{
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 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 7: Ideal Gases"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.1: Theoretical_problem.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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"source": [
"//Chemical Engineering Thermodynamics\n",
"//Chapter 7\n",
"//Ideal Gases\n",
"\n",
"//Example 7.1\n",
"clear;\n",
"clc;\n",
"\n",
"//Given\n",
"//The given example is a theoretical problem and it does not involve any numerical computation\n",
"//end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.2: Theoretical_problem.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"source": [
"//Chemical Engineering Thermodynamics\n",
"//Chapter 7\n",
"//Ideal Gases\n",
"\n",
"//Example 7.2\n",
"clear;\n",
"clc;\n",
"\n",
"//Given\n",
"//The given example is a theoretical problem and it does not involve any numerical computation\n",
"//end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.3: EX7_3.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"source": [
"//Chemical Engineering Thermodynamics\n",
"//Chapter 7\n",
"//Ideal Gases\n",
"\n",
"//Example 7.3\n",
"clear;\n",
"clc;\n",
"\n",
"//Given\n",
"P1 = 15;//initial pressure in Kgf/cm^2\n",
"P2 = 1;//final pressure in Kgf/cm^2\n",
"V1 = 0.012;//initial volume in m^3\n",
"V2 = 0.06;//final volume in m^3\n",
"T1 = 420;//initial temperature in K\n",
"M = 28;//molecular weight of the gas\n",
"Cp = 0.25;//specific heat at constant pressure in Kcal/Kg K\n",
"R = 1.98;//gas constant in Kcal/Kg mole K\n",
"R2 = 848;//gas constant in mKgf/Kgmole K\n",
"//Cv = a+0.0005*T1; Specific heat at constant volume\n",
"\n",
"//To Calculate the final temperature of the ideal gas, work done in an open and closed system,internal energy change for the process\n",
"//(a)Calculation of final temperature\n",
"//Using ideal gas law:(P*V)/(R*T)\n",
"T2 = (P2*V2*T1)/(P1*V1);\n",
"mprintf('(a)The final temperature is %d K',T2);\n",
"\n",
"//(b)Calculation of work in an open and closed system\n",
"//From equation 7.22(page no 147): P1*(V1^n)=P2*(V2^n)\n",
"n = (log(P2/P1))/(log(V1/V2));\n",
"//From equation 7.25(page no 149)\n",
"W = ((P1*V1)-(P2*V2))/(n-1)*10^4;//work in mKgf\n",
"W1 = W/427;//Work in Kcal\n",
"mprintf('\n (b)The work in a closed system is %f Kcal',W1);\n",
"Ws = n*W1;//from equation 7.28(page no 149)\n",
"mprintf('\n    The work in an open system is %f Kcal',Ws);\n",
"\n",
"//(c)Calculation of internal energy change\n",
"R1 = R/M;//gas constant in Kcal/Kg\n",
"Cv = Cp-R1;//specific heat at constant volume in Kcal/Kg K\n",
"a = Cv-(0.0005*T1);\n",
"m = (P1*10^4*V1*M)/(R2*T1);//mass of gas in Kg\n",
"function y = f(T)\n",
"    y = m*(a+(0.0005*T));\n",
"endfunction\n",
"del_E = intg(T1,T2,f);//internal energy change in Kcal/Kg\n",
"del_E1 = M*del_E;//internal energy change in Kcal/Kgmole\n",
"mprintf('\n (c)The internal energy change for the process is %f Kcal/Kgmole',del_E1);"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.4: Theoretical_problem.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"source": [
"//Chemical Engineering Thermodynamics\n",
"//Chapter 7\n",
"//Ideal Gases\n",
"\n",
"//Example 7.4\n",
"clear;\n",
"clc;\n",
"\n",
"//Given\n",
"//The given example is a theoretical problem and it does not involve any numerical computation\n",
"//end"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.5: EX7_5.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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"//Chemical Engineering Thermodynamics\n",
"//Chapter 7\n",
"//Ideal Gases\n",
"\n",
"//Example 7.5\n",
"clear;\n",
"clc;\n",
"\n",
"//Given\n",
"P1 = 1;//Initial pressure of air in atm\n",
"T1 = 15+273;//Initial temperature in K\n",
"P2 = 5;//Final pressure of air in atm\n",
"T2 = 15+273;//Final temperature in K\n",
"Cv = 5;//specific heat of air at constant volume in Kcal/Kgmole K\n",
"Cp = 7;//specific heat of air at constant pressure in Kcal/Kgmole K\n",
"R = 0.082;//gas constant in atm-m^3/Kgmole K\n",
"R1 = 2;//gas constant in Kcal/Kgmole K\n",
"//From the P-V diagram given in page no 155:\n",
"//Line 12 represents Isothermal process\n",
"//Line b2,c2 & 1a represent Isometric process\n",
"//Line a2 & 1c represent Isobaric process\n",
"//Line 1b reprsent Adiabatic process\n",
"\n",
"//To find Approx Value\n",
"function[A]=approx(V,n)\n",
"  A=round(V*10^n)/10^n;//V-Value  n-To what place\n",
"  funcprot(0)\n",
"endfunction  \n",
"\n",
"//To Compute del_H, del_E, Q, W, del_S for the processes given above.\n",
"//To indicate the quantities that are state functions \n",
"//To verify that the work required in an isothermal process is less than that in an adiabatic process\n",
"\n",
"//Basis:1 Kgmole of air\n",
"V1 = (R*T1)/P1;//Initial volume in cubic meter\n",
"V2 = (R*T2)/P2;//Final volume in cubic meter\n",
"\n",
"//(i)Isothermal path 12\n",
"//Equations 7.7 to 7.9 will be used (page no 145)\n",
"del_E_12 = Cv*(T2-T1);\n",
"del_H_12 = Cp*(T2-T1);\n",
"W_12 = R1*T1*log(P1/P2);\n",
"Q_12 = W_12;\n",
"del_S_12 = approx((R1*log(P1/P2)),4);\n",
"mprintf('\n(i)For isothermal process or path 12 change in internal energy is %f',del_E_12);\n",
"mprintf('\n   For isothermal process or path 12 change in enthalpy is %f',del_H_12);\n",
"mprintf('\n   For isothermal process or path 12 heat released is %f Kcal',Q_12);\n",
"mprintf('\n   For isothermal process or path 12 work is %f Kcal',W_12);\n",
"mprintf('\n   For isothermal process or path 12 change in entropy is %f Kcal/Kgmole K',del_S_12);\n",
"\n",
"//(ii)Path 1a2 = 1a(isometric)+a2(isobaric)\n",
"//Equation 7.1 to 7.6 will be used (page no 144 & 145)\n",
"Pa = P2;\n",
"Ta = (Pa/P1)*T1;//in K\n",
"Q_1a = Cv*(Ta-T1);\n",
"del_E_1a = Q_1a;\n",
"del_H_1a = Cp*(Ta-T1);\n",
"W_1a = 0;// Constant volume process\n",
"del_E_a2 = Cv*(T2-Ta);\n",
"del_H_a2 = Cp*(T2-Ta);\n",
"Q_a2 = del_H_a2;\n",
"W_a2 = P2*(V2-V1)*((10^4*1.03)/427);\n",
"del_H_1a2 = del_H_1a+del_H_a2;\n",
"del_E_1a2 = del_E_1a+del_E_a2;\n",
"Q_1a2 = Q_1a+Q_a2;\n",
"W_1a2 = W_1a+W_a2;\n",
"del_S_1a = Cv*log(Ta/T1);\n",
"del_S_a2 = Cp*log(T2/Ta);\n",
"del_S_1a2 = approx((del_S_1a+del_S_a2),4);\n",
"mprintf('\n\n(ii)For path 1a2 change in internal energy is %f',del_E_1a2);\n",
"mprintf('\n   For path 1a2 change in enthalpy is %f',del_H_1a2);\n",
"mprintf('\n   For path 1a2 heat released is %f Kcal',Q_1a2);\n",
"mprintf('\n   For path 1a2 work is %f Kcal',W_1a2);\n",
"mprintf('\n   For path 1a2 change in entropy is %f Kcal/Kgmole K',del_S_1a2);\n",
"\n",
"//(iii)Path 1b2 = 1b(adiabatic)+b2(isometric)\n",
"//From equation 7.11 (page no 146)\n",
"y = Cp/Cv;\n",
"Tb = T1*((V1/V2))^(y-1);\n",
"//From equation 7.1 to 7.3,7.10 & 7.21,(page no 144,146,147)\n",
"Q_1b = 0;//adiabatic process\n",
"del_E_1b = Cv*(Tb-T1);\n",
"del_H_1b = Cp*(Tb-T1);\n",
"W_1b = -del_E_1b;\n",
"Q_b2 = Cv*(T1-Tb);\n",
"del_H_b2 = Cp*(T1-Tb);\n",
"W_b2 = 0;//constant volume prcess\n",
"del_E_b2 = Cv*(T2-Tb);\n",
"del_H_1b2 = del_H_1b+del_H_b2;\n",
"del_E_1b2 = del_E_1b+del_E_b2;\n",
"W_1b2 = W_1b+W_b2;\n",
"Q_1b2 = Q_1b+Q_b2;\n",
"del_S_1b2 = approx((Cv*log(T1/Tb)),4);\n",
"mprintf('\n\n(iii)For path 1b2 change in internal energy is %f',del_E_1b2);\n",
"mprintf('\n   For path 1b2 change in enthalpy is %f',del_H_1b2);\n",
"mprintf('\n   For path 1b2 heat released is %f Kcal',Q_1b2);\n",
"mprintf('\n   For path 1b2 work is %f Kcal',W_1b2);\n",
"mprintf('\n   For path 1b2 change in entropy is %f Kcal/Kgmole K',del_S_1b2);\n",
"\n",
"//(iv)Path 1c2 = 1c(isobaric)+c2(isometric);\n",
"Pc = P1;\n",
"Vc = V2;\n",
"Tc = (Pc/P2)*T2;\n",
"del_E_1c = Cv*(Tc-T1);\n",
"Q_1c = Cp*(Tc-T1);\n",
"del_H_1c = Q_1c;\n",
"W_1c = P1*(Vc-V1)*((10^4*1.03)/427);\n",
"del_E_c2 = Cv*(T2-Tc);\n",
"Q_c2 = del_E_c2;\n",
"del_H_c2 = Cp*(T2-Tc);\n",
"W_c2 = 0;//constant volume process\n",
"del_E_1c2 = del_E_1c+del_E_c2;\n",
"del_H_1c2 = del_H_1c+del_H_c2;\n",
"Q_1c2 = Q_1c+Q_c2;\n",
"W_1c2 = W_1c+W_c2;\n",
"del_S_1c = Cp*log(Tc/T1);\n",
"del_S_c2 = Cv*log(T2/Tc);\n",
"del_S_1c2 = approx((del_S_1c+del_S_c2),4);\n",
"mprintf('\n\n(iv)For path 1c2 change in internal energy is %f',del_E_1c2);\n",
"mprintf('\n   For path 1c2 change in enthalpy is %f',del_H_1c2);\n",
"mprintf('\n   For path 1c2 heat released is %f Kcal',Q_1c2);\n",
"mprintf('\n   For path 1c2 work is %f Kcal',W_1c2);\n",
"mprintf('\n   For path 1c2 change in entropy is %f Kcal/Kgmole K',del_S_1c2);\n",
"\n",
"//Determination of state & path functions\n",
"if((del_E_12 == del_E_1a2)&(del_E_12 == del_E_1b2)&(del_E_12 == del_E_1c2))\n",
"    mprintf('\n\n del_E is a state function');\n",
"else\n",
"    mprintf('\n\n del_E is a path function');\n",
"end\n",
"if((del_H_12 == del_H_1a2)&(del_H_12 == del_H_1b2)&(del_H_12 == del_H_1c2))\n",
"    mprintf('\n\n del_H is a state function');\n",
"else\n",
"    mprintf('\n\n del_H is a path function');\n",
"end\n",
"if(del_S_12 == del_S_1a2)&(del_S_12 == del_S_1b2)&(del_S_12 == del_S_1c2)\n",
"    mprintf('\n\n del_S is a state function');\n",
"else\n",
"    mprintf('\n\n del_S is a path function');\n",
"end\n",
"if((Q_12 == Q_1a2)&(Q_12 == Q_1b2)&(Q_12 == Q_1c2))\n",
"    mprintf('\n\n Q is a state function');\n",
"else\n",
"    mprintf('\n\n Q is a path function');\n",
"end\n",
"if((W_12 == W_1a2)&(W_12 == W_1b2)&(W_12 == W_1c2))\n",
"    mprintf('\n\n W is a state function');\n",
"else\n",
"    mprintf('\n\n W is a path function');\n",
"end\n",
"\n",
"//Comparison of work required by isothermal & adiabatic process\n",
"if(-(W_12)<-(W_1b2))\n",
"    mprintf('\n\n  Work required by isothermal process is less than the work required by an adiabatic process');\n",
"else\n",
"    mprintf('\n\n Statement is incorrect');\n",
"end\n",
"//end"
   ]
   }
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