Problem T07.2(b) and T08.2
Still nobody posted a solution to the problem T07.2(b). So probably I will do so, in a few minutes.
As it turns out, the way to solve T08.2 is also not as clear as I thought. Of course one can calculate the entropy (up to an arbitrary constant) starting from its differential, as long as one does not change the number of particles. I then thought that one can deduce how the entropy must change under a change of the number of particles, by relying on the fact that S must be an extensive quantity. But this is not entirely straight forward, because, in order to use that argument one has to change N and V together such that N/V remains constant.
One thing which may help to find the correct answers, is the solution of T07.2(b). Because it allows to calculate the chemical potential for the van der Waals model directly (even though it is without co-volumen b).
Another thing worth trying is the cross-derivative rule. dS is a differential with three coefficients, dS = A dT + p dV + mu dN, so there are three different cross-derivative relations which must hold the one between T and V, allows to calculate the internal energy, the two which exist between N and V as well as N and T may allow to calculate the chemical potencial. But this is probably rather complicated.
As it turns out, the way to solve T08.2 is also not as clear as I thought. Of course one can calculate the entropy (up to an arbitrary constant) starting from its differential, as long as one does not change the number of particles. I then thought that one can deduce how the entropy must change under a change of the number of particles, by relying on the fact that S must be an extensive quantity. But this is not entirely straight forward, because, in order to use that argument one has to change N and V together such that N/V remains constant.
One thing which may help to find the correct answers, is the solution of T07.2(b). Because it allows to calculate the chemical potential for the van der Waals model directly (even though it is without co-volumen b).
Another thing worth trying is the cross-derivative rule. dS is a differential with three coefficients, dS = A dT + p dV + mu dN, so there are three different cross-derivative relations which must hold the one between T and V, allows to calculate the internal energy, the two which exist between N and V as well as N and T may allow to calculate the chemical potencial. But this is probably rather complicated.
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