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@amcdawes
Created April 11, 2017 19:47
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# The van der Waals model\n",
"A numerical exploration of the van der Waals model. Use the form given in terms of moles:\n",
"$$\\left(P + \\frac{a n^2}{V^2}\\right)\\left(V - nb\\right)=nRT$$\n",
"\n",
"1) Show that this is equivalent to the following if we use $V'$ as `volume per mole`:\n",
"$$\\left(P + \\frac{a}{V'^2}\\right)\\left(V' - b\\right)=RT$$\n",
"2) Solve for $P$ to generate an expression that you can plot: $P(V,T)$\n",
"\n",
"3) Using specific values of the constants $a$ and $b$ for different systems, generate plots that show the critical temperature for each of the systems. Below are some examples of how to plot functions in python. One specific challenge here is finding the appropriate range for the plot.\n",
"\n",
"4) Summarize the effect that $a$ and $b$ have on the shapes in the PV diagram.\n",
"\n",
"### Use the following data table to explore different systems:\n",
"\n",
"<table border=\"1\" cellspacing=\"2\" cellpadding=\"2\"><tbody><tr><td colspan=\"3\"><center>van der Waals Coefficients</center></td></tr>\n",
"<tr><td><center>Gas</center></td><td><center><b>a</b> (Pa m<sup>3</sup>)</center></td><td><center><b>b</b> (m<sup>3</sup>/mol)</center></td></tr>\n",
"\n",
"<tr><td>Helium</td><td><center>3.46 x 10<sup>-3</sup></center></td><td><center>23.71 x 10<sup>-6</sup></center></td></tr>\n",
"<tr><td>Neon</td><td><center>2.12 x 10<sup>-2</sup></center></td><td><center>17.10 x 10<sup>-6</sup></center></td></tr>\n",
"<tr><td>Hydrogen</td><td><center>2.45 x 10<sup>-2</sup></center></td><td><center>26.61 x 10<sup>-6</sup></center></td></tr>\n",
"<tr><td>Carbon dioxide</td><td><center>3.96 x 10<sup>-1</sup></center></td><td><center>42.69 x 10<sup>-6</sup></center></td></tr>\n",
"<tr><td>Water vapor</td><td><center>5.47 x 10<sup>-1</sup></center></td><td><center>30.52 x 10<sup>-6</sup></center></td></tr>\n",
"\n",
"</tbody></table>\n",
"<center>Data from Fishbane, et al.</center>"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x11681af28>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x11690d4e0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Data from hyperphysics, using Pa and m:\n",
"\n",
"\n",
"# Numbers for Helium from http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/waal.html\n",
"a = 3.46e-3 # Pa m^3\n",
"b = 23.71e-6 # m^3/mol\n",
"R = 8.314 \n",
"\n",
"# This is one way to generate a list of volumes: V\n",
"V = np.linspace(0,1,500)\n",
"\n",
"#an example plot (this is *not* the right equation to plot)\n",
"plt.plot(V,V**2)\n",
"\n",
"# Change the above line to plot your function of P(V)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## How to plot several functions for a range of parameters:\n",
"We'll plot $V^c$ for values of $c$ between 1 and 2:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"(0, 0.4)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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frR6DePToUSorK5k6dSq6Dr+ztPRzLJYqkpMf1ezyxwb7M0Z230ouAGTQl5wX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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x116912c50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for c in np.arange(1,2,0.1):\n",
" plt.plot(V,V**c)\n",
"\n",
"plt.ylim([0,0.4]) # Sometimes you want to limit the range of a plot"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.5.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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