{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 5.7 – Reference States and State Properties \n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.7.0 – Learning Objectives\n", "\n", "By the end of this section you should be able to:\n", "\n", "1. Understand reference states and their importance.\n", "2. Understand the steam table chart and its reference point.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.7.1 – Introduction\n", "\n", "Often, we do not know the absolute value of internal energy or enthalpy ($\\hat{U}, \\hat{H}$). To give us a way of measuring these values, a __reference state__ is chosen to represent __0__ and the values are determined as a __difference to the reference state.__ \n", "\n", "This notebook will go over the concept of reference state and state properties.7\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5.7.2 – Internal energy of Water \n", "\n", "Let's look at water at 0 C$^\\circ$ and 1 atm. If asked to find the __specific__ energy $U$ of this water, you might think right away that you can use $C_p\\Delta T$ but this is wrong. We cannot use this formula because we need to consider the $\\Delta T$ which refers to a change in temperature. \n", "\n", "What we can do is use the 0 C$^\\circ$ 1 atm water as a __reference__ and compare it to changes in energy.\n", "\n", "We can take liquid water at 50 C$^\\circ$ 1 atm and say that __in reference to 0__ C$^\\circ$ __water__, 100 C$^\\circ$ water has $210 \\space \\frac{kJ}{kg}$ more energy than 0 C$^\\circ$ liquid water. \n", "\n", "Likewise, 100 C$^\\circ$ liquid water at 1 atm has $420 \\space \\frac{kJ}{kg}$ more energy than water at 0 C$^\\circ$. \n", "\n", "By setting water at 0 C$^\\circ$. We can use the referenced values as variables known as __state variables__ also known as $\\hat{U}$ and $\\hat{H}$. \n", "\n", "A state variable is a variable that its property only depends on its __initial and final state__.\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", " | Temperature (K) | \n", "Pressure (MPa) | \n", "Volume (l/mol) | \n", "Internal Energy (kJ/mol) | \n", "Enthalpy (kJ/mol) | \n", "Entropy (J/mol*K) | \n", "
---|---|---|---|---|---|---|
0 | \n", "600 | \n", "0.0 | \n", "infinite | \n", "51.415 | \n", "56.404 | \n", "500.13 | \n", "
1 | \n", "600 | \n", "1.0 | \n", "4.8861 | \n", "51.123 | \n", "56.009 | \n", "130.11 | \n", "
2 | \n", "600 | \n", "2.0 | \n", "2.3891 | \n", "50.811 | \n", "55.589 | \n", "123.82 | \n", "
3 | \n", "600 | \n", "3.0 | \n", "1.5548 | \n", "50.477 | \n", "55.142 | \n", "119.88 | \n", "
4 | \n", "600 | \n", "4.0 | \n", "1.1361 | \n", "50.119 | \n", "54.664 | \n", "116.88 | \n", "
5 | \n", "600 | \n", "5.0 | \n", "0.8834 | \n", "49.734 | \n", "54.151 | \n", "114.36 | \n", "
6 | \n", "600 | \n", "6.0 | \n", "0.71355 | \n", "49.318 | \n", "53.599 | \n", "112.11 | \n", "
7 | \n", "600 | \n", "7.0 | \n", "0.59087 | \n", "48.864 | \n", "53.000 | \n", "110.03 | \n", "
8 | \n", "600 | \n", "8.0 | \n", "0.49741 | \n", "48.366 | \n", "52.345 | \n", "108.04 | \n", "
9 | \n", "600 | \n", "9.0 | \n", "0.42316 | \n", "47.811 | \n", "51.620 | \n", "106.06 | \n", "
10 | \n", "600 | \n", "10.0 | \n", "0.36195 | \n", "47.183 | \n", "50.802 | \n", "104.05 | \n", "