Question

Problem 6.7. Entropy as an extensive quantity (a) Because the entropy is an extensive quantity, we know that if we double the volume and double the number of particles (thus keeping the density constant), the entropy must double. This condition can be written formally as S(T, WV, AN) = AS(T,V, N). (6.30 Although this behavior of the entropy is completely general, there is no guarantee that an approximate calculation of S will satisfy this condition. Show that the Sackur-Tetrode form of the entropy of an ideal gas of identical particles, (6.27), satisfies this general condition. (b) Show that if the N! term were absent from (6.25) for Zn, S would be given by S = Nk[InV + } ln (20m2T) + 3) (6.31) Is this form of S extensive?

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Answer 1

Sackus Tetrode equation is 2TMKT + + 3 in (2 ) S (T, V, N) = Nk (m v = &v, N'E ANI - As(t, v, N SIZ Zk helmholtz fanction F = – KBT luzy - vots dF - du-Tds - SAT = – P du-sdt lap 5 S = -6), - to us at the 1 1 V - 01 Foluzn & KBT DEN BOT SE NE w terenys) + vnce) en ons UN 2 m kg 13N h2 21 m kg T

sa Nkp in vl MRT Se Whale (o parodys y at 23 3 NKR 3 % S - NkB Snr t 3 in/am kott + mid h2