> restart;#'therm_eq4.mws'.22-6-00.

Chapter 4: Set of pre-written equations available.

Definition of enthalpy, canonical differential form, and specific form for a simple system

> eq4_2a:=H=U+p*V;eq4_2b:=dH=T*dS+V*dp+Sum(mu[i]*n[i],i=1..C);eq4_2c:=dh=T*ds+v*dp;

`:=`(eq4_2a, H = `+`(U, `*`(p, `*`(V))))

`:=`(eq4_2b, dH = `+`(`*`(T, `*`(dS)), `*`(V, `*`(dp)), Sum(`*`(mu[i], `*`(n[i])), i = 1 .. C)))

`:=`(eq4_2c, dh = `+`(`*`(T, `*`(ds)), `*`(v, `*`(dp))))

Definition of Helmholz's function, canonical differential form, and specific form for a simple system

> eq4_3a:=F=U-T*S;eq4_3b:=dF=-S*dT-p*dV+Sum(mu[i]*n[i],i=1..C);eq4_3c:=df=-s*dT-p*dv;

`:=`(eq4_3a, F = `+`(U, `-`(`*`(T, `*`(S)))))

`:=`(eq4_3b, dF = `+`(`-`(`*`(S, `*`(dT))), `-`(`*`(p, `*`(dV))), Sum(`*`(mu[i], `*`(n[i])), i = 1 .. C)))

`:=`(eq4_3c, df = `+`(`-`(`*`(s, `*`(dT))), `-`(`*`(p, `*`(dv)))))

Definition of Gibbs's function, canonical differential form, and specific form for a simple system

> eq4_4a:=G=U+p*V-T*S+Sum(mu[i]*n[i],i=1..C);eq4_4b:=dG=-S*dT+V*dp+Sum(mu[i]*dn[i],i=1..C);eq4_4c:=dg=-s*dT+v*dp;

`:=`(eq4_4a, G = `+`(U, `*`(p, `*`(V)), `-`(`*`(T, `*`(S))), Sum(`*`(mu[i], `*`(n[i])), i = 1 .. C)))

`:=`(eq4_4b, dG = `+`(`-`(`*`(S, `*`(dT))), `*`(V, `*`(dp)), Sum(`*`(mu[i], `*`(dn[i])), i = 1 .. C)))

`:=`(eq4_4c, dg = `+`(`-`(`*`(s, `*`(dT))), `*`(v, `*`(dp))))

Definition of the thermodynamic coefficients cp,alpha,kappa

> eq4_16_1:=c[p]=T*ds_dT_p;eq4_16_2:=alpha=(1/v)*diff(v(T,p),T);eq4_16_3:=kappa=(-1/v)*diff(v(T,p),p);

`:=`(eq4_16_1, c[p] = `*`(T, `*`(ds_dT_p)))

`:=`(eq4_16_2, alpha = `/`(`*`(diff(v(T, p), T)), `*`(v)))

`:=`(eq4_16_3, kappa = `+`(`-`(`/`(`*`(diff(v(T, p), p)), `*`(v)))))

General differential forms for s, h and v in terms of T and p

> eq4_17_1:=ds=c[p]/T*dT-alpha*v*dp;eq4_17_2:=dh=c[p]*dT-(1-alpha*T)*v*dp;eq4_17_3:=dv=alpha*v*dT-kappa*v*dp;

`:=`(eq4_17_1, ds = `+`(`/`(`*`(c[p], `*`(dT)), `*`(T)), `-`(`*`(alpha, `*`(v, `*`(dp))))))

`:=`(eq4_17_2, dh = `+`(`*`(c[p], `*`(dT)), `-`(`*`(`+`(1, `-`(`*`(alpha, `*`(T)))), `*`(v, `*`(dp))))))

`:=`(eq4_17_3, dv = `+`(`*`(alpha, `*`(v, `*`(dT))), `-`(`*`(kappa, `*`(v, `*`(dp))))))

Definition of the compressibility factor

> eq4_30:=Z=p*v/(R*T);

`:=`(eq4_30, Z = `/`(`*`(p, `*`(v)), `*`(R, `*`(T))))

Guggenheim's correlation for the corresponding states vapour pressure

> eq4_37:=ln(p[r])=K*(1-1/T[r]);

`:=`(eq4_37, ln(p[r]) = `*`(K, `*`(`+`(1, `-`(`/`(1, `*`(T[r])))))))

Enthalpy variation for a perfect gas and for a real gas (through the compressibility corrections

> eq4_35_4:=Dh=c[p]*DT;eq4_40_1:=Dh=Dh[id]-Dh[cc2]+Dh[cc1];

`:=`(eq4_35_4, Dh = `*`(c[p], `*`(DT)))

`:=`(eq4_40_1, Dh = `+`(Dh[id], `-`(Dh[cc2]), Dh[cc1]))

WARNING. A list of all variables follows, to copy and paste to the save command (after Maple7 there is no saving all). CAUTION: After pasting all, I must MANUALLY delete system variables: like RealRange_...

> sort([anames()]);

[TypeTools, _Remember, `diff/function`, eq4_16_1, eq4_16_2, eq4_16_3, eq4_17_1, eq4_17_2, eq4_17_3, eq4_2a, eq4_2b, eq4_2c, eq4_30, eq4_35_4, eq4_37, eq4_3a, eq4_3b, eq4_3c, eq4_40_1, eq4_4a, eq4_4b, ...
[TypeTools, _Remember, `diff/function`, eq4_16_1, eq4_16_2, eq4_16_3, eq4_17_1, eq4_17_2, eq4_17_3, eq4_2a, eq4_2b, eq4_2c, eq4_30, eq4_35_4, eq4_37, eq4_3a, eq4_3b, eq4_3c, eq4_40_1, eq4_4a, eq4_4b, ...
[TypeTools, _Remember, `diff/function`, eq4_16_1, eq4_16_2, eq4_16_3, eq4_17_1, eq4_17_2, eq4_17_3, eq4_2a, eq4_2b, eq4_2c, eq4_30, eq4_35_4, eq4_37, eq4_3a, eq4_3b, eq4_3c, eq4_40_1, eq4_4a, eq4_4b, ...

> save eq4_16_1, eq4_16_2, eq4_16_3, eq4_17_1, eq4_17_2, eq4_17_3,eq4_2a, eq4_2b, eq4_2c, eq4_30, eq4_35_4, eq4_37, eq4_3a, eq4_3b, eq4_3c, eq4_40_1, eq4_4a, eq4_4b,eq4_4c, "../therm_eq4.m":`

>