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 Typo on page 502 
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Joined: 12 Jul 2010, 07:44
Posts: 154
Post Typo on page 502
Just above the graph, the formula for blackbody radiation is given as:

\frac{2h\nu^3}{(e^{h\nu /kT}-1)^{-1}}

Clearly the (...)^{-1} in the denominator doesn't belong there - it's already a denominator! Removing it the formula would be:

\frac{2h\nu^3}{e^{h\nu /kT}-1}

The same error appears in the caption to the graph, which contains the similarly incorrect forumla:

I = 2h\nu^3/(e^{h\nu /kT}-1)^{-1}


There is arguably another problem with the above formulae: According to the Wikipedia entry for Planck's Law, there is also a missing factor of c^{-2}, so the correct formula should in fact be:

I = \frac{2hc^{-2}\nu^3}{e^{h\nu /kT}-1}

Similarly a factor of c^{-2} is also missing from Wien's law and the Rayleigh-Jeans curve, both in the figure caption and in the main text on p.503 as well.

It seems that Penrose is once again avoiding factors of c by assuming the use of natural relativistic units in which c \equiv 1. That isn't made clear here though, especially since we are told that this formula was obtained by Planck in 1900: Presumably Planck would not have been using such relativistic units back then!

05 Aug 2012, 06:12
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