your colored paper using equation 2 in the background section of the project. For these calculations use the temperatures you measured for the different colored papers. You'll end up with a power value (P) for each of your colored papers. Equation 3 is an example calculation showing where to plug the data into equation 2. Also, there is an online calculator at this link:
http://hyperphysics.phyastr.gsu.edu/hb ... tefan.html
Equations 4 and 5 in the background section are used to convert the power (P) to a photon emission rate. Equation 5 is an example using the power (0.92 J/sec) calculated in equation 3. You'll calculate a photon emission rate (photons emitted per second) for each colored papers using the power values obtained as described above.
Bar charts would work well for the graphs mentioned in steps 912 of the project procedure. You might put the paper color on the xaxis and have separate charts showing temperature, power, and photons emitted per second on the yaxis.
I hope this helps. Please ask again if you have more questions.
A. Norman
I'm assuming that you're working on the project described here:
https://www.sciencebuddies.org/science ... ioncolors
You can calculate the power radiated from your colored paper using equation 2 in the background section of the project. For these calculations use the temperatures you measured for the different colored papers. You'll end up with a power value (P) for each of your colored papers. Equation 3 is an example calculation showing where to plug the data into equation 2. Also, there is an online calculator at this link:
http://hyperphysics.phyastr.gsu.edu/hb ... tefan.html
Equations 4 and 5 in the background section are used to convert the power (P) to a photon emission rate. Equation 5 is an example using the power (0.92 J/sec) calculated in equation 3. You'll calculate a photon emission rate (photons emitted per second) for each colored papers using the power values obtained as described above.
Bar charts would work well for the graphs mentioned in steps 912 of the project procedure. You might put the paper color on the xaxis and have separate charts showing temperature, power, and photons emitted per second on the yaxis.
I hope this helps. Please ask again if you have more questions.
A. Norman

 Posts: 4
 Joined: Mon Dec 30, 2019 4:59 pm
 Occupation: Student
Re: Help with the StefanBoltzmann Equation
Hi, thank you so much for the response!
I now understand how to calculate the energy emitted per unit time. However, I don't really understand the math involved in equations 4 and 5. When I plug Equation 5 into an online calculator, I get 0, not 4.6 × 1022 photons/sec. Any idea how to figure this out?
Basically, I'm still pretty confused on how to convert the power to the photon emission rate.
You've been so helpful. Thanks again.
( @norman40 )
I now understand how to calculate the energy emitted per unit time. However, I don't really understand the math involved in equations 4 and 5. When I plug Equation 5 into an online calculator, I get 0, not 4.6 × 1022 photons/sec. Any idea how to figure this out?
Basically, I'm still pretty confused on how to convert the power to the photon emission rate.
You've been so helpful. Thanks again.
( @norman40 )
Re: Help with the StefanBoltzmann Equation
Hi thehappinessfund,
Equation 5 shows the math needed to convert from J/sec to photons/sec and includes the units.
And by the way, the term (0.92 J) at the far left of the equation should read (0.92 J/sec).
An equivalent equation (without the units) is
0.92/(1.6e19)/(0.000124) = photons emitted per second
So you can divide 0.92 (or your power value) by 1.6e19 (this is the same as 1.6 x 10^19). Then divide that result by 0.000124. The result is 4.6e22 (4.6 x 10^22). You'll need to use a calculator that allows scientific notation. Or you might use a spreadsheet instead.
I hope this helps. Please ask again if you have more questions.
A. Norman
Equation 5 shows the math needed to convert from J/sec to photons/sec and includes the units.
And by the way, the term (0.92 J) at the far left of the equation should read (0.92 J/sec).
An equivalent equation (without the units) is
0.92/(1.6e19)/(0.000124) = photons emitted per second
So you can divide 0.92 (or your power value) by 1.6e19 (this is the same as 1.6 x 10^19). Then divide that result by 0.000124. The result is 4.6e22 (4.6 x 10^22). You'll need to use a calculator that allows scientific notation. Or you might use a spreadsheet instead.
I hope this helps. Please ask again if you have more questions.
A. Norman

 Posts: 4
 Joined: Mon Dec 30, 2019 4:59 pm
 Occupation: Student
Re: Help with the StefanBoltzmann Equation
Hi again. Thank you so much for the explanation, i definitely understand it now!
Would you be able to read over my hypothesis for the experiment? Obviously, you're not supposed to tell me whether it'll be supported or not, but I'd just like to make sure it's a suitable hypothesis.
(Quick side note: My teacher has told us a specific format to write the hypothesis in: If _____, then _____, because _____. I know that the hypothesis tutorial on this site uses a different format, but whatever.)
If the number of infrared photons emitted per second for six different colors of construction paper (3 warm & 3 cool) is calculated, then the cool colors will emit a larger number of infrared photons, because cool colors have higher energy levels, which causes them to absorb more energy compared to the energy absorption of warm colors.
If you could maybe suggest possible improvements, that'd be great!
Also: What are the reallife applications of this project?
Would you be able to read over my hypothesis for the experiment? Obviously, you're not supposed to tell me whether it'll be supported or not, but I'd just like to make sure it's a suitable hypothesis.
(Quick side note: My teacher has told us a specific format to write the hypothesis in: If _____, then _____, because _____. I know that the hypothesis tutorial on this site uses a different format, but whatever.)
If the number of infrared photons emitted per second for six different colors of construction paper (3 warm & 3 cool) is calculated, then the cool colors will emit a larger number of infrared photons, because cool colors have higher energy levels, which causes them to absorb more energy compared to the energy absorption of warm colors.
If you could maybe suggest possible improvements, that'd be great!
Also: What are the reallife applications of this project?

 Posts: 4
 Joined: Mon Dec 30, 2019 4:59 pm
 Occupation: Student
Re: Help with the StefanBoltzmann Equation
Oh, yeah. I've tweaked the question slightly to be:
"What colors emit the largest number of infrared photons per second: warm colors or cool colors?"
"What colors emit the largest number of infrared photons per second: warm colors or cool colors?"
Re: Help with the StefanBoltzmann Equation
Hi thehappinessfund,
Simply put, a hypothesis is an answer to a question that can be tested with an experiment. Your hypothesis is suitable if it could potentially answer your question.
I think your hypothesis is suitable because it is consistent with your question. Nice job!
You might improve your hypothesis by making it even more directly related to your question. For example “If the paper color is changed from a warm to a cool color then...”.
Absorption and radiation of light are fundamental to many processes like how the sun heats the earth, the greenhouse effect, how we see colors and others. A couple of applications include solar electric cells and passive solar water heaters.
I hope this helps. Please ask again if you have more questions.
A. Norman
Simply put, a hypothesis is an answer to a question that can be tested with an experiment. Your hypothesis is suitable if it could potentially answer your question.
I think your hypothesis is suitable because it is consistent with your question. Nice job!
You might improve your hypothesis by making it even more directly related to your question. For example “If the paper color is changed from a warm to a cool color then...”.
Absorption and radiation of light are fundamental to many processes like how the sun heats the earth, the greenhouse effect, how we see colors and others. A couple of applications include solar electric cells and passive solar water heaters.
I hope this helps. Please ask again if you have more questions.
A. Norman