Annus MirabilisEinstein in 1905
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The equation explained

dS=1TdE.d S = \frac{1}{T} d E.
In wordsThe increase of the radiation's entropy equals one over the absolute temperature, times the increase of the radiation's energy.OverviewThe warming is reversible and the added energy is the heat supplied, so thermodynamics gives the entropy's increase as that heat divided by the absolute temperature.Full explanationThe paper now brings in thermodynamics. The energy dEd E added to the radiation is the heat supplied to it, and the warming is reversible, so by the rule of thermodynamics for a reversible change the entropy grows by the heat divided by the absolute temperature at which it is taken in. This is a second expression for the same dSd S.Every stepdEd EThe energy added to the unit volume of radiation. The paper notes that it equals the heat supplied; the volume stays v=1v = 1, so no work is done.dS=1TdEd S = \frac{1}{T} d EFor a reversible change the entropy increases by the heat supplied divided by the absolute temperature: the printed line.Also

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