{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 7 : Thermodynamic property relations"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.10 Page No : 259"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math \n",
"\n",
"# Variables\n",
"T2 = 150. \t\t\t #temperature at which water it is desired to boil water in degree celsius\n",
"P1 = 0.10133\t\t\t #ambient pressure in MPa\n",
"T1 = 100.\t \t\t #temperature at which water boils corresponding at pressure P1 in degree celsius\n",
"del_hv = 2256.94\t\t #enthalpy of vaporization in kJ/kg\n",
"R = 8.314;\t\t \t #universal gas constant in J/molK\n",
"M = 18*10**-3;\t\t\t #molar mass of water in kg/mol\n",
"\n",
"# Calculations\n",
"T1 = T1+273.15\n",
"T2 = T2+273.15\n",
"P2 = P1*(math.exp(((del_hv*10**3*M)*((1./T1)-(1./T2)))/(R)))\n",
"\n",
"# Results\n",
"print \" The approximate pressure at which the boiler is to be operated = %0.3f MPa\"%(P2);\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The approximate pressure at which the boiler is to be operated = 0.476 MPa\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.11 Page No : 259"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"m = 60. \t\t\t #mass of the person who wants to skate in kg\n",
"T = -2.\t\t\t #temperature of the ice in degree celsius\n",
"A = 15.\t\t\t #area of contact between the skate edges and ice in mm**2\n",
"vs = 1.091*10**-3;\t\t\t #specific volume of ice in m**3/kg (at Tref)\n",
"vf = 1.0*10**-3;\t\t\t #specific volume of water in m**3/kg (at Tref)\n",
"del_hf = 6.002;\t\t \t #enthalpy of melting of ice in kJ/mol\n",
"g = 9.81;\t\t\t #accleration due to gravity in m/s**2\n",
"Tref = 0. \t\t\t #reference temperature at which the specific enthalpy of ice and water are taken in degree celsius\n",
"\n",
"# Calculations\n",
"Tref = Tref+273.15\n",
"del_P = ((m*g)/(A*10**-6))*10**-6\n",
"del_v = (vf-vs)*(18*10**-3);\t\n",
"del_T = (del_P*10**6)/((del_hf*10**3)/(Tref*del_v));\t\t\t \n",
"\n",
"# Results\n",
"print \" The temperature of ice originally = %d degree celsius \"%(T);\n",
"print \" The reduction in melting point of ice due to the additional pressure,computed using the Clayperon equation = %0.2f degree celsius \"%(del_T);\n",
"if del_T<T :\n",
" print \" The ice can melt due to the additional pressure and therefore it will be possible to skate \"\n",
"else:\n",
" print \" The ice will not melt and therefore it will be difficult to skate \"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The temperature of ice originally = -2 degree celsius \n",
" The reduction in melting point of ice due to the additional pressure,computed using the Clayperon equation = -2.93 degree celsius \n",
" The ice can melt due to the additional pressure and therefore it will be possible to skate \n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.12 Page No : 261"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"T1 = 100.\t \t\t #temperature of water in degree celsius\n",
"del_hv1 = 2256.94;\t\t\t #enthalpy of vaporization at T1 in kJ/kg\n",
"T2 = 150. \t\t\t #temperature at which the enthalpy of vaporization is to be determined in degree celsius\n",
"Cp_f = 4.26\t \t\t #isobaric heat capacity of liquid in kJ/kgK\n",
"Cp_g = 1.388\t\t\t #isobaric heat capacity of vapour in kJ/kgK\n",
"\n",
"# Calculations\n",
"del_hv2 = ((Cp_g-Cp_f)*(T2-T1))+del_hv1\n",
"\n",
"# Results\n",
"print \" The enthalpy of vaporization at 150 degree celsius = %0.2f kJ/kg\"%(del_hv2);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The enthalpy of vaporization at 150 degree celsius = 2113.34 kJ/kg\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.13 Page No : 261"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variables\n",
"T1 = 100. \t\t\t #temperature of water in degree celsius\n",
"del_hv1 = 2256.94 \t\t\t #enthalpy of vaporization at T1 in kJ/kg\n",
"T2 = 150. \t\t \t #temperature at which the enthalpy of vaporization is to be determined in degree celsius\n",
"del_hv_kirchoff = 2113.34\t\t\t #enthalpy of vaporization predicted by the Kirchhoff relation taken from Example 7.12 for comparison, in kJ/kg\n",
"del_hv_steam_tables = 2113.25\t\t\t #enthalpy of vaporization taken from the steam tables corresponding to T2,for comparison, in kJ/kg\n",
"Tc = 647.3 \t\t\t #critical temperature of water in K\n",
"\n",
"# Calculations\n",
"T1 = T1+273.15\n",
"T2 = T2+273.15\n",
"Tr1 = T1/Tc\n",
"Tr2 = T2/Tc\n",
"del_hv2 = del_hv1*(((1-Tr2)/(1-Tr1))**0.38)\n",
"\n",
"# Results\n",
"print \" The enthalpy of vaporization at 150 degree celsius using \";\n",
"print \" Watson correlation \\t = %f kJ/kg\"%(del_hv2);\n",
"print \" Kirchhoffs relation \\t = %f kJ/kg\"%(del_hv_kirchoff);\n",
"print \" From steam tables \\t = %f kJ/kg\"%(del_hv_steam_tables);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The enthalpy of vaporization at 150 degree celsius using \n",
" Watson correlation \t = 2090.687877 kJ/kg\n",
" Kirchhoffs relation \t = 2113.340000 kJ/kg\n",
" From steam tables \t = 2113.250000 kJ/kg\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 7.14 Page No : 262"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"# Variables\n",
"T = 373.15 \t\t\t #normal boiling point of water in K (temperature at which the enthalpy of vaporization is to be determined)\n",
"Pc = 221.2\t \t\t #critical pressure of water in bar\n",
"Tc = 647.3\t\t \t #critical temperature of water in K\n",
"R = 8.314\t\t\t #universal gas constant in J/molK\n",
"del_hvn_steam_tables = 2256.94\t\t\t #enthalpy of vaporization at the normal boiling point taken from the steam tables, for comparison, in kJ/kg\n",
"\n",
"# Calculations\n",
"Tbr = T/Tc\t\t\t\n",
"del_hvn = ((1.093*R*Tc*(Tbr*((math.log(Pc)-1.013)/(0.930-Tbr))))*10**-3)/(18*10**-3);\n",
"err = abs((del_hvn-del_hvn_steam_tables)/del_hvn_steam_tables)*100\n",
"\n",
"# Results\n",
"print \" The enthalpy of vaporization at the normal boiling point \";\n",
"print \" Using Riedels correlation \\t = %f kJ/kg\"%(del_hvn);\n",
"print \" From the steam tables \\t \\t = %f kJ/kg\"%(del_hvn_steam_tables);\n",
"print \" Error \\t \\t \\t \\t = %f %% \"%(err);\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" The enthalpy of vaporization at the normal boiling point \n",
" Using Riedels correlation \t = 2337.179008 kJ/kg\n",
" From the steam tables \t \t = 2256.940000 kJ/kg\n",
" Error \t \t \t \t = 3.555212 % \n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}