Choose as a basis function

$y^{(0)}=f(S_{,}{N}_1,N_2,N_3,P)$

and obtain $y_{12}^{(1)}$ in terms of derivatives of the basis function. Discuss how experi$-$

ments could be designed and conducted to obtain numerical values of the $y^{(0)}$

derivatives.

Using your result, consider the following problem. We have a system con$-$

taining, initially, $N_i$ moles of a material. We wish to remove $\frac{N_i}{2}$mol under

conditions where the total entropy and the pressure remain constant. If the

initial temperature is $400K,$ what is the final temperature? Assume that the base

state for entropy is such that at $400K$ and the system pressure, the specific

entropy is $10\frac{J}{m}$olK. Also assume that the heat capacity is $10\frac{J}{m}$olK, inde$-$

pendent of temperature.