PCRT.I.D.06

PCRT.I.D

06 Zustandsfunktionen des idealen Gases bei (S,p;N=const)

A Enthalpie und molare Enthalpie

$(01)$	$H$	$=$	$\frac{5}{2}nR{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$H(S,p,N)$
$(02)$	$h$	$=$	$\frac{5}{2}R{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{s-s_0}{R}\right)$	$h(s,p)$

Übung a

Wir berechnen $(S/H)(\partial H/\partial S)$, $(p/H)(\partial H/\partial p)$, $(Sp/H)({\partial }^{2}H/\partial S\partial p)$ für ein ideales Gas im (S,p,N)-Koordinatensystem.

B Innere Energie und molare innere Energie

$(01)$	$-pV$	$=$	$-nR{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$V(S,p,N)$
$$	$U$	$=$	$H-pV$	$U(S,p,N),H(S,p,N),V(S,p,N)$
$(02)$	$U$	$=$	$\frac{3}{2}nR{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$U(S,p,N)$
$(03)$	$u$	$=$	$\frac{3}{2}R{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{s-s_0}{R}\right)$	$u(s,p)$

C Freie Enthalpie und chemisches Potential

$(01)$	$-TS$	$=$	$-S{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$T(S,p,N)$
$$	$G$	$=$	$H-TS$	$G(S,p,N),H(S,p,N),T(S,p,N)$
$(02)$	$G$	$=$	$(\frac{5}{2}nR-S)T_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$G(S,p,N)$
$(03)$	$\mu$	$=$	$(\frac{5}{2}nR-S)T_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{s-s_0}{R}\right)$	$\mu (s,p)=g(s,p)$

D Freie Energie und molare freie Energie

$$	$-pV$	$=$	$-nR{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$V(S,p,N)$
$$	$-TS$	$=$	$-S{T}_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$T(S,p,N)$
$$	$F$	$=$	$U-TS$	$F(S,p,N),U(S,p,N),T(S,p,N)$
$(01)$	$F$	$=$	$(\frac{3}{2}nR-S)T_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{S-S_0}{nR}\right)$	$F(S,p,N)$
$(02)$	$f$	$=$	$(\frac{3}{2}R-s)T_0{\left(\frac{p}{p_0}\right)}^{2/5}\exp \left(\frac{2}{5}\frac{s-s_0}{R}\right)$	$f(s,p)$