> restart;#'therm_eq2.mws'.20-01-2004.

Chapter 2: Set of pre-written equations available. (REM: use D for Delta instead of E2_E1).

Basic definition of entropy

> eq2_3:=S=-k*Sum(p[i]*ln(p[i]),i=1..N);

`:=`(eq2_3, S = `+`(`-`(`*`(k, `*`(Sum(`*`(p[i], `*`(ln(p[i]))), i = 1 .. N))))))

Entropy sensitivities at equilibrium

> eq2_12:=dS=(1/T)*dU+(p/T)*dV-Sum((mu[i]/T)*dn[i],i=1..C);

`:=`(eq2_12, dS = `+`(`/`(`*`(dU), `*`(T)), `/`(`*`(p, `*`(dV)), `*`(T)), `-`(Sum(`/`(`*`(mu[i], `*`(dn[i])), `*`(T)), i = 1 .. C))))

Fundamental energy equation

> eq2_13:=dU=T*dS-p*dV+Sum(mu[i]*dn[Fi],i=1..C);

`:=`(eq2_13, dU = `+`(`*`(T, `*`(dS)), `-`(`*`(p, `*`(dV))), Sum(`*`(mu[i], `*`(dn[Fi])), i = 1 .. C)))

Entropy variation for a reversible thermar store

> eq2_14:=DSatm=Q/T0:

Entropy variation for a perfect condemsed substance

> eq2_15:=DS=m*c*ln(T2/T1);

`:=`(eq2_15, DS = `*`(m, `*`(c, `*`(ln(`/`(`*`(T2), `*`(T1)))))))

Entropy variation for a perfect gas

> eq2_16:=DS=m*(c[p]*ln(T2/T1)-R*ln(p2/p1));

`:=`(eq2_16, DS = `*`(m, `*`(`+`(`*`(c[p], `*`(ln(`/`(`*`(T2), `*`(T1))))), `-`(`*`(R, `*`(ln(`/`(`*`(p2), `*`(p1))))))))))

Entropy increase and entropy generation

> eq2_17:=dS=(dQ+dE[mdf])/T;eq2_18:=S[gen]=DS-Int(1/T,Q);

`:=`(eq2_17, dS = `/`(`*`(`+`(dQ, dE[mdf])), `*`(T)))

`:=`(eq2_18, S[gen] = `+`(DS, `-`(Int(`/`(1, `*`(T)), Q))))

Gibbs-Duhem's equation

> eq2_20:=0=S*dT-V*dp+Sum(n[i]*dmu[i],i=1..C);

`:=`(eq2_20, 0 = `+`(`*`(S, `*`(dT)), `-`(`*`(V, `*`(dp))), Sum(`*`(n[i], `*`(dmu[i])), i = 1 .. C)))

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()]);

[_Remember, eq2_12, eq2_13, eq2_14, eq2_15, eq2_16, eq2_17, eq2_18, eq2_20, eq2_3, lasterror, lastexception, ln, `type/SymbolicInfinity`]
[_Remember, eq2_12, eq2_13, eq2_14, eq2_15, eq2_16, eq2_17, eq2_18, eq2_20, eq2_3, lasterror, lastexception, ln, `type/SymbolicInfinity`]

> save eq2_12, eq2_13, eq2_14, eq2_15, eq2_16, eq2_17, eq2_18, eq2_20, eq2_3,"../therm_eq2.m":

>