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 ν, Planck's law is written as or

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

or

and from , we have

so 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). -*-

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.

question: where can i find the equations to verify the calculations used? like wikipedia or other physics sources.

known/discovered analyzing your codes: 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))"

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.

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!

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, 01:23:40 pm by lookang »

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 σ as follows:

or The above equation is energy per unit wavelength per unit solid angle. is spectral energy density function with units of energy per unit wavelength per unit volume.

Question1: In school, i taught intensity = power / area. so actually what the y-axis is displaying is intensity/ wavelength ? is spectral energy density function with units of energy per unit wavelength per unit area volume.

Suggestion: Should the applet called it energy density function with units of energy per unit wavelength per unit area

Question2: in your current XML eightpihc2 = 8*pi*h*c*c*1.e40 but i don't understand why has only 1 c, if you code is 2 c's

What is shown in the simulation is . It is the emitted power per unit area of emitting surface, per unit solid angle, and per unit wavelength (in unit of Å :angstrom). If integral over all solid angle, it need to be multipled by 4*π.

by the way, i being trying to figure out how to add text to the AnalyticCurve Family to show

dynamically on the plottingpanel. TS[0] = 1000 TS[1] = TS[2]= . . TS[9]= 6000

Any tips which text do i used? A 2D text ? or a set of 2D text?

I am having difficulty nailing dynamically the position of the text to be at the peak of the function fT

i suspect conceptually, i need to differentiate fT w.r.t. math_failure (math_unknown_error): \lambda \
, equate to zero for the turning point for the highest position PosX, sub back to get the PosY. But i dunno how to do in programming.

the end result is something like this

Thanks for your help. I notice you are doing of things with other members, keep up the good work:)

// code to appear Tmax top position // taken from http://en.wikipedia.org/wiki/Planck%27s_law // This function peaks for hc = 4.97λkT, a factor of 1.76 shorter in wavelength (higher in frequency) than the frequency peak. It is the more commonly used peak in Wien's displacement law. // xm is λ where peak occurs 1. xmred=TXred=h*c/(4.97*k*T)*1.e9; // cos lookang doing nm instead of Am

2. TMSGred="T="+((int)((T*10+0.5)/10.))+"K, peak at "+(int)((xmred*10+0.5)/10.) +" nm";