# a szokásos rutinok betöltése
%pylab inline
from scipy.integrate import * # az integráló rutinok betöltése
from ipywidgets import * # az interaktivitásért felelős csomag
import matplotlib.pyplot as plt
from IPython.core.display import HTML
HTML('''<script>
code_show=true;
function code_toggle() {
if (code_show){
$('div.input').hide();
} else {
$('div.input').show();
}
code_show = !code_show
}
$( document ).ready(code_toggle);
</script>
<form action="javascript:code_toggle()"><input type="submit"
value="Click here to toggle on/off the raw code."></form>''')
rc('text', usetex=True) # az abran a xticks, yticks fontjai LaTeX fontok lesznek
# Abra es fontmeretek
xfig_meret= 9 # 12 nagy abrahoz
yfig_meret= 6 # 12 nagy abrahoz
xyticks_meret= 15 # 20 nagy abrahoz
xylabel_meret= 21 # 30 nagy abrahoz
legend_meret= 21 # 30 nagy abrahoz
def nyomas_VdW(V,T):
pp = 8 *T/(3*V-1)-3/V**2
return (pp)
def nyomas_Berth(V,T):
pp = T/(3*V-1)-3/8/V**2/T
return (pp)
def nyomas_Diet(V, T):
pp=(e**(2 - 2/(T*V)) * T)/(-1 + 2* V)
return(pp)
def nyomas_RK(V, T):
s= 2**(1/3)-1
pp= 3*T/(V-s)-1/s/V/(V+s)/sqrt(T)
return(pp)
$\left(\hat{p}+\frac{3}{\hat{V}^2}\right)\left(3\hat{V}-1 \right) = 8\hat{T}$, ahol $V_c=3bn$, $RT_c =\frac{8}{27}\, \frac{a}{b}$, $p_c=\frac{1}{27}\, \frac{a}{b^2} $.
Npont=100
T1=0.85
T2=0.9
T3=0.95
T4=1.
T5=1.1
Vmin= .5
Vmax = 4
VV=linspace(Vmin,Vmax,Npont) #mintavételezési pontok legyártása
figsize(xfig_meret,yfig_meret)
plot(VV,nyomas_VdW(VV,T1),label=r'$T/T_c=\, $'+str(T1),lw=3,ls='-',color='brown')
plot(VV,nyomas_VdW(VV,T2),label=r'$T/T_c=\, $'+str(T2),lw=3,ls='-',color='blue')
plot(VV,nyomas_VdW(VV,T3),label=r'$T/T_c=\, $'+str(T3),lw=3,ls='-',color='green')
plot(VV,nyomas_VdW(VV,T4),label=r'$T/T_c=\, $'+str(T4),lw=3,ls='-',color='red')
plot(VV,nyomas_VdW(VV,T5),label=r'$T/T_c=\, $'+str(T5),lw=3,ls='-',color='black')
legend(loc='upper right',fontsize=legend_meret)
xlabel(r'$\hat{V}$',fontsize=xylabel_meret)
ylabel(r'$\hat{p}$',fontsize=xylabel_meret,rotation='horizontal')
xticks(fontsize=xyticks_meret)
yticks(fontsize=xyticks_meret);
xlim(0.,Vmax)
ylim(0,2.1)
ax = gca()
ax.yaxis.set_label_coords(-0.08, 0.6); # ylabel position
#title(r'$E(T)$ ', fontsize=20)
#savefig('xxxxx.eps',pad_inches=0.0,bbox_inches='tight'); # Abra kimentese
M. W. Zemansky and R. H Dittman: Heat and Thermodynamics, page 135.
$\left(\hat{p}+\frac{3}{8}\, \frac{1}{\hat{V}^2\hat{T}}\right)\left(3\hat{V}-1 \right) = \hat{T}$, ahol $V_c=3bn$, $RT_c^2 =\frac{8}{27}\, \frac{a}{b}$, $p_c=\frac{8}{27}\, \frac{a}{b^2}\, \frac{1}{T_c} $.
Figyelem, itt az $a$ paraméter jelentése más, mint a van der Waals-gáznál!
Npont=100
T1=0.94
T2=0.96
T3=0.98
T4=1.
T5=1.1
Vmin= .5
Vmax = 4
VV=linspace(Vmin,Vmax,Npont) #mintavételezési pontok legyártása
figsize(xfig_meret,yfig_meret)
plot(VV,nyomas_Berth(VV,T1),label=r'$T/T_c=\, $'+str(T1),lw=3,ls='-',color='brown')
plot(VV,nyomas_Berth(VV,T2),label=r'$T/T_c=\, $'+str(T2),lw=3,ls='-',color='blue')
plot(VV,nyomas_Berth(VV,T3),label=r'$T/T_c=\, $'+str(T3),lw=3,ls='-',color='green')
plot(VV,nyomas_Berth(VV,T4),label=r'$T/T_c=\, $'+str(T4),lw=3,ls='-',color='red')
plot(VV,nyomas_Berth(VV,T5),label=r'$T/T_c=\, $'+str(T5),lw=3,ls='-',color='black')
legend(loc='upper right',fontsize=legend_meret)
xlabel(r'$\hat{V}$',fontsize=xylabel_meret)
ylabel(r'$\hat{p}$',fontsize=xylabel_meret,rotation='horizontal')
xticks(fontsize=xyticks_meret)
yticks(fontsize=xyticks_meret);
xlim(0.,Vmax)
ylim(0,0.25)
ax = gca()
ax.yaxis.set_label_coords(-0.08, 0.65); # ylabel position
#title(r'$E(T)$ ', fontsize=20)
#savefig('xxxxx.eps',pad_inches=0.0,bbox_inches='tight'); # Abra kimentese
M. W. Zemansky and R. H Dittman: Heat and Thermodynamics, page 135.
$\hat{p} = \frac{\hat{T}}{2 \hat{V}-1}\, e^{2-\frac{2}{\hat{V}\hat{T}}}$, ahol $V_c=2 bn$, $RT_c = \frac{a}{4b}$, $p_c=\frac{a}{4 e^2b^2}$.
Figyelem, itt az $a$ és a $b$ paraméterek jelentése más, mint a van der Waals-gáznál!
Npont=100
T1=0.85
T2=0.9
T3=0.95
T4=1.
T5=1.1
Vmin= .55
Vmax = 2
VV=linspace(Vmin,Vmax,Npont) #mintavételezési pontok legyártása
figsize(xfig_meret,yfig_meret)
plot(VV,nyomas_Diet(VV,T1),label=r'$T/T_c=\, $'+str(T1),lw=3,ls='-',color='brown')
plot(VV,nyomas_Diet(VV,T2),label=r'$T/T_c=\, $'+str(T2),lw=3,ls='-',color='blue')
plot(VV,nyomas_Diet(VV,T3),label=r'$T/T_c=\, $'+str(T3),lw=3,ls='-',color='green')
plot(VV,nyomas_Diet(VV,T4),label=r'$T/T_c=\, $'+str(T4),lw=3,ls='-',color='red')
plot(VV,nyomas_Diet(VV,T5),label=r'$T/T_c=\, $'+str(T5),lw=3,ls='-',color='black')
legend(loc='upper right',fontsize=legend_meret)
xlabel(r'$\hat{V}$',fontsize=xylabel_meret)
ylabel(r'$\hat{p}$',fontsize=xylabel_meret,rotation='horizontal')
xticks(fontsize=xyticks_meret)
yticks(fontsize=xyticks_meret);
xlim(0.,Vmax)
ylim(0.5,2.2)
ax = gca()
ax.yaxis.set_label_coords(-0.08, 0.65); # ylabel position
#title(r'$E(T)$ ', fontsize=20)
#savefig('xxxxx.eps',pad_inches=0.0,bbox_inches='tight'); # Abra kimentese
Az állapotegyenlet: $\left(p+\frac{a n^2}{\sqrt{T}V \left(V+bn\right)}\right)\left(V- bn \right) = n R T$.
Az átskálázott állapotegyenlet: $\left(\hat{p}+\frac{1}{v_0 \hat{V} \left(\hat{V}+v_0\right)\sqrt{\hat{T}}}\right)\left(\hat{V}-v_0\right) = 3 \hat{T}$,
ahol $v_0=2^{1/3}-1$,
$V_c= \left(1+2^{1/3}+2^{2/3}\right)\, bn \approx 3.85\, bn$,
$T_c = \left(1+2^{4/3}-2^{5/3}\right)\, {\left(\frac{a}{b}\right)}^{2/3}\, R^{-2/3} \approx 0.345\, {\left(\frac{a}{b}\right)}^{2/3}\, R^{-2/3}$,
$p_c = \frac{\left(1+2^{1/3}\right)\left(2^{7/3}-5 \right)}{3}\, \frac{b^{5/3}}{a^{2/3}}\, R^{-1/3} \approx 0.03 \, \frac{b^{5/3}}{a^{2/3}}\, R^{-1/3}$
Npont=100
T1=0.9
T2=0.925
T3=0.95
T4=1.
T5=1.05
Vmin= .3
Vmax = 3
VV=linspace(Vmin,Vmax,Npont) #mintavételezési pontok legyártása
figsize(xfig_meret,yfig_meret)
plot(VV,nyomas_RK(VV,T1),label=r'$T/T_c=\, $'+str(T1),lw=3,ls='-',color='brown')
plot(VV,nyomas_RK(VV,T2),label=r'$T/T_c=\, $'+str(T2),lw=3,ls='-',color='blue')
plot(VV,nyomas_RK(VV,T3),label=r'$T/T_c=\, $'+str(T3),lw=3,ls='-',color='green')
plot(VV,nyomas_RK(VV,T4),label=r'$T/T_c=\, $'+str(T4),lw=3,ls='-',color='red')
plot(VV,nyomas_RK(VV,T5),label=r'$T/T_c=\, $'+str(T5),lw=3,ls='-',color='black')
legend_meret1 = 0.9* legend_meret
legend(loc='upper right',fontsize=legend_meret1)
xlabel(r'$\hat{V}$',fontsize=xylabel_meret)
ylabel(r'$\hat{p}$',fontsize=xylabel_meret,rotation='horizontal')
xticks(fontsize=xyticks_meret)
yticks(fontsize=xyticks_meret);
xlim(0.,Vmax)
ylim(0,2.)
ax = gca()
ax.yaxis.set_label_coords(-0.08, 0.65); # ylabel position
#title(r'$E(T)$ ', fontsize=20)
#savefig('xxxxx.eps',pad_inches=0.0,bbox_inches='tight'); # Abra kimentese