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diff --git a/Thermodynamics_by_K._M._Gupta/ch2.ipynb b/Thermodynamics_by_K._M._Gupta/ch2.ipynb new file mode 100644 index 00000000..ab6e43b2 --- /dev/null +++ b/Thermodynamics_by_K._M._Gupta/ch2.ipynb @@ -0,0 +1,627 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 : Gas Laws Ideal and Real Gases" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1 Page No : 41" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The air pressure in the tyre in bar is : 1.8\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "p1= 2.;\t\t\t# in bar\n", + "v1= 30.;\t\t\t# in litre\n", + "T1= 27.+273;\t\t\t# in K\n", + "T2= -3.+273;\t\t\t# in K\n", + "v2= v1;\t\t\t# in litre\n", + "\n", + "# Calculations\n", + "# Gas law p1*v1/T1= p2*v2/T2\n", + "p2= p1*v1*T2/(T1*v2);\t\t\t# in bar\n", + "\n", + "# Results\n", + "print \"The air pressure in the tyre in bar is :\",p2\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2 Page No : 42" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mass of Nitrogen gas stored in the vessel in kg is : 333.64\n", + "The mass of Oxygen gas stored in the vessel in kg is : 381.08\n", + "The mass of Carbon dioxide gas stored in the vessel in kg is : 524.00\n", + "Molar volume of the gas mixture in m**3 is : 2.10\n", + "density of the gas mixture in kg/m**3 is : 49.55\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "p= 12.;\t\t\t# in bar\n", + "p=p*10**5;\t\t\t# in N/m**2\n", + "v= 25.;\t\t\t# in m**3\n", + "T= 30.+273;\t\t\t# in K\n", + "# Part (a) Mass of each gas\n", + "#Formula p*v=m*R*T\n", + "R_U= 8314.;\t\t\t# in J/kg-mole K\n", + "M_N2= 28.016;\t\t\t# in mole\n", + "M_O2= 32.;\t\t\t# in mole\n", + "M_CO2= 44.;\t\t\t# in mole\n", + "\n", + "# Calculations and Results\n", + "R_N2= R_U/M_N2;\t\t\t# in J/kg K\n", + "R_O2= R_U/M_O2;\t\t\t# in J/kg K\n", + "R_CO2= R_U/M_CO2;\t\t\t# in J/kg K\n", + "m_of_N2= p*v/(R_N2*T);\t\t\t# in kg\n", + "m_of_O2= p*v/(R_O2*T);\t\t\t# in kg\n", + "m_of_CO2= p*v/(R_CO2*T);\t\t\t# in kg\n", + "print \"The mass of Nitrogen gas stored in the vessel in kg is : %.2f\"%(m_of_N2)\n", + "print \"The mass of Oxygen gas stored in the vessel in kg is : %.2f\"%m_of_O2\n", + "print \"The mass of Carbon dioxide gas stored in the vessel in kg is : %.2f\"%round(m_of_CO2)\n", + "\n", + "# Part (b) Molar Volume\n", + "# Formula v_molar= M*R*T/p= R_U*T/p\n", + "v_molar= R_U*T/p;\t\t\t# in m**3\n", + "print \"Molar volume of the gas mixture in m**3 is : %.2f\"%v_molar\n", + "\n", + "# Part (c) Average density\n", + "# rho_avg= total mass/total volume\n", + "rho_avg= (m_of_N2+m_of_O2+m_of_CO2)/v;\t\t\t# in kg/m**3\n", + "print \"density of the gas mixture in kg/m**3 is : %.2f\"%rho_avg\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3 Page No : 47" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The value of Cp in kJ/kg°C 15.375\n", + "The value of Cv in kJ/kg°C 9.9375\n", + "The value of R in kJ/kg°C 5.4375\n", + "Molecular weight of the gas is : 1.529\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "Qp = 1230.;\t\t\t# kJ/kg\n", + "Qv = 795.; \t\t\t# kJ/kg\n", + "t1 = 16.;\t\t\t# in °C\n", + "t2 = 96.;\t\t\t# in °C\n", + "R_U = 8.314;\n", + "\n", + "# Calculations and Results\n", + "delta_T= t2-t1;\t\t\t# in °C\n", + "Cp= Qp/delta_T;\t\t\t# in kJ/kg °C\n", + "print \"The value of Cp in kJ/kg°C\",Cp\n", + "\n", + "Cv= Qv/delta_T;\t\t\t# in kJ/kg °C\n", + "print \"The value of Cv in kJ/kg°C\",Cv\n", + "\n", + "R= Cp-Cv;\t\t\t# in kJ/kg °C\n", + "print \"The value of R in kJ/kg°C\",R\n", + "\n", + "molecular_weight= R_U/R;\n", + "print \"Molecular weight of the gas is : %.3f\"%molecular_weight\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4 Page No : 48" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Change in enthalpy in MJ is : 204.137\n", + "change in internal energy in MJ is : 136.092\n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "a= 0.85;\n", + "b= 0.00004;\n", + "c= 5*10**-5;\n", + "T1= 300;\t\t\t# in K\n", + "T2= 2300;\t\t\t# in K\n", + "gama= 1.5;\t\t\t# the ratio of specific heats\n", + "m=1;\t\t\t# in kg\n", + "\n", + "# Calculations and Results\n", + "def f1(T): \n", + " return a+b*T+c*T**2\n", + "\n", + "delta_H= m* quad(f1,T1,T2)[0]\n", + "\n", + "print \"Change in enthalpy in MJ is : %.3f\"%(delta_H*10**-3)\n", + "\n", + "# Formula delta_U= integration of m*Cv = integration of m*Cp/gama= delta_H/gama\n", + "delta_U= delta_H/gama;\t\t\t# in kJ\n", + "print \"change in internal energy in MJ is : %.3f\"%(delta_U*10**-3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5 Page No : 52" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using perfect gas law the pressure for unit mass of hydrogen in bar is : 54.457\n", + "Using Van der waals equation, the pressure in bar is : 56.246\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "v= 0.9/3;\t\t\t# in m**3/kg\n", + "v= 2*v;\t\t\t# in m**3/kg mole (as M_hydrogen = 2)\n", + "T=120+273;\t\t\t# in K\n", + "R=8314;\t\t\t# in J/kg mole K\n", + "a=2.51*10**4;\t\t\t# in Nm**4/(kg mole)**2\n", + "b= 0.0262;\n", + "\n", + "# Calculations and Results\n", + "# Part (a)\n", + "p= R*T/v;\t\t\t# in N/m**2\n", + "p= p*10**-5;\t\t\t# in bar\n", + "print \"Using perfect gas law the pressure for unit mass of hydrogen in bar is : %.3f\"%p\n", + "\n", + "# Part (b)\n", + "p= R*T/(v-b)-a/v**2;\t\t\t# N/m**2\n", + "p= p*10**-5;\t\t\t# in bar\n", + "print \"Using Van der waals equation, the pressure in bar is : %.3f\"%p\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6 Page No : 55" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "density of the gas under the changed condition in kg/m**3 is : 1.36\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "p1= 0.98;\t\t\t# in bar\n", + "p2= 0.6;\t\t\t# in bar\n", + "v1= 0.45;\t\t\t# in m**3/kg\n", + "\n", + "# Calculations\n", + "# Applying Boyle's law\n", + "v2= p1*v1/p2;\t\t\t# in m**3/kg\n", + "rho2= 1/v2; \t\t\t# in kg/m**3\n", + "\n", + "# Results\n", + "print \"density of the gas under the changed condition in kg/m**3 is : \",round(rho2,2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example 2.7 Page No : 55" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Payload that can be lifted along with the balloon in kg is : 580.67\n" + ] + } + ], + "source": [ + "# Exa 2.7\n", + "import math \n", + "\n", + "# Variables\n", + "r=5;\t\t\t # in cm\n", + "R_U= 8314\n", + "T= 27+273;\t\t\t# in K\n", + "\n", + "# Calculations\n", + "V= 4./3*math.pi*r**3;\t\t\t# volume of balloon in cm**3\n", + "# atmPressure= 75 cm off mercury = 75/76*1.01325 \n", + "atmPressure= round(75./76*1.01325) ;\t\t\t# in bar\n", + "p= atmPressure;\t\t\t# pressure of hydrogen in balloon in bar\n", + "p=p*10**5;\t\t\t# in N/m**2\n", + "R= R_U/2;\t\t\t# in J/kg K\n", + "m1= p*V/(R*T);\t\t\t# in kg\n", + "# The volume of air print laced = the volume of balloon, so\n", + "R=287;\n", + "T=20+273;\t\t\t# in K\n", + "m2= p*V/(R*T);\t\t\t# in kg\n", + "payload= m2-m1;\t\t\t# in kg\n", + "\n", + "# Results\n", + "print \"Payload that can be lifted along with the balloon in kg is : %.2f\"%payload\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12 Page No : 57" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The pressure in the space is 7.148 aPa\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "AvogadroNo= 6.023*10**23;\n", + "n= 5/AvogadroNo;\t\t\t# number of moles\n", + "v=10**-6;\t\t\t# in m**3\n", + "T= -270+273;\t\t\t# in K\n", + "R= 0.287;\n", + "\n", + "# Calculations\n", + "p= n*R*T/v;\t\t\t# in kPa\n", + "p= p*10**18;\t\t\t# in aPa\n", + "\n", + "# Results\n", + "print \"The pressure in the space is %.3f aPa\"%p;\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13 Page No : 57" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Change in enthalpy in kJ/kg is : 1934.8\n" + ] + } + ], + "source": [ + "# Exa 2.13\n", + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "T1 = 300;\t\t\t# in K\n", + "T2 = 900;\t\t\t# in K\n", + "m = 2; \t\t\t# in kg\n", + "\n", + "# Calculations\n", + "def f3(T): \n", + " return 40-600/math.sqrt(T)+7000/T\n", + "\n", + "delta_H=m* quad(f3,T1,T2)[0]\n", + "\n", + "delta_H= delta_H/17.03;\t\t\t# in kJ/kg\n", + "\n", + "# Results\n", + "print \"Change in enthalpy in kJ/kg is : %.1f\"%delta_H\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.14 Page No : 58" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Molecular weight is : 38.84\n", + "Gas constant in kJ/kg K is : 0.214\n", + "The pressure of the gas in bar is : 0.569\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "m = 12.;\t\t\t# in kg mol\n", + "v = 723.7;\t\t\t# in m**3\n", + "T = 140.;\t\t\t# in °C\n", + "T = T+273;\t\t\t# in K\n", + "rho = 0.644;\t\t\t# in kg/m**3\n", + "Ro = 8314;\t\t\t# in J/kg-mole K\n", + "\n", + "# Calculations and Results\n", + "# rho= m/v, where m in Kg , so rho= m*M/v\n", + "M = rho*v/m;\n", + "m = m*M;\t\t\t# in kg\n", + "print \"Molecular weight is : %.2f\"%M\n", + "\n", + "# Part (b)\n", + "R = Ro/M;\t\t\t# in J/kg K\n", + "print \"Gas constant in kJ/kg K is : %.3f\"%(R*10**-3)\n", + "\n", + "# Part(c)\n", + "p = m*R*T/v;\t\t\t# in N/m**2\n", + "p = p*10**-5;\t\t\t# in bar\n", + "print \"The pressure of the gas in bar is : %.3f\"%p\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.15 Page No : 58" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The load that can be lifted with the air of aerostat in N is : 770.11\n" + ] + } + ], + "source": [ + "\n", + "# Variables\n", + "p = 0.98; \t\t\t# in bar\n", + "p = p*10**5;\t\t\t# in N/m**2\n", + "v = 1000;\t \t\t# in m**3\n", + "T = 27+273;\t\t \t# in K\n", + "g = 9.8;\n", + "M = 2;\n", + "Ro = 8314;\t\t\t # in J/kg-mole K\n", + "\n", + "# Calculations\n", + "R = Ro/M;\t\t \t# in kg K\n", + "m = p*v/(R*T);\t\t\t# in kg\n", + "W = m*g;\t\t\t # in N\n", + "\n", + "# Results\n", + "print \"The load that can be lifted with the air of aerostat in N is : %.2f\"%W\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.16 Page No : 59" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Change in enthalpy in kcal/kg mole is : 7459.40\n" + ] + } + ], + "source": [ + "import math \n", + "from scipy.integrate import quad \n", + "\n", + "# Variables\n", + "T1= 500;\t\t\t# in K\n", + "T2= 2000;\t\t\t# in K\n", + "m=1;\t\t\t# in kg\n", + "\n", + "# Calculations\n", + "def f2(T): \n", + " return 11.515-172/math.sqrt(T)-1530/T\n", + "\n", + "delta_H=m* quad(f2,T1,T2)[0]\n", + "\n", + "# Results\n", + "print \"Change in enthalpy in kcal/kg mole is : %.2f\"%delta_H\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.17 Page No : 59" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The value of Cv in kJ/kg-K is : 0.178\n", + "The value of Cp in kJ/kg-K is : 1.005\n" + ] + } + ], + "source": [ + "from scipy.misc import derivative\n", + "\n", + "# Variables\t\t\t\n", + "duBydt= 0.718;\n", + "\n", + "# Calculations\n", + "\n", + "def f1(t):\n", + " return 196. + 0.178 * t\n", + "\n", + "Cv = round(derivative(f1,1.0, dx=1e-6),3)\n", + "\n", + "def f2(t):\n", + " return 273.351 + 1.005*t\n", + "\n", + "Cp = round(derivative(f2,1.0, dx=1e-6),3)\n", + "# Results\n", + "print \"The value of Cv in kJ/kg-K is : \",Cv\n", + "print \"The value of Cp in kJ/kg-K is : \",Cp\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |