Black body Thermal Radiation - Thermal Pack error?

[Ángel Martin]

I've been looking at the Black body thermal radiation program in the Thermal Pac, and wonder if there's some errors in the equations used - or in the program itself.

The first issue is a typo in the manual: in page 49 it describes the Stefan-Boltzmann constant (from the total emissive power) with the wrong units dimensions. Where it says "W/m^2.T" it should say "W/m^2.T^4"

The second one is with the Plank's Equation itself. The manual shows the numerator of the formula as: "2.pi.c1", with c1= 5.9544 E-17 W*m^2

However the referenced literature indicates a numerator of: "8.pi.h.c", with h being Plank's constant and c the speed of light in vacuum. If you do the math those two values aren't equal: (using SI units: h=6,6260689633 E-34 J.s ; and c=2,99792458 E8 m/s

2.pi.c1 = 3.7412598 E-16
8.pi.h.c = 4,99248207512 E-24

As far as I can tell the assumptions are the same (Energy by unit of volume per unit of wavelength), but these definitions are always tricky (medium's constants, sphere's volumes?). Does anybody see the obvious mistake I'm making, or is this a genuine issue in the Thermal Pac?

BTW, I find it strange they use Energy units instead of Power units (which is what it's being calculated), and also it's surprising they didn't employ the instruction E^X-1 in the "EbL" subroutine (for the denominator of the emissive power formula).

PS. Funny how the "referenced literature" varies: I found another site where the formula is different and this one matches the one used by HP in the Thermal Pac !

According to this reference the numerator is: "2.pi. h.c^2"
and sure enough h.c^2 = 5.9552147-17 [J.m^2/s]

which perfectly agrees with the c1 value in page 49.

Oh well, this manual is not up to HP's standards for sure!

The morale of the story: "Don't trust blindly what you find on the internet"


Cheers,
ÁM