{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "*This notebook contains course material from [CBE20255](https://jckantor.github.io/CBE20255)\n", "by Jeffrey Kantor (jeff at nd.edu); the content is available [on Github](https://github.com/jckantor/CBE20255.git).\n", "The text is released under the [CC-BY-NC-ND-4.0 license](https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode),\n", "and code is released under the [MIT license](https://opensource.org/licenses/MIT).*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Gases with One Condensable Component](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.01-Gases-with-One-Condensable-Component.ipynb) | [Contents](toc.ipynb) | [Operating Limits for a Methanol Lighter](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/07.03-Operating-Limits-for-a-Methanol-Lighter.ipynb) >
"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "yP9LBLF6p4qQ"
},
"source": [
"# Vapor-Liquid Equilibrium for Pure Components"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "yP9LBLF6p4qQ"
},
"source": [
"## Summary\n",
"\n",
"This [Jupyter notebook](http://jupyter.org/notebook.html) describes the modeling of vapor-liquid equilibrium with Antoine's equation, including the calculation of saturation pressure, saturation temperature, and normal boiling points."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "k8bnw65Zp4qT"
},
"source": [
"## Gibb's Phase Rule"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "fLhbzTN-p4qT"
},
"source": [
"The Gibb's phase rule shows how many independent intensive thermodynamic variables (e.g. $T$, $P$, $\\hat{V}$, or $x_i$) are required to completely specify the state of a substance.\n",
"\n",
"$$ F = C + 2 - \\Pi - r$$\n",
"\n",
"where\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"F & = \\mbox{Thermodynamic Degrees of Freedom} \\\\\n",
"C & = \\mbox{Number of Components} \\\\\n",
"\\Pi & = \\mbox{Number of Phases} \\\\\n",
"r & = \\mbox{number of independent reactions at equilibrium}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"This simple rule that has profound implications for engineering analysis."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "pbzZr-W4p4qV"
},
"source": [
"## Phase Diagram for a Pure Component"
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "OIC0QEjVp4qV"
},
"source": [
"For a pure component (i.e., $C = 1$) and no reactions (i.e., $r=0$), the Gibb's phase rule reads\n",
"\n",
"$$ F = 3-\\Pi$$\n",
"\n",
"which shows:\n",
"\n",
"* Two independent thermodynamic variables, such as $T$ and $P$, are sufficient to specify the state of a single phase.\n",
"* If two phases are in coexistence, then there must be a relationship between $T$ and $P$.\n",
"* The coexistence of three phases completely specifies the thermodynamic state.\n",
"\n",
"These observations are demonstrated in a 2-dimensional phase diagram for a pure substance.\n",
"\n",
"![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Phase-diag2.svg/500px-Phase-diag2.svg.png) \n",
"[By Matthieumarechal, CC BY-SA 3.0](https://commons.wikimedia.org/w/index.php?curid=4623701)\n",
"\n",
"The green line shows the solid/liquid coexistence (the dashed green line showing the anomolous special case of water)."
]
},
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "wElXeCCHp4qV"
},
"source": [
"### Triple Point"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 336
},
"colab_type": "code",
"executionInfo": {
"elapsed": 741,
"status": "ok",
"timestamp": 1539185455925,
"user": {
"displayName": "Jeffrey Kantor",
"photoUrl": "",
"userId": "09038942003589296665"
},
"user_tz": 240
},
"id": "SSK498Rdp4qX",
"outputId": "41483d2e-2f09-491d-f872-e47218cc502b"
},
"outputs": [
{
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