{
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 {
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	   "metadata": {},
	   "source": [
       "# Chapter 11: Real Gas"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.1: Calculate_the_specific_volume_of_propane.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.1 | Page number 394 \n\n');\n",
"//Calculate specific volume of propane and ideal gas\n",
"//Given data\n",
"P = 70e5 //Pa\n",
"T = 150 + 273 //K\n",
"Z = 0.55 //Compressibility factor\n",
"R = 8314.3/44 //J/kgK\n",
"//Solution\n",
"//For propane\n",
"v = Z*R*T/P //m^3/kg\n",
"printf('Specific volume for propane = %.6f m^3/kg\n',v)\n",
"//ideal gas\n",
"v = R*T/P //m^3/kg\n",
"printf('Specific volume for ideal gas = %.6f m^3/kg',v)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.2: Find_the_reduced_properties_of_air.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.2 | Page number 396 \n\n');\n",
"//Find reduced properties for air at 10 bar, 27°C\n",
"//Given data\n",
"Z = 1.04 //Compressiblity factor\n",
"pc = 3.77e6 //Pa //crticial pressure\n",
"Tc = 132.5 //K\n",
"vc = 0.0883 //m^3/kmol\n",
"p = 10e5 //Pa\n",
"T = 300 //K\n",
"//Solution\n",
"R = 287 //J/kgK\n",
"pR = p/pc //reduced pressure\n",
"TR = T/Tc //reduced temperature\n",
"v = Z*R*T/p //m^3/kg\n",
"vR = v/vc //reduced volume\n",
"\n",
"printf('Reduced pressure = %.5f \n',pR)\n",
"printf('Reduced temperature = %.5f \n',TR)\n",
"printf('Reduced volume = %.5f \n',vR)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.3: At_what_temperature_and_pressure_steam_be_similar_to_air.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.3 | Page number 397 \n\n');\n",
"//Find temperature and pressure at which steam will beahve similar to air\n",
"//Given Data\n",
"pR = 0.26525 //reduced pressure\n",
"TR = 2.26415 //reduced temperature\n",
"pc = 22.09 //bar //critical pressure of water\n",
"Tc = 647.3 //K //critical temperature of water\n",
"//Solution\n",
"p = pR*pc //bar\n",
"T = TR*Tc //K\n",
"printf('Temperature at which steam would beahve similar to air at 10 bar and 27°C = %.1f K\n',T)\n",
"\n",
"printf('Pressure at which steam would beahve similar to air at 10 bar and 27°C = %.2f bar\n',p)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.4: Find_Z_for_air.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.4 | Page number 399 \n\n');\n",
"//Find Z for air at 5.65 MPa and 27°C\n",
"//Given data\n",
"pc = 3.77e6 //Pa //critical pressure\n",
"p = 5.65e6 //Pa\n",
"Tc = 132.5 //K //critical temperature\n",
"T = 300 //K\n",
"\n",
"//Solution\n",
"pR = p/pc //reduced pressure\n",
"TR = T/Tc //reduced temperature\n",
"//from generalized compressibilty chart\n",
"Z =0.97\n",
"printf('From the generalized compressiblity chart, at reduced pressure of %.1f and reduced temperature of %.2f, Z = %.2f',pR,TR,Z)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.5: Calculate_specific_volume_of_gaseous_propane.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.5 | Page number 399 \n\n');\n",
"//Calculate specific volume for gaseous propane using:\n",
"//(i) ideal gas equation\n",
"//(ii) generalized compressiblity chart\n",
"//Given data\n",
"T =150+273 //K\n",
"p = 7e6 //Pa\n",
"\n",
"//Part (i)\n",
"printf('Part(i)\n')\n",
"v = (8314.3/44)*T/p //m^3/kg\n",
"printf('Specific volume for gaseous propane using ideal gas equation = %.4f m^3/kg\n\n',v)\n",
"\n",
"//Part(ii)\n",
"printf('Part(ii)\n')\n",
"pc = 4.26e6 //Pa //critical pressure\n",
"Tc = 370 //K //critical temperature\n",
"\n",
"pR = p/pc //reduced pressure\n",
"TR = T/Tc //reduced temperature\n",
"Z = 0.56 //compressibility factor\n",
"printf('From the generalized compressiblity chart, at reduced pressure of %.1f and reduced temperature of %.2f, Z = %.2f\n',pR,TR,Z)\n",
"v = Z*v\n",
"printf('Specific volume for gaseous propane using generalized compressiblity chart = %.5f m^3/kg\n\n',v)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.6: Determine_the_pressure_exerted_by_Carbon_dioxide.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.6 | Page number 404 \n\n');\n",
"//Find pressure exerted using (i) ideal gas equation of state (ii) van der Waals equation of state\n",
"//Given data\n",
"m = 5//kg //mass of CO2\n",
"T = 300 //K\n",
"R = 8314.3/44 //J/kgK\n",
"V = 1.5 //m^3\n",
"\n",
"//Part(i)\n",
"printf('Part(i)\n')\n",
"p = m*R*T/V\n",
"printf('Pressure exerted by CO2(using ideal gas equation) = %.2f kPa\n\n',p*.001)\n",
"\n",
"//Part(ii)\n",
"printf('Part(ii)\n')\n",
"R = 8.3143 //J/kmolK\n",
"a = 0.3658e3 //kPam^6/kmol^2\n",
"b = 0.0428 //m^3.kmol\n",
"v = 44*V/m //m^3/kmol\n",
"p = T*R/(v-b) - a/v^2\n",
"printf('Pressure exerted by CO2(using van der Waals equation) = %.1f kPa\n\n',p)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 11.7: Determine_the_pressure_in_rigid_vessel.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc\n",
"clear\n",
"printf('Example 11.7 | Page number 406 \n\n');\n",
"//Determine the pressure using:\n",
"//(i) ideal gas equation of state\n",
"//(ii) generalised compressibility chart\n",
"//(iii) van der Waals equation\n",
"//(iv) Redlich-Kwong equation of state\n",
"//(v) Bettie-Bridgeman equation\n",
"\n",
"//Given Data\n",
"M = 28 //g/mol\n",
"m = 3.5//kg\n",
"V = 0.015 //m^3\n",
"v = V/m //m^3/kg\n",
"T = 473 //K\n",
"R = 8314.3/M //J/kgK\n",
"//Solution\n",
"\n",
"//Part(i)\n",
"printf('Part(i)\n')\n",
"p = m*R*T/V //Pa\n",
"printf('Pressure (using ideal gas equation of state) = %.2f MPa\n\n',p*(1e-6))\n",
"\n",
"//Part(ii)\n",
"printf('Part(ii)\n')\n",
"pc = 3.39e6 //Pa //critical pressure\n",
"Tc = 126.2 //K //critical temperature\n",
"vc = 0.0899 //m^3/kmol //critical volume\n",
"\n",
"TR = T/Tc //reduced temperature\n",
"vR = v/(R*Tc/pc) //reduced volume\n",
"Z = 1.1 //Compressibility factor\n",
"printf('From the generalized compressiblity chart, at reduced volume of %.4f and reduced temperature of %.2f, Z = %.2f\n',vR,TR,Z)\n",
"p = Z*R*T/v //Pa\n",
"printf('Pressure (using generalised compressibility chart) = %.3f MPa\n\n',p*(1e-6))\n",
"\n",
"//Part(iii)\n",
"printf('Part(iii)\n')\n",
"a = 0.1366e6 //Pam^5/kmol^2\n",
"b = 0.0386 //m^3/kmol\n",
"p = (8314.3*T/(v*M - b)) - a/(v*M)^2\n",
"printf('Pressure (using van der Waals equation) = %.2f MPa\n\n',p*(1e-6))\n",
"\n",
"//Part(iv)\n",
"printf('Part(iv)\n')\n",
"a = (0.427*(R*M)^2*Tc^2.5/pc)\n",
"b = 0.0866*(R*M*Tc/pc)\n",
"\n",
"p = (R*M*T/(v*M-b))-(a/(((v*M)^2 + v*M*b)*(T^0.5)))\n",
"printf('Pressure (using Redlich-Kwong equation of state) = %.2f MPa\n\n',p*(1e-6))\n",
"\n",
"//---Note--- //Solution to Part(iv) in the textbook is 40.58 MPa which is wrong. The correct solution (38.13 MPa) is computed here.\n",
"\n",
"//Part(v)\n",
"printf('Part(v)\n')\n",
"A0 = 136.2315\n",
"a = 0.02617\n",
"B0 = 0.05046\n",
"b = -0.00691\n",
"c = 42000\n",
"\n",
"A = A0*(1 - a/(v*M))\n",
"B = B0*(1 - b/(v*M))\n",
"eps = c/(T^3 * v*M)\n",
"p = ((8314.3)*T*(1-eps)*(v*M+B))/(v*M)^2 - 1e3*A/(v*M)^2\n",
"printf('Pressure (using ideal gas equation of state) = %.2f MPa\n\n',p*(1e-6))"
   ]
   }
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