Thermodynamics

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By Irodov I.E.

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1) In complete analogy to the above we can now conclude that Yf(9 1,92) or 1(9 1,92 ) =112 are universal and equal for all possible reversible engines working between 9 1 and 9 2 , 2* 20 Thermodynamics To obtain more information about 1(9 1 , 92 ) we introduce a third bath 83 < 8 2 and a second engine working between 9 2 and 9 3 , The quantities referring to this second engine are denoted by a dash. The dimensions of both engines are chosen ----r=-=r=~-lJi ----~==ig-- ~ A - QI (1-f(lJi, 17-z)) Qz - Q/hJ;,~) = Qi -----"='===='--- ~ Fig.

With i5q = de = cd T and ds = cd TIT we obtain s(T) =s(To)+cln(TITo) for each piece. Further, we choose Tl = To + 8and T2 = To -8. The total entropy of the two separate pieces is given by T2 S(8) = S(Tl) + s(T2) = S(To) + c In -Tl -2To = (8 S(To) + c In 1 - 2 ) -2 To . If we bring the two metals into thermal contact, their temperatures will equalize. The common final temperature will be To, which follows from conservation of energy [e(Td + e(Tz ) = 2e(To) independent of 8] during the process going on in a closed system.

This consideration does 23 The increase of entropy in closed systems not enter into the question of how the last step is actually performed in order to come back to the initial state. Therefore it might be useful to discuss a simple example, namely the equalization of temperature of two bodies initially at different temperatures. For the sake of simplicity we take equally large pieces of metal with temperatures Tl > T 2. 4e. The energy e of each piece depends, then, only on temperature. If we work in a relatively small interval oftemperature, around To, we can expand e(T) = e(To) + c(T - To), neglecting higher order contributions; c is the heat capacity.

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