Typo on page 502

deant · 05 Aug 2012, 06:12

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:

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

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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

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!