{ "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", "< [Water and Steam Calculator](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.02-Water-and-Steam-Calculator.ipynb) | [Contents](toc.ipynb) | [Energy Balances for a Steam Turbine](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.04-Energy-Balances-for-a-Steam-Turbine.ipynb) >

\"Open" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Energy Computations" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "g8TFZSxmXmVm" }, "source": [ "## Computing Enthalpy and Internal Energy Changes for Common Situations\n", "\n", "Internal energy ($U$) and enthalpy ($H = U + PV$) are thermodynamic state variables. We can use this property to compute changes in internal energy or enthalpy due to changes in pressure, temperature, phase, composition, and mixing/solution. The following table presents basic formulas for these calculations.\n", "\n", "\n", "| Change in | $\\Delta\\hat{H}=\\Delta\\hat{U} + P\\Delta\\hat{V}$ | $\\Delta\\hat{U}$ | Comments |\n", "| :--- | :--- | :--- | :--- |\n", "| Pressure | ~ 0 (gas)
~$\\hat{V}\\Delta P$ (solid or liquid) | ~ 0 | Generally neglected except for large pressure changes.\n", "| Temperature | $\\int_{T_1}^{T_2} C_p(T) dT$

$\\approx \\bar{C}_p(T_2 - T_1)$ | $\\int_{T_1}^{T_2} C_v(T)dT$

$\\approx \\bar{C}_v(T_2 - T_1)$| Expressions available for $C_p(T)$
$C_p \\approx C_v + R$ (gases)
$C_p \\approx C_v$ (liquids and solids) |\n", "| Phase | $\\Delta\\hat{H}_{vap}$ (liquid to vapor)
$\\Delta\\hat{H}_{m}$ (solid to liquid) | $\\Delta\\hat{U}_{vap}\\approx\\Delta\\hat{H}_{vap}-RT_b$
$\\Delta\\hat{U}_m\\approx\\Delta\\hat{H}_m$ | |\n", "| Composition due
to Reaction | $\\Delta\\hat{H}^\\circ_r =\\sum_i \\nu_i \\Delta\\hat{H}^\\circ_{f,i}$
$\\Delta\\hat{H}^\\circ_r = -\\sum_i \\nu_i \\Delta\\hat{H}^\\circ_{c,i}$ | $\\Delta\\hat{U}_r \\approx \\Delta\\hat{H}_r - RT \\Delta n_r$
$\\Delta\\hat{U}_r \\approx \\Delta\\hat{H}_r$ (solid or liquid) | $\\Delta n_r$ is the cange in moles due to reaction
Standard conditions are 25$^\\circ$C and 1 atm.
Be sure all data uses same standard conditions.|\n", "| Composition due
to Mixing/Sol'n | $\\Delta\\hat{H}_{soln}$
$\\Delta\\hat{H}_{mix}$ | $\\Delta\\hat{U}_{soln} \\approx \\Delta\\hat{H}_{soln}$
$\\Delta\\hat{U}_{mix} \\approx \\Delta\\hat{H}_{mix}$ | Important for non-ideal mixtures.
Typical units are per mole of solute, not solution. |\n", "| |                                                    |                                                    |" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Examples" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "EzN7g0dxtmWe" }, "source": [ "### Pumping a Fluid \n", "\n", "For a particular fire-fighting situation, it is determined that 1,250 gpm is required. The fire hydrant will supply sufficient water at a pressure of 35 psig. A pressure of 180 psig is needed to reach the top of the 212 foot bulding. What size engine (in Hp) is required to power the fire pump?" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 51 }, "colab_type": "code", "executionInfo": { "elapsed": 303, "status": "ok", "timestamp": 1542579341053, "user": { "displayName": "Jeffrey Kantor", "photoUrl": "https://lh5.googleusercontent.com/-8zK5aAW5RMQ/AAAAAAAAAAI/AAAAAAAAKB0/kssUQyz8DTQ/s64/photo.jpg", "userId": "09038942003589296665" }, "user_tz": 300 }, "id": "iBIZ8l6SXatb", "outputId": "ac5073c4-796b-42a0-f55d-562d015ce364" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fire pump requirement [watts] = 78841.96681903958\n", "fire pump requirement [hp] = 105.68628259924876\n" ] } ], "source": [ "Vdot = 1250/264.172/60 # flow in m**3/s\n", "dP = (180 - 35)*101325/14.696 # pressure change in pascals (N/m**2)\n", "\n", "P = Vdot*dP # power in N-m/sec = watts\n", "print(\"fire pump requirement [watts] =\", P)\n", "print(\"fire pump requirement [hp] =\", P/746)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "HkmliWRIGHQM" }, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Vaporization of Phenol\n", "\n", "Solid phenol at 25°C and 1 atm is converted to phenol vapor at 300°C and 3 atm. How much heat will be required?" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "colab": {}, "colab_type": "code", "id": "ki1iR8JT5FA7" }, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "< [Water and Steam Calculator](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.02-Water-and-Steam-Calculator.ipynb) | [Contents](toc.ipynb) | [Energy Balances for a Steam Turbine](http://nbviewer.jupyter.org/github/jckantor/CBE20255/blob/master/notebooks/08.04-Energy-Balances-for-a-Steam-Turbine.ipynb) >

\"Open" ] } ], "metadata": { "colab": { "name": "Basic_Energy_Calculations.ipynb", "provenance": [], "version": "0.3.2" }, "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }