Rename module directories (module 6 → module_6, module 7 → module_7) to fix Google Colab "Open in Colab" link compatibility. Update Colab badge URL in Peng_Robinson_EOS.ipynb accordingly. Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>
1472 lines
356 KiB
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1472 lines
356 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "7af16f2a",
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"metadata": {},
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"source": [
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"# Goal of this notebook\n",
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"\n",
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"The goal of this notebook is to reproduce the following figures in chapters 6 and 7 of Stanley I. Sandler, *Chemical, Biochemcial and Engineering Thermodynamics*, 5th ed. These illustrations are based on the van der Waals equation of state.\n",
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"\n",
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"- Fig 6.6-1 -- five isotherms illustrated around the critical isotherm\n",
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"- Fig 7.3-1 -- five isotherms labeled with local maxima and minima\n",
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"- Fig 7.3-2 -- a diagram showing the isotherm construction for a sub-critical temperature\n",
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"- Fig 7.3-3 -- the resulting isotherm for a sub-critical temperature\n",
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"- Fig 7.3-4 -- the van der Waals EOS PV diagram with multiple isotherms and two phase region\n",
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"\n",
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"<small>\n",
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"Copyright (c) 2025 Eric M. Furst\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3c29e0e8",
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"metadata": {},
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"source": [
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"## van der Waals equation of state\n",
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"\n",
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"Below are routines to calculate the van der Waals equation of state.\n",
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"\n",
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"The van der Waals equation of state (vdW EOS) is\n",
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"\n",
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"$$ P = \\frac{RT}{\\underline{V}-b} - \\frac{a}{\\underline{V}^2} \\tag{Eq. 6.2-38b}$$\n",
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"\n",
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"Like other cubic equations of state, calculating the pressure $P$ given $\\underline{V}$ and $T$ is straightforward, but to calculate the molar volume given $P$ and $T$, we need to solve a cubic equation of the form\n",
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"\n",
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"$$ Z^3 + \\alpha Z^2 + \\beta Z + \\gamma = 0 \\tag{Eq. 6.4-4}$$\n",
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"\n",
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"where $Z$ is the compressibility factor\n",
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"\n",
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"$$ Z = \\frac{P \\underbar{V{}}}{RT} $$\n",
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"\n",
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"For the van der Waals EOS (see SIS **Table 6.4-3**),\n",
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"\n",
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"$$ \\alpha = -1 - B $$\n",
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"$$ \\beta = A $$\n",
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"$$ \\gamma = -AB $$\n",
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"\n",
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"and \n",
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"\n",
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"$$ A = \\frac{aP}{(RT)^2} $$\n",
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"$$ B = \\frac{bP}{RT} $$\n",
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"\n",
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"Here, we will use the reduced van der Waals equation of state\n",
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"\n",
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"$$ \\left ( P_r + \\frac{3}{\\underline{V}_r} \\right )(3\\underline{V}_r - 1) = 8T_r \\tag{Eq. 6.6-6}$$\n",
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"\n",
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"This can be written in the form \n",
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"\n",
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"$$ \\underline{V}_r^3 + \\alpha \\underline{V}_r^2 + \\beta \\underline{V}_r + \\gamma = 0 $$\n",
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"\n",
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"with\n",
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"\n",
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"$$\\alpha = -\\frac{P_r+8T_r}{3P_r}$$\n",
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"$$\\beta = \\frac{3}{P_r}$$\n",
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"$$\\gamma = -\\frac{1}{P_r}$$\n",
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"\n",
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"which is left as an exercise for the reader."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "47da809f",
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"metadata": {},
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"outputs": [],
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"source": [
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"\"\"\"\n",
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"Reduced van der Waals equation of state \n",
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"rvdw_P returns the pressure given Vr, Tr\n",
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"rvdw_V returns all reduced molar volumes (real roots of EOS) given Pr and Tr\n",
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"\"\"\"\n",
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"import numpy as np\n",
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"from numpy.polynomial import Polynomial\n",
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"\n",
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"\n",
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"# Calculate the reduced presure given Vr, Tr for reduced vdw EOS\n",
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"def rvdw_P(Vr,Tr):\n",
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"\n",
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" return 8*Tr/(3*Vr-1) - 3/Vr**2\n",
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"\n",
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"# Calculate the reduced molar volume given Pr, Tr\n",
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"# Note that we can return multiple real roots (up to three)\n",
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"# The largest and smallest will be the vapor and liquid, respectively\n",
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"def rvdw_V(Pr, Tr):\n",
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"\n",
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" # Definitions of alpha, beta, gamma in SIS Table 6.4-3 for PR EOS\n",
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" alpha = -(Pr+8*Tr)/3/Pr\n",
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" beta = 3/Pr\n",
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" gamma = -1/Pr\n",
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"\n",
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" # polynomial with coefficients in increasing order: c0 + c1 x + c2 x**2 + ...\n",
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" p = Polynomial([ gamma, beta, alpha, 1 ]) \n",
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"\n",
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" roots = p.roots() # returns all (possibly complex) roots of Z\n",
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" real_roots = roots.real[abs(roots.imag) < 1e-12] # filter real ones\n",
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"\n",
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" return real_roots\n",
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"\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2f55b187",
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"metadata": {},
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"source": [
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"# Figure 6.6-1 -- The pressure-volume behavior of the van der Waals equation of state\n",
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"\n",
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"We begin by plotting isotherms on the reduced scale. We'll plot a few above and below the critical isotherm."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "fd028ebd",
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"metadata": {},
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"outputs": [
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{
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"data": {
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",
|
||
"text/plain": [
|
||
"<Figure size 500x450 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import matplotlib as mpl\n",
|
||
"from matplotlib.transforms import offset_copy\n",
|
||
"\n",
|
||
"# May cause problems in Colab or installations without LaTeX\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"# Good PDF defaults\n",
|
||
"mpl.rcParams.update({\n",
|
||
" \"pdf.fonttype\": 42, # keep text as text in PDF\n",
|
||
" \"ps.fonttype\": 42,\n",
|
||
"})\n",
|
||
"\n",
|
||
"# Function to make plot labels\n",
|
||
"def label_curve(\n",
|
||
" ax,\n",
|
||
" x, y, text,\n",
|
||
" *,\n",
|
||
" dx=0, dy=3, # offset in points\n",
|
||
" ha=\"left\", va=\"bottom\",\n",
|
||
" fontsize=9,\n",
|
||
" bbox=True\n",
|
||
"):\n",
|
||
" \"\"\"\n",
|
||
" Place a text label in data coordinates with a point offset.\n",
|
||
" \"\"\"\n",
|
||
" transform = offset_copy(ax.transData, fig=ax.figure, x=dx, y=dy, units=\"points\")\n",
|
||
"\n",
|
||
" bbox_kw = None\n",
|
||
" if bbox:\n",
|
||
" bbox_kw = dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\")\n",
|
||
"\n",
|
||
" ax.text(float(x), float(y), text, ha=ha, va=va, fontsize=fontsize, transform=transform,\n",
|
||
" bbox=bbox_kw)\n",
|
||
"\n",
|
||
"# Make the plot\n",
|
||
"fig, ax = plt.subplots(figsize=(5.0, 4.5)) # choose size you like\n",
|
||
"\n",
|
||
"# Range of reduced molar volumes\n",
|
||
"Vr_max = 3\n",
|
||
"Vr_min = 0.5\n",
|
||
"Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
"# plot the labeled lines, 0.95, 1.0, 1.05\n",
|
||
"Tr = 0.95\n",
|
||
"ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n",
|
||
"label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T < T_c$\", dy=15)\n",
|
||
"\n",
|
||
"Tr = 1.0\n",
|
||
"ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n",
|
||
"label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T = T_c$\")\n",
|
||
"\n",
|
||
"Tr = 1.05\n",
|
||
"ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n",
|
||
"label_curve(ax, 1, rvdw_P(1,Tr), rf\"$T > T_c$\")\n",
|
||
"\n",
|
||
"# plot several isotherms above the critical temperature\n",
|
||
"for Tr in np.array([0.9, 1.1]): \n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
"plt.ylim([0.4,1.4])\n",
|
||
"plt.xlabel(r\"$\\underline{V}$\", labelpad=15)\n",
|
||
"plt.ylabel(r'$P$', rotation=0, labelpad=20)\n",
|
||
"\n",
|
||
"fig.tight_layout()\n",
|
||
"\n",
|
||
"ax.tick_params(\n",
|
||
" labelbottom=False,\n",
|
||
" labelleft=False\n",
|
||
")\n",
|
||
"\n",
|
||
"# ---- SAVE HIGH-QUALITY PDF ----\n",
|
||
"fig.savefig(\"pdf/Fig_6.6-1.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ce9572ad",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Figure 7.3-1 Isotherms of the van der Waals equation in the pressure-volume plane\n",
|
||
"\n",
|
||
"This figure is similar to figure 6.6-1, but it labels the curves differently."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"id": "b3546598",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 500x450 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import matplotlib as mpl\n",
|
||
"from matplotlib.transforms import offset_copy\n",
|
||
"\n",
|
||
"# May cause problems in Colab or installations without LaTeX\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"# Good PDF defaults\n",
|
||
"mpl.rcParams.update({\n",
|
||
" \"pdf.fonttype\": 42, # keep text as text in PDF\n",
|
||
" \"ps.fonttype\": 42,\n",
|
||
"})\n",
|
||
"\n",
|
||
"# Function to make plot labels\n",
|
||
"def label_curve(ax, x, y, text, *, dx=2, dy=3, ha=\"left\", va=\"bottom\", fontsize=9, bbox=False):\n",
|
||
" # Place a text label in data coordinates with a point offset.\n",
|
||
" transform = offset_copy(ax.transData, fig=ax.figure, x=dx, y=dy, units=\"points\")\n",
|
||
"\n",
|
||
" bbox_kw = None\n",
|
||
" if bbox:\n",
|
||
" bbox_kw = dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\")\n",
|
||
"\n",
|
||
" ax.text(float(x), float(y), text, ha=ha, va=va, fontsize=fontsize, transform=transform,\n",
|
||
" bbox=bbox_kw)\n",
|
||
"\n",
|
||
"# Function to label local minimum and maximum for isotherms below Tc\n",
|
||
"def label_loop_extrema(ax, Vr, P, *, label_min=\"A\", label_max=\"B\",\n",
|
||
" dy_min=-8, dy_max=6, marker=True):\n",
|
||
" # numerical derivative\n",
|
||
" dP = np.gradient(P, Vr)\n",
|
||
" s = np.sign(dP)\n",
|
||
"\n",
|
||
" # sign flips\n",
|
||
" imax = np.where((s[:-1] > 0) & (s[1:] < 0))[0] + 1 # + to - : local max\n",
|
||
" imin = np.where((s[:-1] < 0) & (s[1:] > 0))[0] + 1 # - to + : local min\n",
|
||
"\n",
|
||
" if len(imax) == 0 or len(imin) == 0:\n",
|
||
" return None # no loop/extrema found (near/above critical)\n",
|
||
"\n",
|
||
" iB = imax[0] # local maximum\n",
|
||
" iA = imin[0] # local minimum\n",
|
||
"\n",
|
||
" if marker:\n",
|
||
" ax.plot(Vr[iA], P[iA], \"o\", ms=4, color=\"black\")\n",
|
||
" ax.plot(Vr[iB], P[iB], \"o\", ms=4, color=\"black\")\n",
|
||
"\n",
|
||
" label_curve(ax, Vr[iA], float(P[iA]), label_min, dx=-2, dy=dy_min, \n",
|
||
" ha=\"left\", va=\"top\", bbox=False)\n",
|
||
" label_curve(ax, Vr[iB], float(P[iB]), label_max, dx =-2, dy=dy_max, \n",
|
||
" ha=\"left\", va=\"bottom\", bbox=False)\n",
|
||
"\n",
|
||
" return (Vr[iA], P[iA], Vr[iB], P[iB])\n",
|
||
"\n",
|
||
"# Make the plot\n",
|
||
"fig, ax = plt.subplots(figsize=(5.0, 4.5)) # choose size you like\n",
|
||
"\n",
|
||
"# Range of reduced molar volumes\n",
|
||
"Vr_max = 3\n",
|
||
"Vr_min = 0.5\n",
|
||
"Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
"\"\"\"\n",
|
||
"Plot five isotherms\n",
|
||
"\"\"\"\n",
|
||
"label_horiz_Vr = 2\n",
|
||
"\n",
|
||
"# These are the labels for the sub-critical isotherm minima and maxima\n",
|
||
"extrema_labels = {\n",
|
||
" 0.9: (r\"$A$\", r\"$B$\"),\n",
|
||
" 0.95: (r\"$A'$\", r\"$B'$\"),\n",
|
||
"}\n",
|
||
"\n",
|
||
"for k, Tr in enumerate([0.9, 0.95, 1.0, 1.1, 1.2], start=1):\n",
|
||
" P = rvdw_P(Vr, Tr)\n",
|
||
" ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
" # label the isotherm itself\n",
|
||
" i = np.argmin(np.abs(Vr - label_horiz_Vr))\n",
|
||
" label_curve(ax, Vr[i], float(P[i]), rf\"$T_{k}$\", dy=2)\n",
|
||
"\n",
|
||
" # label loop extrema for the subcritical ones\n",
|
||
" labels = extrema_labels.get(Tr)\n",
|
||
" if labels is not None:\n",
|
||
" label_loop_extrema(\n",
|
||
" ax, Vr, P,\n",
|
||
" label_min=labels[0],\n",
|
||
" label_max=labels[1],\n",
|
||
" dy_min=15,\n",
|
||
" dy_max=5\n",
|
||
" )\n",
|
||
"\n",
|
||
"# Mark and label the critical point\n",
|
||
"plt.plot(1, 1, \"o\", ms=4, color=\"black\")\n",
|
||
"label_curve(ax, 1.0, float(np.asarray(rvdw_P(1.0, 1.0)).squeeze()), \n",
|
||
" \"C\", dx = -2, dy=6, bbox=True)\n",
|
||
"\n",
|
||
"# Plot scaling and axes labels\n",
|
||
"plt.ylim([0.4,1.4])\n",
|
||
"plt.xlabel(r\"$\\underline{V}$\", labelpad=15)\n",
|
||
"plt.ylabel(r'$P$', rotation=0, labelpad=20)\n",
|
||
"\n",
|
||
"fig.tight_layout()\n",
|
||
"\n",
|
||
"# Hide the tick labels\n",
|
||
"ax.tick_params(\n",
|
||
" labelbottom=False,\n",
|
||
" labelleft=False\n",
|
||
")\n",
|
||
"\n",
|
||
"# ---- SAVE HIGH-QUALITY PDF ----\n",
|
||
"fig.savefig(\"pdf/Fig_7.3-1.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "0acfc455",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Fugacity calculation for VLE\n",
|
||
"\n",
|
||
"Next, we will build the vapor-liquid equilibrium line using a fugacity calculation. This will give us the vapor and liquid molar volumes at the vapor pressure. We use this to draw tie lines through the vapor-liquid equlibrium."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "cbffc9d7",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Fugacity calculation for the van der Waals equation of state\n",
|
||
"\n",
|
||
"The fugacity of the van der Waals equation of state is\n",
|
||
"\n",
|
||
"$$ \\ln \\frac{f}{P} = (Z-1) -\\ln (Z-B) - \\frac{A}{Z} $$\n",
|
||
"\n",
|
||
"First we define a function that evaluates the equation. Then we define a function to calculate the residual of the vapor and liquid fugacities."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"id": "38cd8c8e",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\"Fugacity coefficient of the van der Waals EOS\n",
|
||
"Returns the natural log of the fugacity coefficient\n",
|
||
"\"\"\"\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"def fugacity_vdw(Z,A,B):\n",
|
||
" return (Z-1) - np.log(Z-B)-A/Z"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "fa8878ef",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Residual calculation\n",
|
||
"\n",
|
||
"The following function calculates the residual between the liquid and vapor fugacities from the EOS. We will use this and Newton's method to solve\n",
|
||
"\n",
|
||
"$$ \\ln \\frac{f^V}{P} - \\ln \\frac{f^L}{P} = 0$$\n",
|
||
"\n",
|
||
"After defining the function, we test it with a calculation.\n",
|
||
"\n",
|
||
"Newton's method will fail if the the reduced pressure guess is too far off. In this case, the pressure will be outside of the van der Waals loops of the isotherm. We can see this using the calculation above and noting the local maximum and minimum (reduced) pressures from the isotherms we plotted earlier.\n"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"id": "a8782881",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Function that returns the residual of the fugacity calculation\n",
|
||
"def residual_lnphi(Pr):\n",
|
||
" \"\"\"\n",
|
||
" Returns ln(phi_L) - ln(phi_V) at given the reduced pressure Pr.\n",
|
||
" At P_r^sat, this should be zero.\n",
|
||
" As written, requires globals Tr\n",
|
||
" \"\"\"\n",
|
||
" \n",
|
||
" A = 27*Pr/64/Tr**2\n",
|
||
" B = Pr/8/Tr\n",
|
||
"\n",
|
||
" # All compressibility roots\n",
|
||
" V_real = rvdw_V(Pr,Tr)\n",
|
||
" Z_real = V_real*Pr/Tr*3/8\n",
|
||
"\n",
|
||
" ZL = np.min(Z_real) # liquid root (smallest Z)\n",
|
||
" ZV = np.max(Z_real) # vapor root (largest Z)\n",
|
||
"\n",
|
||
" ln_f_L = fugacity_vdw(ZL, A, B) # ln(phi_L)\n",
|
||
" ln_f_V = fugacity_vdw(ZV, A, B) # ln(phi_V)\n",
|
||
"\n",
|
||
" return ln_f_L - ln_f_V"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b02b7331",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Create a dataframe of the resulting VLE\n",
|
||
"\n",
|
||
"With a method for calculating the vapor-liquid equilibrium line using fugacity, we construct a dataframe of the values. The dataframe will be a table that gives the equilibrium temperature, pressure, and molar volumes of the liquid and vapor in reduced values. We also include the vapor and liquid compressibility factors.\n",
|
||
"\n",
|
||
"We use a large number of points to get close to the critical point. Each guess of the vapor pressure for a higher isotherm is the previous vapor pressure. "
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"id": "3f46e5d9",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<div>\n",
|
||
"<style scoped>\n",
|
||
" .dataframe tbody tr th:only-of-type {\n",
|
||
" vertical-align: middle;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe tbody tr th {\n",
|
||
" vertical-align: top;\n",
|
||
" }\n",
|
||
"\n",
|
||
" .dataframe thead th {\n",
|
||
" text-align: right;\n",
|
||
" }\n",
|
||
"</style>\n",
|
||
"<table border=\"1\" class=\"dataframe\">\n",
|
||
" <thead>\n",
|
||
" <tr style=\"text-align: right;\">\n",
|
||
" <th></th>\n",
|
||
" <th>T</th>\n",
|
||
" <th>P</th>\n",
|
||
" <th>vL</th>\n",
|
||
" <th>vV</th>\n",
|
||
" <th>zL</th>\n",
|
||
" <th>zV</th>\n",
|
||
" </tr>\n",
|
||
" </thead>\n",
|
||
" <tbody>\n",
|
||
" <tr>\n",
|
||
" <th>0</th>\n",
|
||
" <td>0.620000</td>\n",
|
||
" <td>0.104701</td>\n",
|
||
" <td>0.438683</td>\n",
|
||
" <td>14.146629</td>\n",
|
||
" <td>0.027781</td>\n",
|
||
" <td>0.895866</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>1</th>\n",
|
||
" <td>0.620038</td>\n",
|
||
" <td>0.104737</td>\n",
|
||
" <td>0.438695</td>\n",
|
||
" <td>14.142255</td>\n",
|
||
" <td>0.027789</td>\n",
|
||
" <td>0.895842</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>2</th>\n",
|
||
" <td>0.620076</td>\n",
|
||
" <td>0.104773</td>\n",
|
||
" <td>0.438707</td>\n",
|
||
" <td>14.137883</td>\n",
|
||
" <td>0.027798</td>\n",
|
||
" <td>0.895818</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>3</th>\n",
|
||
" <td>0.620114</td>\n",
|
||
" <td>0.104809</td>\n",
|
||
" <td>0.438719</td>\n",
|
||
" <td>14.133512</td>\n",
|
||
" <td>0.027806</td>\n",
|
||
" <td>0.895794</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>4</th>\n",
|
||
" <td>0.620152</td>\n",
|
||
" <td>0.104845</td>\n",
|
||
" <td>0.438731</td>\n",
|
||
" <td>14.129143</td>\n",
|
||
" <td>0.027815</td>\n",
|
||
" <td>0.895770</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>...</th>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" <td>...</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9995</th>\n",
|
||
" <td>0.998848</td>\n",
|
||
" <td>0.995400</td>\n",
|
||
" <td>0.936057</td>\n",
|
||
" <td>1.072259</td>\n",
|
||
" <td>0.349809</td>\n",
|
||
" <td>0.400709</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9996</th>\n",
|
||
" <td>0.998886</td>\n",
|
||
" <td>0.995551</td>\n",
|
||
" <td>0.937057</td>\n",
|
||
" <td>1.070984</td>\n",
|
||
" <td>0.350223</td>\n",
|
||
" <td>0.400278</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9997</th>\n",
|
||
" <td>0.998924</td>\n",
|
||
" <td>0.995702</td>\n",
|
||
" <td>0.938076</td>\n",
|
||
" <td>1.069691</td>\n",
|
||
" <td>0.350644</td>\n",
|
||
" <td>0.399840</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9998</th>\n",
|
||
" <td>0.998962</td>\n",
|
||
" <td>0.995854</td>\n",
|
||
" <td>0.939116</td>\n",
|
||
" <td>1.068376</td>\n",
|
||
" <td>0.351073</td>\n",
|
||
" <td>0.399394</td>\n",
|
||
" </tr>\n",
|
||
" <tr>\n",
|
||
" <th>9999</th>\n",
|
||
" <td>0.999000</td>\n",
|
||
" <td>0.996005</td>\n",
|
||
" <td>0.940177</td>\n",
|
||
" <td>1.067041</td>\n",
|
||
" <td>0.351509</td>\n",
|
||
" <td>0.398941</td>\n",
|
||
" </tr>\n",
|
||
" </tbody>\n",
|
||
"</table>\n",
|
||
"<p>10000 rows × 6 columns</p>\n",
|
||
"</div>"
|
||
],
|
||
"text/plain": [
|
||
" T P vL vV zL zV\n",
|
||
"0 0.620000 0.104701 0.438683 14.146629 0.027781 0.895866\n",
|
||
"1 0.620038 0.104737 0.438695 14.142255 0.027789 0.895842\n",
|
||
"2 0.620076 0.104773 0.438707 14.137883 0.027798 0.895818\n",
|
||
"3 0.620114 0.104809 0.438719 14.133512 0.027806 0.895794\n",
|
||
"4 0.620152 0.104845 0.438731 14.129143 0.027815 0.895770\n",
|
||
"... ... ... ... ... ... ...\n",
|
||
"9995 0.998848 0.995400 0.936057 1.072259 0.349809 0.400709\n",
|
||
"9996 0.998886 0.995551 0.937057 1.070984 0.350223 0.400278\n",
|
||
"9997 0.998924 0.995702 0.938076 1.069691 0.350644 0.399840\n",
|
||
"9998 0.998962 0.995854 0.939116 1.068376 0.351073 0.399394\n",
|
||
"9999 0.999000 0.996005 0.940177 1.067041 0.351509 0.398941\n",
|
||
"\n",
|
||
"[10000 rows x 6 columns]"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import pandas as pd\n",
|
||
"from scipy.optimize import newton\n",
|
||
"\n",
|
||
"# Temperature, pressure, and volume are in reduced units\n",
|
||
"\n",
|
||
"# Example temperature grid\n",
|
||
"# Many points are used to keep the solver working near the c.p.\n",
|
||
"T_min = 0.62\n",
|
||
"T_max = 0.999\n",
|
||
"n_T = 10000\n",
|
||
"\n",
|
||
"T_list = np.linspace(T_min, T_max, n_T)\n",
|
||
"\n",
|
||
"rows = []\n",
|
||
"P_guess = 0.2 # A good guess for Tr close to 0.7\n",
|
||
"\n",
|
||
"for Tr in T_list:\n",
|
||
" Psat = newton(residual_lnphi, P_guess)\n",
|
||
"\n",
|
||
" V_roots = np.array(rvdw_V(Psat, Tr), dtype=complex)\n",
|
||
" V_real = V_roots[np.isreal(V_roots)].real\n",
|
||
" V_real = V_real[np.isfinite(V_real)]\n",
|
||
"\n",
|
||
" if V_real.size == 0:\n",
|
||
" rows.append({\"T\": Tr, \"P\": Psat, \"vL\": np.nan, \"vV\": np.nan})\n",
|
||
" continue\n",
|
||
"\n",
|
||
" vL = V_real.min()\n",
|
||
" vV = V_real.max()\n",
|
||
"\n",
|
||
" zL = vL*Psat/Tr*3/8\n",
|
||
" zV = vV*Psat/Tr*3/8\n",
|
||
"\n",
|
||
" rows.append({\"T\": Tr, \"P\": Psat, \"vL\": vL, \"vV\": vV, \"zL\": zL, \"zV\": zV})\n",
|
||
" P_guess = Psat\n",
|
||
"\n",
|
||
"df_eq = pd.DataFrame(rows)\n",
|
||
"df_eq"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "a7184f6c",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Figure 7.3-2 A low-temperature isotherm of the van der Waals equation\n",
|
||
"\n",
|
||
"Here we reconstruct Figure 7.3-2, which shows an isotherm below $T_c$.\n",
|
||
"\n",
|
||
"This is a busy plot. We have to identify and label points on the curve. Several helper functions are defined in order to create the labels."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"id": "1fa98126",
|
||
"metadata": {},
|
||
"outputs": [],
|
||
"source": [
|
||
"\"\"\" \n",
|
||
"These are helper functions for generating plot 7.3-2\n",
|
||
"\n",
|
||
"find_loop_extrema -- finds the local min and max of the isotherm\n",
|
||
"draw_loop_extrema -- labels the local min and max\n",
|
||
"root_between_extrema_bisect -- finds the unstable solution molar volume\n",
|
||
"label_bottom_axis -- routine for adding bottom axis labels\n",
|
||
"label_left_axis -- routine for adding left axis labels\n",
|
||
"\"\"\"\n",
|
||
"\n",
|
||
"\n",
|
||
"# --- Find the local maximum and minimum along a van der Waals loop\n",
|
||
"def find_loop_extrema(Vr, P):\n",
|
||
" \"\"\"\n",
|
||
" Find local minimum (A) and local maximum (B) on a vdW loop.\n",
|
||
"\n",
|
||
" Returns a dict with:\n",
|
||
" - iA, VA, PA : index/coords of local minimum\n",
|
||
" - iB, VB, PB : index/coords of local maximum\n",
|
||
" or None if no extrema are found.\n",
|
||
" \"\"\"\n",
|
||
" Vr = np.asarray(Vr)\n",
|
||
" P = np.asarray(P)\n",
|
||
"\n",
|
||
" dP = np.gradient(P, Vr)\n",
|
||
" s = np.sign(dP)\n",
|
||
"\n",
|
||
" imax = np.where((s[:-1] > 0) & (s[1:] < 0))[0] + 1 # + -> - : max\n",
|
||
" imin = np.where((s[:-1] < 0) & (s[1:] > 0))[0] + 1 # - -> + : min\n",
|
||
"\n",
|
||
" if len(imax) == 0 or len(imin) == 0:\n",
|
||
" return None\n",
|
||
"\n",
|
||
" iB = int(imax[0])\n",
|
||
" iA = int(imin[0])\n",
|
||
"\n",
|
||
" return {\n",
|
||
" \"iA\": iA, \"VA\": float(Vr[iA]), \"PA\": float(P[iA]),\n",
|
||
" \"iB\": iB, \"VB\": float(Vr[iB]), \"PB\": float(P[iB]),\n",
|
||
" }\n",
|
||
"\n",
|
||
"# --- Given a minimum or maximum, label the point on the curve\n",
|
||
"def draw_loop_extrema(ax, extrema, *, label_min=\"A\", label_max=\"B\",\n",
|
||
" dx=-2, dy_min=-8, dy_max=6, marker=True, bbox=False):\n",
|
||
" \"\"\"\n",
|
||
" Given the output of find_loop_extrema, draw markers + labels on ax.\n",
|
||
" \"\"\"\n",
|
||
" if extrema is None:\n",
|
||
" return None\n",
|
||
"\n",
|
||
" VA, PA = extrema[\"VA\"], extrema[\"PA\"]\n",
|
||
" VB, PB = extrema[\"VB\"], extrema[\"PB\"]\n",
|
||
"\n",
|
||
" if marker:\n",
|
||
" ax.plot(VA, PA, \"o\", ms=4, color=\"black\")\n",
|
||
" ax.plot(VB, PB, \"o\", ms=4, color=\"black\")\n",
|
||
"\n",
|
||
" label_curve(ax, VA, PA, label_min, dx=dx, dy=dy_min,\n",
|
||
" ha=\"left\", va=\"top\", bbox=bbox)\n",
|
||
" label_curve(ax, VB, PB, label_max, dx=dx, dy=dy_max,\n",
|
||
" ha=\"left\", va=\"bottom\", bbox=bbox)\n",
|
||
"\n",
|
||
" return extrema\n",
|
||
"\n",
|
||
"# --- Routine to find the unstable molar volume where P = Pvap\n",
|
||
"def root_between_extrema_bisect(Tr, Pvap, VA, VB, *, tol=1e-10, max_iter=200):\n",
|
||
" lo, hi = (VB, VA) if VB < VA else (VA, VB)\n",
|
||
"\n",
|
||
" def f(V):\n",
|
||
" return float(np.asarray(rvdw_P(V, Tr)).squeeze()) - Pvap\n",
|
||
"\n",
|
||
" flo, fhi = f(lo), f(hi)\n",
|
||
" if flo == 0.0: return lo\n",
|
||
" if fhi == 0.0: return hi\n",
|
||
" if flo * fhi > 0:\n",
|
||
" return None # not bracketed\n",
|
||
"\n",
|
||
" for _ in range(max_iter):\n",
|
||
" mid = 0.5 * (lo + hi)\n",
|
||
" fmid = f(mid)\n",
|
||
"\n",
|
||
" if abs(fmid) < tol or (hi - lo) < tol:\n",
|
||
" return mid\n",
|
||
"\n",
|
||
" if flo * fmid < 0:\n",
|
||
" hi, fhi = mid, fmid\n",
|
||
" else:\n",
|
||
" lo, flo = mid, fmid\n",
|
||
"\n",
|
||
" return 0.5 * (lo + hi)\n",
|
||
"\n",
|
||
"from matplotlib.transforms import blended_transform_factory\n",
|
||
"\n",
|
||
"# --- Routine to label x-axis\n",
|
||
"def label_bottom_axis(ax, x, text, *, dy=-10, fontsize=9):\n",
|
||
" trans = blended_transform_factory(ax.transData, ax.transAxes)\n",
|
||
" text_trans = offset_copy(trans, fig=ax.figure, y=dy, units=\"points\")\n",
|
||
"\n",
|
||
" ax.text(\n",
|
||
" x, 0.0, text,\n",
|
||
" transform=text_trans,\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"top\",\n",
|
||
" fontsize=fontsize\n",
|
||
" )\n",
|
||
"\n",
|
||
"# -- Routine to label y-axis\n",
|
||
"def label_left_axis(ax, y, text, *, dx=-5, fontsize=9):\n",
|
||
" trans = blended_transform_factory(ax.transAxes, ax.transData)\n",
|
||
" text_trans = offset_copy(trans, fig=ax.figure, x=dx, units=\"points\")\n",
|
||
"\n",
|
||
" ax.text(\n",
|
||
" 0.0, y, text,\n",
|
||
" transform=text_trans,\n",
|
||
" ha=\"right\",\n",
|
||
" va=\"center\",\n",
|
||
" fontsize=fontsize\n",
|
||
" )"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"id": "ce25198f",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 500x250 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import matplotlib as mpl\n",
|
||
"\n",
|
||
"# May cause problems in Colab or installations without LaTeX\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"# Good PDF defaults\n",
|
||
"mpl.rcParams.update({\n",
|
||
" \"pdf.fonttype\": 42, # keep text as text in PDF\n",
|
||
" \"ps.fonttype\": 42,\n",
|
||
"})\n",
|
||
"\n",
|
||
"# Make the plot\n",
|
||
"fig, ax = plt.subplots(figsize=(5.0, 2.5)) # choose size you like\n",
|
||
"\n",
|
||
"\"\"\"\n",
|
||
"Plot one isotherm and add plot annotations\n",
|
||
"\"\"\"\n",
|
||
"# Range of reduced molar volumes\n",
|
||
"Vr_min = 0.5\n",
|
||
"Vr_max = 2.1\n",
|
||
"Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
"# Plot the isotherm and label it\n",
|
||
"Tr = 0.95\n",
|
||
"P = rvdw_P(Vr, Tr)\n",
|
||
"ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
"i = np.argmin(np.abs(Vr - label_horiz_Vr))\n",
|
||
"label_curve(ax, 0.8*Vr_max, rvdw_P(0.8*Vr_max, Tr), rf\"$T<T_c$\", dy=15)\n",
|
||
"\n",
|
||
"# label loop extrema for the isotherm\n",
|
||
"ext = find_loop_extrema(Vr, P) # get VA,PA,VB,PB for calculations\n",
|
||
" # ext[\"VA\"], ext[\"PA\"], ext[\"VB\"], ext[\"PB\"]\n",
|
||
"\n",
|
||
"draw_loop_extrema(ax, ext, label_min=r\"$a$\", label_max=r\"$b$\",\n",
|
||
" dy_min=-3, dy_max=5, marker=False, bbox=False)\n",
|
||
"\n",
|
||
"# Add a line at the vapor pressure of for this isotherm\n",
|
||
"# This finds the closest tie line in the dataframe\n",
|
||
"# Include markers at the vapor and liquid molar volumes\n",
|
||
"row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
"Pvap = row[\"P\"]\n",
|
||
"vL = row[\"vL\"]\n",
|
||
"vV = row[\"vV\"]\n",
|
||
"ax.plot([Vr_min, Vr_max],[Pvap, Pvap], color=\"gray\", linewidth=1)\n",
|
||
"ax.plot(vL,Pvap,\"o\",ms=4,color=\"black\")\n",
|
||
"ax.plot(vV,Pvap,\"o\",ms=4,color=\"black\")\n",
|
||
"\n",
|
||
"# Add P_a and P_b lines and labels\n",
|
||
"VA, PA = ext[\"VA\"], ext[\"PA\"]\n",
|
||
"VB, PB = ext[\"VB\"], ext[\"PB\"]\n",
|
||
"ax.plot([Vr_min, VA],[PA, PA], \"--\", color=\"black\", linewidth=0.5)\n",
|
||
"ax.plot([Vr_min, VB],[PB, PB], \"--\", color=\"black\", linewidth=0.5)\n",
|
||
"label_left_axis(ax, PA, r\"$P_a$\")\n",
|
||
"label_left_axis(ax, PB, r\"$P_b$\")\n",
|
||
"label_left_axis(ax, Pvap, r\"$P_\\alpha$\")\n",
|
||
"\n",
|
||
"# Add V-alpha and V-alpha-prime lines and labels\n",
|
||
"ax.plot([vL, vL],[0.6, Pvap], \":\", color=\"black\", linewidth=1)\n",
|
||
"label_bottom_axis(ax, vL, r\"$\\underline{V}_\\alpha$\")\n",
|
||
"ax.plot([vV, vV],[0.6, Pvap], \":\", color=\"black\", linewidth=1)\n",
|
||
"label_bottom_axis(ax, vV, r\"$\\underline{V}_\\alpha'$\")\n",
|
||
"\n",
|
||
"# Label the unstable molar volume of the isotherm, V-alpha-doubleprime\n",
|
||
"VU = root_between_extrema_bisect(Tr, Pvap, ext[\"VA\"], ext[\"VB\"])\n",
|
||
"PU = Pvap\n",
|
||
"ax.plot(VU, PU, \"o\", ms=4, color=\"black\")\n",
|
||
"ax.plot([VU, VU],[0.6, Pvap], \":\", color=\"black\", linewidth=1)\n",
|
||
"label_bottom_axis(ax, VU, r\"$\\underline{V}_\\alpha''$\")\n",
|
||
"\n",
|
||
"# Label area I and area II\n",
|
||
"ax.text((((VU-vL)/2+vL)-VA)/2+VA, (Pvap-PA)/2+PA, \n",
|
||
" r\"$I$\", ha=\"center\", va=\"center\", fontsize=10)\n",
|
||
"ax.text(VB, (PB-Pvap)/2+Pvap, r\"$II$\", ha=\"center\", va=\"center\", fontsize=10)\n",
|
||
"\n",
|
||
"\"\"\"\n",
|
||
"Adjust plot scaling, axis labels, and figure properties\n",
|
||
"\"\"\" \n",
|
||
"\n",
|
||
"# Plot scaling\n",
|
||
"plt.ylim([0.72,0.9])\n",
|
||
"plt.xlim([0.6,0.9*Vr_max])\n",
|
||
"\n",
|
||
"# Axes labels\n",
|
||
"plt.xlabel(r\"$\\underline{V}$\", labelpad=16)\n",
|
||
"plt.ylabel(r'$P$', rotation=0, labelpad=20)\n",
|
||
"\n",
|
||
"# Hide the tick labels\n",
|
||
"ax.tick_params(\n",
|
||
" labelbottom=False,\n",
|
||
" labelleft=False\n",
|
||
")\n",
|
||
"\n",
|
||
"fig.tight_layout()\n",
|
||
"\n",
|
||
"# ---- SAVE HIGH-QUALITY PDF ----\n",
|
||
"fig.savefig(\"pdf/Fig_7.3-2.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "e4165ccf",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Figure 7.3-3 A low-temperature isotherm of a real fluid\n",
|
||
"\n",
|
||
"This is a simpler plot of the resulting isotherm through the two-phase region."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"id": "116ce547",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAeoAAADvCAYAAAA915c9AAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjUsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvWftoOwAAAAlwSFlzAAAPYQAAD2EBqD+naQAAE1pJREFUeJzt3X1sVlcdB/DTjqUwAnQQVHBlrDC3Bd0c7A9fYrIoNRrj/IeaqH/4Ekdjpk7RQTAxjsQE6TTGF2LEaYwmmg1MzJzL5ojTv3wbODembqG8NnbqBoW9QIej5pynZaWj9LbjPvc+z/18kieHMspzuXtyvj2/83JbhoeHhwMAUEqtRV8AADAxQQ0AJSaoAaDEBDUAlJigBoASE9QAUGKCGgBKbEZoEENDQ+k16vTp0+HIkSNhwYIFoaWlpdBrA4CpiEeYPPvss2Hx4sWhtbW1OYJ68+bNYdOmTUVfBgBcMIcPHw6XXXbZef9MS6OcTDZ+RH3s2LGwZMmS9I+cO3futP7Om266KcyfPz/8+Mc/voBXCgDnd/z48dDR0REGBwfDvHnzmmNE3dbWll7jxZCeblDHm3TgwIFpfz8AvBpZpm4rvZgszg0MDAwUfRkAMKFKB/WiRYvCv/71rzSpDwBl1Fr1EfWJEyfSfDcAlFHlgzpS/gagrFqrXvqOYvkbAMpIUAtqAEqs0kF9ySWXpP1rSt8AlFWlg3p0ntqIGoCyqnxQx/K3ETUAZVX5oDaiBqDMBLWgBqDEKh/UTicDoMwqH9Tx8WInT54MR48eLfpSAOAVBPXIc0Dj4zIBoGwqH9TxUZdRf39/0ZcCAK9Q+aB+3eteFy666CIjagBKqfJBHUM6rvw2ogagjCof1KPz1IIagDIS1CNBrfQNQBkJ6pEFZUbUAJSRoB4zonboCQBlI6hHRtQnTpxw6AkApSOoHXoCQIkJaoeeAFBignrMoSeCGoCyEdRjDj1R+gagbAT1CIeeAFBGgnrMPLURNQBlI6hHGFEDUEaCeoRDTwAoI0E9YsmSJenQk2eeeaboSwGAMwT1iKVLl6b24MGDRV8KAJwhqEdcfvnlqT1w4EDRlwIAZwjqEQsWLAizZ882ogagVAT1iJaWllT+NqIGoEwE9bjyt6AGoEwE9RhxRK30DUCZCOoxRkvf9lIDUBaCelzp+/jx42FwcLDoSwGARFCPYS81AGUjqM8R1BaUAVAWgnqMhQsXhlmzZglqAEpDUI/bSx3nqZW+ASgLQT2OQ08AKBNBPY4RNQBlIqjHMaIGoExmhAYxNDSUXqPifue8gvro0aPh2LFjYd68ebm8BwA0XVBv3rw5bNq0Kff36ezsTO2+ffvC9ddfn/v7AVRJV1dXerW3t4ft27en3+vu7k4HTd11111h165dDfU+9dAwQb1x48awbt26s0bUHR0dF/x9li1bltq+vj5BDXAB7dy5M2zZsiWsXLkyff39738/9e1r1qxpyPepl4YJ6ra2tvTK2/z581PJe+/evbm/F0CVxNHs6tWrz3y9e/fus74erWhm1dvbm9r169fn+j5Fa5igrude6uXLl6cRNQAXztgRbQzPGJixNH2u/z5ZQPf19YUNGzacM3Qv1PuUhaCeoPwtqAHyE8vTY0e5WWzbti3NLU8U0BfqfcrG9qwJglrpGyA/Dz74YFi1alWmP7tjx47Q09MTbrjhhjTfPJXS9VTep6wE9QRB3d/ff9Z2MAAunKmMdI8cOVKX9ykrQX0OcY56eHg47N+/v+hLAWg6cftrnDPOOjJeu3ZtGknH0I0j6/j9r+Z94rx1LJ/Hue648KzsBPUkW7QAuDBiKMYydgzJ0TnnqQTl+vXrU2CPlsInCuzJ3ufmm28+s33r1YzW66VlOA4dG1DcRx23UcUTxObOnXtB/+7Tp0+HSy65JP2PvPXWWy/o3w3AhdHb25tGzHHEnVUclceAn8r3FJ1hVn2fQ2trayqVGFEDlNf6cfuns4gL0mLpOwb26H7rsVu3ykhQT8BeaoDm097ePq2AL5I56gnYSw1AGQjq8wR1nMd46aWXir4UACpMUE/gyiuvDKdOnQoHDx4s+lIAqDBBPYGrrroqtU888UTRlwJAhQnqCSxZsiTMnDlTUANQKEF9ni1ab3jDGwQ1AIUS1JOUvwU1AEUS1JME9T//+c+iLwOAChPUkwT1wMBAOuoNAIogqM/j6quvTu2TTz5Z9KUAUFGC+jziYrLIPDUARRHU5xGfaLJo0SLz1AAURlBPwspvAIokqCchqAEokqDOsKAsLiY7ffp00ZcCQAUJ6klcc8014eTJk+HAgQNFXwoAFSSoJ/HGN74xtXv27Cn6UgCooGkFdW9vb2hpaQk9PT1h27Zt6evu7u7062azePHi0N7eLqgBKETL8PDw8FS/aXBwMFx66aVh/LfG8N61a1dYuXJlyFs8LWzevHnh2LFjaRtVnt7xjneEjo6O8LOf/SzX9wGgGo5PIcOmNaJ++OGHQ2dn5zn/2759+0Izlr8ff/zxoi8DgAqaVlA/+OCDYfXq1Wf93s6dO1OJeM2aNaHZrFixIh16curUqaIvBYCKmVZQx1Du6uo66+stW7aksncziiPqF198Mezdu7foSwGgYmZM55t2796dStw7duxIX8cyeBxlN6s4oo7igrK4XQsAShvUoyXu9evXh6pYuHBheO1rX5vmqePqdgAobek7jqZvuOGGUDWx/G2LFgClH1HHEvfY+ekqPfLyvvvuSz+oAJC/559/Pj1r4UMf+lCYPXt2qKrMQT06Jz1a+o6BVY/90mUxf/78cPDgwbBq1aqiLwWgUnp7e8OGDRvChz/84TBr1qxQNdM68KQM6nngSdTf3x8eeeSR9HzqeLALAPmKD0P605/+FH7961+H+++/Px209clPfjJ86lOfCkuXLg2NbCoZNq1V31X0wgsvhK9//evpmNRYBgcgX/HJhdu3b0/97owZM8LWrVvTr2Nf/P73vz985jOfCe985zubfvDkoRwZXXzxxeGyyy5LLQD17Xc7OzvDN77xjVTd/N73vhf6+vrSwVtxoW/8+rnnngvNSukbgIYzPDwcfv/734fvfOc74Ze//GWYM2dO+PjHPx5uueWWsHz58hCqftZ3Ff3vf/8LR44cSS0Axfa7LS0t4cYbbwy/+MUvwv79+9O89U9/+tM0Nfm+970vPPDAA694cFSjEtQZPfroo2HBggWpBaA8/e6SJUvC5s2bw+HDh8MPf/jDMDAwEN7znveksvgPfvCDcOLEidDIBHVGV1xxRfrJLbYAlK/fnTVrVip/x+dOxLJ4HF339PSkIP/yl78cnnrqqdCIzFED0LT6+vrCt7/97fCjH/0oDA0NpcNTPv/5z4c3v/nNhV6XOeocPP300+HOO+9MLQCN0e8uW7YsfOtb30pl8Vge/93vfheuv/76tK3rV7/6VdqrXXaCOqNDhw6Fm2++ObUANFa/297eHr7whS+kEfZdd92V5q1vuummcPXVV6f92fG40rJqmNJ3LFnE19iyQUdHh9I3ANPyxz/+MXzzm99M8+AxR9auXRs+/elPp73beWvK0ncsWcR/1OgrhjQATNdb3vKWNLqOo+xPfOIT6eCUuHAtnilepgcwNUxQb9y4Mf3kMfqK8w31tHfv3rQ3L7YANE+/e/nll6djSeOpZ/H0szjSjg9giiefxTPGiy48N0xQt7W1pfLA2Fc9tba2pmuILQDN1+/OmTMnfPazn01njMeRdhwUvve97w3XXXdd+MlPfhJefPHFUISGmaMez/YsAOpxTOkdd9wR7rvvvvD6178+fO5zn0sL3GL+vBpNOUddtLiEPy5ma4Sl/ADNoOh+t2XkmNL4mM09e/aEd7/73eFLX/pSOkDltttuS6XyehDUGcVnUc+cOTO1AFSr312xYkU6NOXAgQPpXPF4NGlcePbRj340PPbYY7m+t6DOKD6kPB743ugPKwdoFGXsdxcvXhy+9rWvpQXNW7ZsCQ899FC49tpr01z2b3/721wWnpmjBoBpOnXqVLj77rvTPPbf/va3sHLlyvDFL34xdHd3hxkzZkz4feaocxAftfbzn/88tQDkrxH63Ysvvjh85CMfCX/961/Db37zm/S0r7gPOz4T+7vf/W544YUXXvV7COqM4rxEvPmxBSB/jdTvtrS0hK6urhTWcU797W9/e1ohHvdof/WrXw1Hjx6d/t+t9J3NSy+9FE6ePJkWNlx00UW5vx9A1TV6v7t///50gEp8RnYsg8dHbq5bty7Ncyt95yB+SGbPnt2QHxaARtTo/e4VV1yRyt8HDx4Mt956a3oSWPy9uA97KqetCeqM9u3blxYHxBaA/DVLv/ua17wmlb/jU8Bie++996YjSrMS1FMowcRSRWwByF+z9btz585NB6XEknh8RnZW5qgBoM7MUQNAkxDUGcVnk8ZVe2V6RilAM9Pv1gjqjDo6OsLWrVtTC0D+9Ls15qgBoM7MUedgcHAw3HPPPakFIH/63RpBnVHcx/eBD3yg4ffzATQK/W7NxI/24CxvetObwn/+85/Q3t5e9KUAVIJ+t0ZQT+EJKQsXLiz6MgAqQ79bo/SdUXx6y8c+9rGGeIoLQDPQ79YI6oyGhobSIeqxBSB/+t0a27MAoM5szwKAJiGoM3rkkUfSTz2xBSB/+t0aQZ3RokWLwu23355aAPKn360xRw0AdWaOOqebunPnztQCkD/9bo2gzihuEejq6kotAPnT79Y4mSyjFStWhP3791d+rgSgXvS7NYI6o7a2trB06dKiLwOgMvS7NUrfGR06dCjccsstqQUgf/rdGkGd0fPPPx/+8Ic/pBaA/Ol3a2zPAoA6sz0LAJqEoM7o0UcfTSsPYwtA/vS7NYI6o/jw8riowUPMAepDv1tjjhoA6swcdQ6ee+65tPowtgDkT79bI6gzevLJJ8Pb3va21AKQP/1ujZPJMrrmmmvCnj17QmdnZ9GXAlAJ+t0aQZ3RrFmz0rmzANSHfrdG6Tuj/v7+cNttt6UWgPzpd2sEdUZxZd4999yTWgDyp9+tsT0LAOrM9iwAaBKCOqPHH388LF++PLUA5E+/22CrvoeGhtJrbNmgntrb20N3d3dqAciffrfB5qhvv/32sGnTplf8vjlqABpNU85Rb9y4Mf2DRl+HDx+u6/ufOHEiPcEltgDkT7/bYEHd1taWfuoY+6qnf/zjH+G6665LLQD50+82WFAX7aqrrgp//vOfUwtA/vS7DTZHPZ591AA0qqacoy7awMBAWtAWWwDyp9+tEdQZPf300+HOO+9MLQD50+/WKH0DQJ0pfQNAkxDUGf39738P1157bWoByJ9+t0ZQZzRnzpxw4403phaA/Ol3a8xRA0CdmaPOwcmTJ8PevXtTC0D+9Ls1gjqjOEdy5ZVXVn6uBKBe9Ls1gjqj+GF56KGHUgtA/vS7NeaoAaDOzFHn4N///ne44447UgtA/vS7NYI6o6eeeips3rw5tQDkT79bo/QNAHWm9A0ATUJQZ/TEE0+Et771rakFIH/63RpBndHMmTPDihUrUgtA/vS7NeaoAaDOzFHn4NSpU2FgYCC1AORPv1sjqDN67LHHwuLFi1MLQP70uzWCOqNly5aFe++9N7UA5E+/W2OOGgDqzBx1Dv773/+GrVu3phaA/Ol3awR1Rv39/WHdunWpBSB/+t0GL33HckF7e3s4fPiw0jcADVf67ujoCIODg6kEfj4zQoN65plnUhv/oQDQiJ599tnmDer58+en9tChQ5P+I6vyk5nqgnsxlntxNvfjZe5F8fciFrNjSMftZ5Np2KBuba1Nr8eQrvoHbVS8D+5FjXvxMvfibO7Hy9yLYu9F1kGmxWQAUGKCGgBKrGGDuq2tLXzlK19JbdW5Fy9zL17mXpzN/XiZe9FY96Jht2cBQBU07IgaAKpAUANAiQlqACgxQQ0AJSaoAaDEBDUAlJigHqenpydceumlYdu2bWf9fvx62bJlYefOnYVdG0Az0u+en33U4+zbty99MMbflh07doSVK1eGzs7Owq4NoBnpd8/PiHqc0Q9E/OCMis8LHfvfALhw9LvnJ6jPIX4wxn5g7r777rBmzZpCrwmgmel3JyaoJ/nA7N69O6xevbroSwJoavrdiQnqCT4wfX196dcPP/yw0gtAzvS7ExPU5xAXNcSf7OKKw7Vr1xZ9OQBNT787MUF9DnGVYdwOMNlPdPED1dXVlco0AOTb7/b09KTX2AVnVeiDBfU5xA/KBz/4wUxzJN3d3ekDBkC+/W53d/dZX8cS+fbt25u+D7aP+lWIH5otW7aYSwGog8HBwfCud70r7Nq1K/06BnUVFp3NKPoCyqSlpSXzn40/38Ryy9iQjh+c9vb2nK4OoPlMtd8dHNlfHcvkVdm+pfQ97kOQ9RU/LGNDOp6gc+TIkUKvH6CZ+90o9rtxfVAVRtKjjKinacOGDWn0HAM6rlT8y1/+Upmf7gCK0tXVlcK6StVLc9QAUGJK38CZKlGcL4zbX8afubxq1ao0kqn6U4ygCEbUwBkxqOOK2vHbXXp7e8P69esLuy6oMiNqYMIHI1RtdS2UkaAGzhvU8WtnBUBxBDVwzgcjRM5dhuIJauAVD0aIjKShHAQ1cM7SdzwjoEqHSkBZCWrgFUEdQ9oCMigHQQ2cMVrqjsfhKntDOdhHDZwlHm4S91ID5SCoAaDElL4BoMQ8PQuY0jOBI4U4qB9BDQheKDGlbwAoMUENACUmqAGgxAQ1AJSYoAaAEhPUAFBighoASkxQA0Aor/8D79q0WLkYf4YAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"<Figure size 500x250 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import matplotlib as mpl\n",
|
||
"\n",
|
||
"# May cause problems in Colab or installations without LaTeX\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"# Good PDF defaults\n",
|
||
"mpl.rcParams.update({\n",
|
||
" \"pdf.fonttype\": 42, # keep text as text in PDF\n",
|
||
" \"ps.fonttype\": 42,\n",
|
||
"})\n",
|
||
"\n",
|
||
"# Make the plot\n",
|
||
"fig, ax = plt.subplots(figsize=(5.0, 2.5)) # choose size you like\n",
|
||
"\n",
|
||
"\"\"\"\n",
|
||
"Plot one isotherm and add plot annotations\n",
|
||
"\"\"\"\n",
|
||
"# Range of reduced molar volumes\n",
|
||
"Vr_min = 0.5\n",
|
||
"Vr_max = 2.1\n",
|
||
"Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
"# Plot the isotherm and label it\n",
|
||
"# Plot from Vr_min to vL\n",
|
||
"# at Pvap from vL to vV\n",
|
||
"# from vV to Vr_max\n",
|
||
"\n",
|
||
"Tr = 0.95\n",
|
||
"P = rvdw_P(Vr, Tr)\n",
|
||
"\n",
|
||
"i = np.argmin(np.abs(Vr - label_horiz_Vr))\n",
|
||
"label_curve(ax, 0.8*Vr_max, rvdw_P(0.8*Vr_max, Tr), rf\"$T<T_c$\", dy=15)\n",
|
||
"\n",
|
||
"# Add a line at the vapor pressure of for this isotherm\n",
|
||
"# This finds the closest tie line in the dataframe\n",
|
||
"# Include markers at the vapor and liquid molar volumes\n",
|
||
"row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
"Pvap = row[\"P\"]\n",
|
||
"vL = row[\"vL\"]\n",
|
||
"vV = row[\"vV\"]\n",
|
||
"\n",
|
||
"# Isotherm above vapor line\n",
|
||
"V = np.linspace(row[\"vV\"], Vr_max, 1000)\n",
|
||
"ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
"# Isotherm below liquid line\n",
|
||
"V = np.linspace(row[\"vL\"], Vr_min, 1000)\n",
|
||
"ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
"# Isotherm through the VLE\n",
|
||
"ax.plot([vL, vV],[Pvap,Pvap],color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
"# Add V_L and V_V lines and labels\n",
|
||
"ax.plot([vL, vL],[0.6, Pvap], \":\", color=\"black\", linewidth=1)\n",
|
||
"label_bottom_axis(ax, vL, r\"$\\underline{V}_L$\")\n",
|
||
"ax.plot([vV, vV],[0.6, Pvap], \":\", color=\"black\", linewidth=1)\n",
|
||
"label_bottom_axis(ax, vV, r\"$\\underline{V}_V$\")\n",
|
||
"\n",
|
||
"\"\"\"\n",
|
||
"Adjust plot scaling, axis labels, and figure properties\n",
|
||
"\"\"\" \n",
|
||
"\n",
|
||
"# Plot scaling\n",
|
||
"plt.ylim([0.72,0.9])\n",
|
||
"plt.xlim([0.6,0.9*Vr_max])\n",
|
||
"\n",
|
||
"# Axes labels\n",
|
||
"plt.xlabel(r\"$\\underline{V}$\", labelpad=16)\n",
|
||
"plt.ylabel(r'$P$', rotation=0, labelpad=20)\n",
|
||
"\n",
|
||
"# Hide the tick labels\n",
|
||
"ax.tick_params(\n",
|
||
" labelbottom=False,\n",
|
||
" labelleft=False\n",
|
||
")\n",
|
||
"\n",
|
||
"fig.tight_layout()\n",
|
||
"\n",
|
||
"# ---- SAVE HIGH-QUALITY PDF ----\n",
|
||
"fig.savefig(\"pdf/Fig_7.3-3.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "964803b5",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Figure 7.3-4 The van der Waals fluid with the vapor-liquid coexistence region identified.\n",
|
||
"\n",
|
||
"Generate a high-resolution PDF version of the van der Waals PV plot."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"id": "3d18811d",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 600x450 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import seaborn as sns\n",
|
||
"import matplotlib as mpl\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib.transforms import offset_copy\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"# Good PDF defaults\n",
|
||
"mpl.rcParams.update({\n",
|
||
" \"pdf.fonttype\": 42, # keep text as text in PDF\n",
|
||
" \"ps.fonttype\": 42,\n",
|
||
"})\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots(figsize=(6.0, 4.5)) # choose size you like\n",
|
||
"\n",
|
||
"# plot several isotherms above the critical temperature\n",
|
||
"for Tr in np.arange(1, 3.5, 0.5):\n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min, Vr_max, 1000)\n",
|
||
"\n",
|
||
" P = rvdw_P(Vr, Tr)\n",
|
||
" ax.plot(Vr, P, '-', color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
" # Label at Vr=8.5 using the already-computed curve (scalar-safe)\n",
|
||
" Vlab = 8.5\n",
|
||
" i = np.argmin(np.abs(Vr - Vlab))\n",
|
||
" Plab = float(np.asarray(P[i]).squeeze())\n",
|
||
"\n",
|
||
" text_transform = offset_copy(ax.transData, fig=ax.figure, y=3, units='points')\n",
|
||
" ax.text(\n",
|
||
" float(Vr[i]),\n",
|
||
" Plab,\n",
|
||
" rf\"$T/T_c = {Tr:.1f}$\",\n",
|
||
" ha=\"left\",\n",
|
||
" va=\"bottom\",\n",
|
||
" fontsize=9,\n",
|
||
" transform=text_transform,\n",
|
||
" bbox=dict(facecolor=\"white\", edgecolor=\"none\", boxstyle=\"round,pad=0.2\"),\n",
|
||
" )\n",
|
||
"\n",
|
||
"# plot several isotherms below the critical temperature\n",
|
||
"for Tr in np.array([0.7, 0.8, 0.9]):\n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min, Vr_max, 1000)\n",
|
||
"\n",
|
||
" row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
" P = row[\"P\"]\n",
|
||
" vL = row[\"vL\"]\n",
|
||
" vV = row[\"vV\"]\n",
|
||
"\n",
|
||
" ax.plot([vL, vV], [P, P], color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
" text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n",
|
||
" ax.text(\n",
|
||
" 0.5 * (vL + vV),\n",
|
||
" P,\n",
|
||
" rf\"$T/T_c = {Tr:.1f}$\",\n",
|
||
" color=\"black\",\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"top\",\n",
|
||
" transform=text_transform,\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Above vapor line\n",
|
||
" V = np.linspace(row[\"vV\"], Vr_max, 1000)\n",
|
||
" ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
" # Below liquid line\n",
|
||
" V = np.linspace(row[\"vL\"], Vr_min, 1000)\n",
|
||
" ax.plot(V, rvdw_P(V, row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
"# coexistence lines behind\n",
|
||
"sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"gray\", linewidth=1,\n",
|
||
" ax=ax, linestyle=\"--\", zorder=0, legend=False)\n",
|
||
"sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"gray\", linewidth=1,\n",
|
||
" ax=ax, linestyle=\"--\", zorder=0, legend=False)\n",
|
||
"\n",
|
||
"ax.set_xlim(.01, 10)\n",
|
||
"ax.set_ylim(0, 1.4)\n",
|
||
"ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n",
|
||
"ax.set_ylabel(r\"$P/P_c$\")\n",
|
||
"\n",
|
||
"fig.tight_layout()\n",
|
||
"\n",
|
||
"# ---- SAVE HIGH-QUALITY PDF ----\n",
|
||
"fig.savefig(\"pdf/Fig_7.3-4.pdf\", bbox_inches=\"tight\", pad_inches=0.02)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "2b4181bf",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Exercises\n",
|
||
"\n",
|
||
"1. Plot the van der Waals PV diagram on a log-log scale.\n",
|
||
"2. Locate and plot the spinodal in addition to the binodal."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "ec213591",
|
||
"metadata": {},
|
||
"source": [
|
||
"# Extra figures\n",
|
||
"\n",
|
||
"Here we build plots of the van der Waals EOS vapor-liquid equilibrium using different scales and incorporating the isotherms with the van der Waals loops. We draw tie lines for several reduced temperatures below the critical temperature in color and grayscale."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"id": "8a37ffca",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import seaborn as sns\n",
|
||
"import matplotlib as mpl\n",
|
||
"\n",
|
||
"# This line can cause problems in Google Colab\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots()\n",
|
||
"\n",
|
||
"\n",
|
||
"# plot several isotherms above the critical temperature\n",
|
||
"for Tr in np.arange(1, 3.5, 0.5) : \n",
|
||
" Vr_max = 10\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n",
|
||
"\n",
|
||
"# plot several isotherms below the critical temperature\n",
|
||
"for Tr in np.array([0.7, 0.8, 0.9]) : \n",
|
||
" Vr_max = 10\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n",
|
||
"\n",
|
||
" # tie lines given Tr\n",
|
||
" # This finds the closest tie line in the dataframe\n",
|
||
" row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
" P = row[\"P\"]\n",
|
||
" vL = row[\"vL\"]\n",
|
||
" vV = row[\"vV\"]\n",
|
||
" ax.plot([vL, vV], [P, P], color=\"magenta\", linewidth=2) \n",
|
||
"\n",
|
||
"# Plot the vapor coexistence line\n",
|
||
"sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"blue\", linewidth=2, ax=ax, legend=False)\n",
|
||
"\n",
|
||
"# Plot the liquid coexistence line\n",
|
||
"sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"red\", linewidth=2, ax=ax, legend=False)\n",
|
||
"\n",
|
||
"#ax.grid(color='gray', linestyle='--', linewidth=0.5, alpha=0.7)\n",
|
||
"ax.set_xlim(.01, 10)\n",
|
||
"ax.set_ylim(0, 1.4)\n",
|
||
"ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n",
|
||
"ax.set_ylabel(r\"$P/P_c$\")\n",
|
||
"ax.set_title(r\"$P-V$ diagram for van der Waals EOS\")\n",
|
||
"\n",
|
||
"#ax.set_xscale(\"log\")\n",
|
||
"\n",
|
||
"#plt.legend(frameon=True, fancybox=True, edgecolor='none')\n",
|
||
"#plt.tight_layout()\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"id": "18b7a6d0",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import seaborn as sns\n",
|
||
"import matplotlib as mpl\n",
|
||
"\n",
|
||
"# For label spacing on tie lines\n",
|
||
"from matplotlib.transforms import offset_copy\n",
|
||
"\n",
|
||
"# This line can cause problems in Google Colab\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots()\n",
|
||
"\n",
|
||
"# plot several isotherms above the critical temperature\n",
|
||
"for Tr in np.arange(1, 3.5, 0.5) : \n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n",
|
||
"\n",
|
||
"# plot several isotherms below the critical temperature\n",
|
||
"for Tr in np.array([0.65, 0.8, 0.9]) : \n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"gray\", linewidth=0.5)\n",
|
||
"\n",
|
||
" # tie lines given Tr\n",
|
||
" # This finds the closest tie line in the dataframe\n",
|
||
" row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
" P = row[\"P\"]\n",
|
||
" vL = row[\"vL\"]\n",
|
||
" vV = row[\"vV\"]\n",
|
||
" ax.plot([vL, vV], [P, P], color=\"magenta\", linewidth=2) \n",
|
||
"\n",
|
||
" text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n",
|
||
"\n",
|
||
" ax.text(\n",
|
||
" 0.5 * (vL + vV),\n",
|
||
" P,\n",
|
||
" rf\"$T_r = {Tr:.2f}$\",\n",
|
||
" color=\"black\",\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"top\",\n",
|
||
" transform=text_transform\n",
|
||
" )\n",
|
||
"\n",
|
||
"# Plot the vapor coexistence line\n",
|
||
"sns.lineplot(data=df_eq, x=\"vV\", y=\"P\", color=\"blue\", linewidth=2, ax=ax, legend=False)\n",
|
||
"\n",
|
||
"# Plot the liquid coexistence line\n",
|
||
"sns.lineplot(data=df_eq, x=\"vL\", y=\"P\", color=\"red\", linewidth=2, ax=ax, legend=False)\n",
|
||
"\n",
|
||
"ax.set_xlim(.4, 14)\n",
|
||
"ax.set_ylim(0.1, 2)\n",
|
||
"ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n",
|
||
"ax.set_ylabel(r\"$P/P_c$\")\n",
|
||
"#ax.set_title(r\"$P-V$ diagram for van der Waals EOS\")\n",
|
||
"ax.plot(1,1,\"mo\")\n",
|
||
"\n",
|
||
"\n",
|
||
"#ax.set_xscale(\"log\")\n",
|
||
"\n",
|
||
"#plt.legend(frameon=True, fancybox=True, edgecolor='none')\n",
|
||
"#plt.tight_layout()\n",
|
||
"\n",
|
||
"ax.set_xscale(\"log\")\n",
|
||
"ax.set_yscale(\"log\")\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"id": "b1cb7c4f",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Grayscale, log-log scale\n",
|
||
"\n",
|
||
"Notice that the \"equal areas\" of the van der Waals loop is more difficult to see on this scale. One of the interesting things about this plot is the shape of the binodal along the vapor curve and the fact that, far from the critical point, the vapor isotherms as they approach the binodal behave nearly ideally. That is an assumption made deriving the Clausius-Clapeyron equation."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"id": "c50cde2b",
|
||
"metadata": {},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"import seaborn as sns\n",
|
||
"import matplotlib as mpl\n",
|
||
"\n",
|
||
"# For label spacing on tie lines\n",
|
||
"from matplotlib.transforms import offset_copy\n",
|
||
"\n",
|
||
"# This line can cause problems in Google Colab\n",
|
||
"mpl.rcParams[\"text.usetex\"] = True\n",
|
||
"\n",
|
||
"fig, ax = plt.subplots()\n",
|
||
"\n",
|
||
"# plot several isotherms above the critical temperature\n",
|
||
"for Tr in np.arange(1, 3.5, 0.5) : \n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '-',label=Tr, color=\"black\", linewidth=1)\n",
|
||
"\n",
|
||
"# plot several isotherms below the critical temperature\n",
|
||
"for Tr in np.array([0.65, 0.8, 0.9]) : \n",
|
||
" Vr_max = 14\n",
|
||
" Vr_min = 0.4\n",
|
||
" Vr = np.linspace(Vr_min,Vr_max,1000)\n",
|
||
"\n",
|
||
" ax.plot(Vr, rvdw_P(Vr,Tr), '',label=Tr, color=\"gray\", linewidth=0.5)\n",
|
||
"\n",
|
||
" # tie lines given Tr\n",
|
||
" # This finds the closest tie line in the dataframe\n",
|
||
" row = df_eq.loc[(df_eq[\"T\"] - Tr).abs().idxmin()]\n",
|
||
" P = row[\"P\"]\n",
|
||
" vL = row[\"vL\"]\n",
|
||
" vV = row[\"vV\"]\n",
|
||
" ax.plot([vL, vV], [P, P], color=\"black\", linewidth=1) \n",
|
||
"\n",
|
||
" text_transform = offset_copy(ax.transData, fig=ax.figure, y=-5, units='points')\n",
|
||
"\n",
|
||
" ax.text(\n",
|
||
" 0.5 * (vL + vV),\n",
|
||
" P,\n",
|
||
" rf\"$T_r = {Tr:.2f}$\",\n",
|
||
" color=\"black\",\n",
|
||
" ha=\"center\",\n",
|
||
" va=\"top\",\n",
|
||
" transform=text_transform\n",
|
||
" )\n",
|
||
"\n",
|
||
" # Plot the isotherm above the vapor line\n",
|
||
" V = np.linspace(row[\"vV\"],Vr_max,1000)\n",
|
||
" plt.plot(V, rvdw_P(V,row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
" # Plot the isotherm below the liquid line\n",
|
||
" V = np.linspace(row[\"vL\"],Vr_min,1000)\n",
|
||
" plt.plot(V, rvdw_P(V,row[\"T\"]), color='black', linestyle='-', linewidth=1)\n",
|
||
"\n",
|
||
"# Plot the vapor coexistence line\n",
|
||
"sns.lineplot(data=df_eq, \n",
|
||
" x=\"vV\", y=\"P\", \n",
|
||
" color=\"gray\", \n",
|
||
" linewidth=1, \n",
|
||
" ax=ax, \n",
|
||
" linestyle=\"--\",\n",
|
||
" zorder=0,\n",
|
||
" legend=False)\n",
|
||
"\n",
|
||
"# Plot the liquid coexistence line\n",
|
||
"sns.lineplot(data=df_eq, \n",
|
||
" x=\"vL\", y=\"P\", \n",
|
||
" color=\"gray\", \n",
|
||
" linewidth=1, \n",
|
||
" ax=ax, \n",
|
||
" linestyle=\"--\",\n",
|
||
" zorder=0,\n",
|
||
" legend=False)\n",
|
||
"\n",
|
||
"ax.set_xlim(.4, 14)\n",
|
||
"ax.set_ylim(0.1, 2)\n",
|
||
"ax.set_xlabel(r\"$\\underline{V}/ \\underline{V}_c$\")\n",
|
||
"ax.set_ylabel(r\"$P/P_c$\")\n",
|
||
"\n",
|
||
"ax.set_xscale(\"log\")\n",
|
||
"ax.set_yscale(\"log\")\n",
|
||
"plt.show()"
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"kernelspec": {
|
||
"display_name": ".venv",
|
||
"language": "python",
|
||
"name": "python3"
|
||
},
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.12.11"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 5
|
||
}
|