light quanta

The equation explained

d S = \int_{\nu = 0}^{\nu = \infty} \frac{\partial \varphi}{\partial \varrho} d \varrho d \nu,

In wordsThe increase of the radiation's entropy in a unit volume, when it is warmed a little, is the sum over every frequency of the rate at which the entropy density grows with the energy density, times that density's increase.OverviewWarm black radiation in a unit volume a little: at each frequency its entropy grows by the rate ∂φ/∂ρ times the increase of the density there, and these add up over all frequencies.Full explanationSection 3 now asks what the common value of

\partial \varphi / \partial \varrho

is. Take black radiation of volume

v = 1

and raise its temperature by

d T

. The density at each frequency grows by

d \varrho

, and the entropy per unit volume and frequency grows by

\frac{\partial \varphi}{\partial \varrho} d \varrho

; adding over all frequencies gives the whole increase of entropy,

d S

. With

v = 1

the entropy is the integral of the section's first display itself.Every step

S = \int_0^\infty \varphi(\varrho, \nu) d \nu

The entropy of the section's first display, with

v = 1

d \varphi = \frac{\partial \varphi}{\partial \varrho} d \varrho

At a fixed frequency

\varphi

changes only because the density does: by its rate of change with the density times the change of density.

d S = \int_{\nu = 0}^{\nu = \infty} \frac{\partial \varphi}{\partial \varrho} d \varrho d \nu

Add the changes over every frequency: the printed line.AlsoOverviewFull explanationEvery step

Read it in the paper