{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 11: THERMODYNAMIC PROPERTY RELATIONS"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.1: MERECTS_BOILER_EXPERIMENT.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"p1=150; p2=200; p3=250; p4=300; p5=350; p6=400; p7=450; p8=500; p9=550; p10=600; p11=650; p12=700; p13=750; p14=800; p15=850; p16=900; //  Pressures of merect's  boiler experiment in kPa\n",
"t1=111.4; t2=120.2; t3=127.4; t4=133.6; t5=138.9; t6=143.6; t7=147.9; t8=151.9;  t9=155.5; t10=158.9; t11=162; t12=165; t13=167.8; t14=170.4; t15=173; t16=175.4; // Temperatures of merect's boiler experiment in degree celcius\n",
"n=16; // Total number of readings taken\n",
"// Values of constant A & B\n",
"s_y= log10 (p1*p2*p3*p4*p5*p6*p7*p8*p9*p10*p11*p12*p13*p14*p15*p16);\n",
"s_x=1/(t1+273)+1/(t2+273)+1/(t3+273)+1/(t4+273)+1/(t5+273)+1/(t6+273)+1/(t7+273)+1/(t8+273)+1/(t9+273)+1/(t10+273)+1/(t11+273)+1/(t12+273)+1/(t13+273)+1/(t14+273)+1/(t15+273)+1/(t16+273);\n",
"s_xy=((log10 (p1))*1/(t1+273))+ ((log10 (p2))*1/(t2+273))+ ((log10 (p3))*1/(t3+273))+ ((log10 (p4))*1/(t4+273))+ ((log10 (p5))*1/(t5+273))+ ((log10 (p6))*1/(t6+273))+ ((log10 (p7))*1/(t7+273))+ ((log10 (p8))*1/(t8+273))+ ((log10 (p9))*1/(t9+273))+ ((log10 (p10))*1/(t10+273))+ ((log10 (p11))*1/(t11+273)) + ((log10 (p12))*1/(t12+273)) + ((log10 (p13))*1/(t13+273)) + ((log10 (p14))*1/(t14+273)) + ((log10 (p15))*1/(t15+273)) + ((log10 (p16))*1/(t16+273));\n",
"s_x2=(1/(273+t1))^2+(1/(273+t2))^2+(1/(273+t3))^2+(1/(273+t4))^2+(1/(273+t5))^2+(1/(273+t6))^2+(1/(273+t7))^2+(1/(273+t8))^2+(1/(273+t9))^2+(1/(273+t10))^2+(1/(273+t11))^2+(1/(273+t12))^2+(1/(273+t13))^2+(1/(273+t14))^2+(1/(273+t15))^2+(1/(273+t16))^2;\n",
"B= ((n*s_xy)-(s_x*s_y))/((n*s_x2)-((s_x)^2)); // Constant B\n",
"A=((s_y)-(B*s_x))/n; // Constant A\n",
"disp (B,'B =',A,'A =','Values of constant A & B');\n",
"// The latent heat of vapourization\n",
"T=150; // The latent heat of vapourization at this temperature in degree celcius\n",
"d_T=20; d_p=258.7;// Temperature and pressure difference\n",
"vg=0.3928; vf=0.0011; // specific volume in m^3/kg\n",
"hfg=(T+273)*(vg-vf)*d_p/d_T; // Clapeyron equztion\n",
"disp ('kJ/kg',hfg,'The latent heat of vapourization at 150 oC =');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.3: ENTHALPY_CALCULATION_USING_R_K_EQUATION.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"p5=6000; // Pressure of superheated steam in kPa\n",
"T5=723.15; // Temperature of superheated steam in kelvin\n",
"p1=0.6113; // Pressure at reference state in kPa\n",
"T1=273.16; // Temperature at reference state in kelvin\n",
"hfg1=2501.3; // Latent heat of vapourization of water at reference state in kJ/kg\n",
"R_1=8.3143; // Universal gas constant of air in kJ/kmol K\n",
"// The critical state properties of water\n",
"pc=2.09; // pressure in MPa\n",
"Tc=647.3; // Temperature in kelvin\n",
"h1=0; // Reference state in kJ/kg\n",
"h2=h1+hfg1; // specific enthalpy in kJ/kg \n",
"// At point 2\n",
"p2=p1; T2=T1;\n",
"z=0.9986;\n",
"r=18.015;\n",
"A2=(0.4278/(pc*10^4))*(Tc/T2)^2.5; // Constants\n",
"B=(0.0867/(pc*10^4))*(Tc/T2); // Constants\n",
"h2_h3=R_1*(T2/r)*(((-3/2)*(A2/B)*log (1+(B*p2/z)))+z-1); // Enthalpy difference between state 2 & 3\n",
"// At point 5\n",
"z1=0.9373;\n",
"A2=(0.4278/(pc*10^4))*(Tc/T5)^2.5; // Constants\n",
"B=(0.0867/(pc*10^4))*(Tc/T5); // Constants\n",
"h5_h4=R_1*(T5/r)*(((-3/2)*(A2/B)*log (1+(B*p5/z1)))+z1-1); // Enthalpy difference between state 5 & 4\n",
"a=1.6198;b=6.6*10^-4; // Constants\n",
"h4_h3=a*(T5-T1)+b*(T5^2-T1^2)/2; // Enthalpy difference between state 3 & 4\n",
"h5=h2-h2_h3+h5_h4+h4_h3; // Specific enthalpy at state 5 \n",
"disp ('kJ/kg',h5,'Specific enthalpy at state 5 = ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.4: ENTHALPY_CALCULATION_FROM_GENERALIZED_CHARTS.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"T2=373; // Temperature of CO2 gas in kelvin\n",
"p2=100; // Pressure of CO2 gas in atm\n",
"T1=0; // Reference state temperature in kelvin\n",
"// The crictical constants for CO2 are \n",
"Tc=304.2; // Temperature in kelvin\n",
"Pc=72.9; // Pressure in atm\n",
"zc=0.275;\n",
"// Refer figure 11.7 for state definition\n",
"h1_0=((-3.74*T2)+((30.53/(100^0.5))*((T2^1.5)/1.5))-((4.1/100)*((T2^2)/2))+((0.024/(100^2))*((T2^3)/3)));\n",
"Tr=T2/Tc; Pr=p2/Pc; // Reduced properties\n",
"// From generalized chart figure 11.6\n",
"hR_Tc=10.09;\n",
"h1_2=hR_Tc*Tc;\n",
"M=44; // Molecular weight\n",
"h10=h1_0/M; h12=h1_2/M;\n",
"h373=h10-h12; // The required enthalpy of CO2 gas at 373 K and 100 atm\n",
"disp ('kJ/kg',h373,'The required enthalpy of CO2 gas at 373 K and 100 atm = ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.5: CALCULATIONS_FOR_REVERSIBLE_ISOTHERMAL_COMPRESSION_FROM_GENERALIZED_CAHRTS.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"p1=11; // Initial pressure in bar\n",
"T1=40; // Initial temperature in degree celcius\n",
"p2=60; //  Final pressure in bar\n",
"R_1=8.3143; // Universal gas constant  in kJ/kmol K\n",
"// The crictical properties for natural gas \n",
"Tc=161; // Temperature in kelvin\n",
"Pc=46.4; // Pressure in bar\n",
"// Reduced properties are\n",
"Pr1=p1/Pc; Pr2=p2/Pc;\n",
"Tr1=(T1+273)/Tc;\n",
"// T2=T1, The ideal gas enthalpy h2*=h1*=h1\n",
"h21=-47.5; // From generalized enthalpy departure chart\n",
"M=16; // Molecular weight\n",
"Sp2_1=(R_1/M)*log (p2/p1)// for the difference in ideal gas entropies\n",
"Sp2_Sp_2=-0.1125; Sp_2_Sp_1=-2.1276; // Entropies in kJ/kg K\n",
"s2_s1=(Sp2_Sp_2)+(Sp_2_Sp_1);\n",
"q=(T1+273)*s2_s1; // Heat transfer\n",
"w=q-h21; // Work of compression\n",
"disp ('kJ/kg',w,'Work of compression = ','kJ/kg',q,'Heat transfer = ');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.8: CALCULATIONS_FOR_COOLING_IN_A_THROTTLING_PROCESS_USING_GENERALIZED_CHART.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"p1=10; // Initial pressure in MPa\n",
"T1=263; // Initial temperature in Kelvin\n",
"p2=1.5; //  Final pressure in MPa\n",
"R_1=8.3143; // Universal gas constant  in kJ/kmol K\n",
"M=28; // Molecular mass\n",
"// The crictical properties for nitrogen gas \n",
"Tc=126.2; // Temperature in kelvin\n",
"Pc=3.39; // Pressure in MPa\n",
"// Reduced properties are\n",
"Pr1=p1/Pc; Pr2=p2/Pc;\n",
"Tr1=T1/Tc;\n",
"// From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
"h_11=8.7*Tc/M;\n",
"// The solution involves iteration procedure. Assume T2 and check if h2_h1=0\n",
"// First approximation T2=200 K\n",
"T2=200; // In K\n",
"Tr2=T2/Tc;\n",
"Cpr=1.046;\n",
"h_21=Cpr*(T2-T1);\n",
"// From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
"h_22=1*Tc/M;\n",
"h2_h1=h_11-T2+T1-h_22;\n",
"// Second approximation \n",
"T2=190; // In K\n",
"Tr2=T2/Tc;\n",
"Cpr=1.046;\n",
"h_21=Cpr*(T2-T1);\n",
"// From the generalized chart for enthalpy departure at Pr1 & Tr1\n",
"h_22=1.5*Tc/M;\n",
"h2_h1=h_11-T2+T1-h_22;\n",
"disp ('Here also h2-h1 != 0. Therefore the temperature is dropping.Thus Joule-Thomson coefficient is positive.There is cooling in this process');"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.9: CALCULATIONS_OF_LATENT_HEAT_BY_SIMILARITY_METHOD.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc;\n",
"Tcammonia=405.9;\n",
"Tcwater=647.3;\n",
"Tr=0.576; // Condition of similarity\n",
"Twater=Tcwater*Tr; // At reduced temperature Temperature of water\n",
"Tammonia=Tcammonia*Tr;//At reduced temperature Temperature of  ammonia\n",
"// From steam table at Twater\n",
"hfgwater=2257;// specific enthalpy in kJ/kg \n",
"hfgammonia=Tcammonia/Tcwater *hfgwater; // Latent heat of vaporization of ammonia\n",
"disp ('kJ/kg',hfgammonia,'Latent heat of vaporization of ammonia =');"
   ]
   }
],
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		   "language": "scilab",
		   "name": "scilab"
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		  "language_info": {
		   "file_extension": ".sce",
		   "help_links": [
			{
			 "text": "MetaKernel Magics",
			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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