8 8 D O C U M E N T 8 0 S E P T E M B E R 1 9 2 5 80. To Erwin Schrödinger[1] Berlin, 26 September 1925 Dear Colleague, I read with great interest your illuminating arguments about the entropy of the ideal gas. I also find the exposition on the classical theory of relativity interesting.[2] Here I would just like to tell you my opinion of Planck’s ideas. I, too, find the fundamental thought plausible on its own, especially considering that it offers a way for the individual molecule to take on any velocity value.[3] But in any case one is then not permitted to especially “quantize” the individual molecules, as you also said.[4] [Planck’s consideration contains some other faults about which I would like to remain silent. I immediately made him aware of these things after I heard his talk at the Academy. He unfortunately allowed it to be printed nonethe- less.] The most natural implementation of Planck’s idea seems to me to be the fol- lowing, although it leads to formulas that are out of the question. Because molecules are interchangeable, N! quantum states of the gas each have the same energy.[5] I therefore denote them as one state. In the sum of the states, each such state has the weight N! Therefore,[6] , …(1) where means the energy of the nth state of differing energy. The phase volume between two immediately following states (ind[ex] n or ) would then conse- quently have to be chosen as equal to[7] . From this one finds …(2) (unless a couple of minor errors have crept into the calculation).[8] At any rate, the abhorrent factor is correct. The thermodynamic law contained in (1) and (2) is not only very ugly, but it also does not correspond to Nernst’s theorem, because for T = 0, (1) should reduce to [9] I think that except for Planck’s basic hypothesis, no arbitrary assumption is ¢behind² used here. I would like to ask you S E T --- κlog¦¨ N!e ε κT·n ------ -– © ¹ ¸ § 0 = εn n 1+ N!h3N εn 3N 2e¹ ------· - © § 2 3 --² - ¢ h2 2mV3 2 -- - ------------------------- n3N 2 ------- 22 /3² ¢ π -------------- - = n3N 2 ------- S κlogN! =
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