> restart:#"m07_p13"

Sabiendo que el incremento de entropía en un proceso ideal de mezclado es S= nR_xilnxi, calcular _S/_ni.

Datos:

> S:=-nt*R*sum(x[i]*ln(x[i]),i=1..C);

`:=`(S, `+`(`-`(`*`(nt, `*`(R, `*`(sum(`*`(x[i], `*`(ln(x[i]))), i = 1 .. C)))))))

> nt:=sum(n[i],i=1..C);S_:=subs(x[i]=n[i]/nt,S);

`:=`(nt, sum(n[i], i = 1 .. C))

`:=`(S_, `+`(`-`(`*`(sum(n[i], i = 1 .. C), `*`(R, `*`(sum(`/`(`*`(n[i], `*`(ln(`/`(`*`(n[i]), `*`(sum(n[i], i = 1 .. C)))))), `*`(sum(n[i], i = 1 .. C))), i = 1 .. C)))))))

> Sni:=diff(S_,n[i]);#No funciona.

`:=`(Sni, `+`(`-`(`*`(C, `*`(R, `*`(sum(`/`(`*`(n[i], `*`(ln(`/`(`*`(n[i]), `*`(sum(n[i], i = 1 .. C)))))), `*`(sum(n[i], i = 1 .. C))), i = 1 .. C))))), `-`(`*`(sum(n[i], i = 1 .. C), `*`(R, `*`(sum(...
`:=`(Sni, `+`(`-`(`*`(C, `*`(R, `*`(sum(`/`(`*`(n[i], `*`(ln(`/`(`*`(n[i]), `*`(sum(n[i], i = 1 .. C)))))), `*`(sum(n[i], i = 1 .. C))), i = 1 .. C))))), `-`(`*`(sum(n[i], i = 1 .. C), `*`(R, `*`(sum(...

> C:=3:Sni:=diff(S_,n[1]);

`:=`(Sni, `+`(`-`(`*`(R, `*`(`+`(`/`(`*`(n[1], `*`(ln(`/`(`*`(n[1]), `*`(`+`(n[1], n[2], n[3])))))), `*`(`+`(n[1], n[2], n[3]))), `/`(`*`(n[2], `*`(ln(`/`(`*`(n[2]), `*`(`+`(n[1], n[2], n[3])))))), `*...
`:=`(Sni, `+`(`-`(`*`(R, `*`(`+`(`/`(`*`(n[1], `*`(ln(`/`(`*`(n[1]), `*`(`+`(n[1], n[2], n[3])))))), `*`(`+`(n[1], n[2], n[3]))), `/`(`*`(n[2], `*`(ln(`/`(`*`(n[2]), `*`(`+`(n[1], n[2], n[3])))))), `*...
`:=`(Sni, `+`(`-`(`*`(R, `*`(`+`(`/`(`*`(n[1], `*`(ln(`/`(`*`(n[1]), `*`(`+`(n[1], n[2], n[3])))))), `*`(`+`(n[1], n[2], n[3]))), `/`(`*`(n[2], `*`(ln(`/`(`*`(n[2]), `*`(`+`(n[1], n[2], n[3])))))), `*...

> C:=3:Sni:=combine(simplify(diff(S_,n[1])),ln);Sni_:=-R*ln('x[i]');

`:=`(Sni, `+`(`-`(`*`(R, `*`(ln(`/`(`*`(n[1]), `*`(`+`(n[1], n[2], n[3])))))))))

`:=`(Sni_, `+`(`-`(`*`(R, `*`(ln(x[i]))))))

>