### Author Topic: Blackbody radiation curves for different temperatures  (Read 72095 times)

#### Fu-Kwun Hwang

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##### Blackbody radiation curves for different temperatures
« on: February 25, 2007, 03:39:04 pm »
Planck's law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature T. As a function of frequency ?, Planck's law is written as
\$I(
u,T) = frac{2 h
u^3 }{c^2} frac{1}{e^{h
u/kT}-1}\$ or

It can be converted to an expression for I'(?,T) in wavelength units by substituting ? by c / ? and evaluating

\$ I'(lambda,T) = I(
u,T)left|frac{d
u}{dlambda}ight| \$ or

\$frac{2 h
u^3 }{c^2}=frac{2 h(clambda)^3 }{c^2}=frac{2hc}{lambda^3}\$
and from \$
u= clambda\$, we have
\$d
u=-frac{c}{lambda^2}dlambda\$
so
\$I(lambda,T)=frac{2hc^2}{lambda^5}frac{1}{e^{hc/lambda kT}-1}\$ or
The above equation is energy per unit wavelength per unit solid angle.

This applets will show six black cureves of blackbody radiation curve betwen Tmin and Tmax.
Another curve in red is also shown (it's temperature can be adjusted with left slider bar)
Maximum wavelength shown can be adjusted with right slider bar.
You can use it for study the intensity for blackbody radiation.
If you want to study different temperature range, You can change Tmin and Tmax, to change the temperature range,too.
The wavelength unit in the simulation is Å (angstrom).
-*-

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is the spectral energy density function with units of energy per unit wavelength per unit volume.

#### lookang

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• http://weelookang.blogspot.com
##### Re: Blackbody radiation curves for different temperatures
« Reply #1 on: March 15, 2009, 09:04:49 pm »

another quality simulation from
a good applet too

just wondering if it is a good idea to allow temperatures from 300K minimum.

i got time to remix for you
« Last Edit: March 15, 2009, 09:15:08 pm by lookang »

#### Fu-Kwun Hwang

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• Posts: 3062
##### Re: Blackbody radiation curves for different temperatures
« Reply #2 on: March 16, 2009, 09:23:07 am »
If you want to study different temperature range, You can change Tmin and Tmax, to change the temperature range,too.
Tmin an Tmax are text field, so you can enter your own range. But the intensity will change a lot.
So you might want to change to log scale to view all the range.
The yscale can be changed between 0-100 with slider at the right side.

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #3 on: March 16, 2009, 09:59:12 pm »
question: where can i find the equations to verify the calculations used? like wikipedia or other physics sources.

h = PLANCK = 6.6252 E-34
h4 = 4.*h*1.e47   = 2.65008.e14    // what is this?
c =the speed of light = 299 792 458 m / s
k =Boltzman k, 1.38E-23 J/K
cst = h*c/(k*1.e-10)  = 1.43.e8  // // what is this constant?
fT = "h4/((Math.exp(cst/(r*T))-1)*(r*r*r))"

what i am trying to do.
change the lamda to nanometre nm instead of 1 Ångström   ?   1×10-10   metre http://en.wikipedia.org/wiki/Metre

i am guessing i need to change h4 = 4.*h*1.e46  for the nanometer calculation, i am guessing your calculation are for Ångström metre.

am i correct?

some references i look at.
http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html#c4

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/uvcatas.gif

http://hyperphysics.phy-astr.gsu.edu/hbase/imgmod/bb7b.gif

Thanks!
« Last Edit: March 16, 2009, 11:02:41 pm by lookang »

#### Fu-Kwun Hwang

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• Posts: 3062
##### Re: Blackbody radiation curves for different temperatures
« Reply #4 on: March 16, 2009, 11:25:28 pm »

cst= hc/k; add 1.e-10 because I use Ångström instead of m as unit for length.

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #5 on: March 17, 2009, 12:16:04 am »
thanks!

#### lookang

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• http://weelookang.blogspot.com
##### Re: Blackbody radiation curves for different temperatures
« Reply #6 on: March 17, 2009, 09:56:12 am »
another question

is it possible to make the x axis number always 100, 200, 300, 400, nm
instead of currently auto calculation now 0.1 , 0.2 , 0.3 , 0.4 X10^3 nm

what is desired

what is current

i tried changing the X format to 0000 but doesn't seem to work the way i hoped.
« Last Edit: March 17, 2009, 10:01:49 am by lookang »

#### Fu-Kwun Hwang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #7 on: March 17, 2009, 10:00:25 am »
I guest you were using auto-scale in the drawingPanel.
Set up your xmin,xmax properly. You should be able to get what you want.
Try it by yourself first. You will get to know it better.

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #8 on: March 17, 2009, 10:21:43 am »
but is it possible to display 4000 instead of 4.0x10^3 ?

look at my attached pictures

it is already not autoscale X,

rmin and rmax are already setup
rmin = 50
rmax = 3000

ok i try again

#### Fu-Kwun Hwang

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• Posts: 3062
##### Re: Blackbody radiation curves for different temperatures
« Reply #9 on: March 17, 2009, 11:02:28 am »
There are X Format/Y Format properties, but I can not find any document at paco's web site.
http://www.um.es/fem/EjsWiki/index.php/Main/ElementsPlottingPanel

I have never used that before.
If I really need it, I will use drawingPanel  instead and I can draw those grid lines/labels with build in GUI elements.
May be it can be done by setting proper value for X Format, but I do not know. Sorry!

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #10 on: March 17, 2009, 12:42:39 pm »
Not to worry.
Maybe it can't be done yet.
I will explore abit more and move on to other parts of XML .

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #11 on: March 18, 2009, 02:20:09 pm »
yes it is confirm it currently cannot be done http://www.um.es/fem/EjsWiki/index.php/FeedbackEn/00026
quote:
Resolution
The axes do not allow formatting the ticks. The Format X property refers to the way the coordinates of the point appear (in a yellow box at the lower left corner of the panel) when you click on a point in the panel.
unquote:

BTW

I am puzzled by the equation used.

I look at the equation and i look at the equation in the XML fT = "h4/((Math.exp(cst/(r*T))-1)*(r*r*r))"

shouldn't fT = "2*h*c*c/((Math.exp(cst/(r*T))-1)*(r*r*r*r*r))" ?

strangely i tried to implement the new fT ="2*h*c*c/((Math.exp(cst/(r*T))-1)*(r*r*r*r*r))" but the graph is very low and flat and near zero in value.
« Last Edit: March 18, 2009, 02:23:40 pm by lookang »

#### Fu-Kwun Hwang

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• Posts: 3062
##### Re: Blackbody radiation curves for different temperatures
« Reply #12 on: March 18, 2009, 06:53:53 pm »
The above equation is a normalized function, i.e., integration will give you 1.

So you can multiple it by any number.
If you change the y-axis to log-scale, you will know how big/small it is.

#### lookang

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##### Re: Blackbody radiation curves for different temperatures
« Reply #13 on: March 18, 2009, 08:23:29 pm »
The above equation is a normalized function, i.e., integration will give you 1.
So you can multiple it by any number.
ok i understand normalized function http://mathworld.wolfram.com/NormalDistribution.html
ok i also understand the area under this normalized function is 1

but i am  puzzled by the missing r*r.

equation on http://en.wikipedia.org/wiki/Planck%27s_law

equation in your XML : fT = "h4/((Math.exp(cst/(r*T))-1)*(r*r*r))"

notice your XML : fT has only r*r*r but the equation on wikipedia has r*r*r*r*r

unless when normalized the r*r is absorbed? then it make sense to me now! I don't really know why now but at least i can accept the logic. (it that correct ?)......hahaha.

If you change the y-axis to log-scale, you will know how big/small it is.
log scale i understand. i try to experiment more

Maybe i lack the prior knowledge, sorry!
i don't remember encountering this equation for black body radiation, only vaguely remember
Stefan–Boltzmann law Main article: Stefan–Boltzmann law

This law states that amount of thermal radiations emitted per second per unit area of the surface of a black body is directly proportional to the fourth power of its absolute temperature. The total energy radiated per unit area per unit time j^{star} (in watts per square meter) by a black body is related to its temperature T (in kelvins) and the Stefan–Boltzmann constant ? as follows:

where sigma=5.67 x 10-8Wm-2K-4
http://en.wikipedia.org/wiki/Black_body
« Last Edit: March 18, 2009, 08:40:29 pm by lookang »