{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 3: Second Law of Thermodynamics" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.10: Time_required_to_freeze_water.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.10\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "m=0.8;//Kg\n", "hi=335;//KJ/Kg-water\n", "T1=24+273;//K\n", "T2=0+273;//K\n", "Wdot=400;//W\n", "Wdot=Wdot/1000;//KW\n", "Q2=m*hi;//KJ\n", "ActualCOP=T2/(T1-T2)*30/100;\n", "Q2dot=ActualCOP/Wdot;//KJ/s\n", "T=Q2/Q2dot;//sec\n", "disp(T,'Time required to freeze the water in sec : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.11: Possibilty_of_claim.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.11\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=727+273;//K\n", "T2=27+273;//K\n", "Wdot=76;//KW\n", "FuelBurned=4;//Kg/hr\n", "FuelBurned=4/3600;//Kg/sec\n", "FuelHeatingValue=75000;//KJ/Kg\n", "Q1dot=FuelBurned*FuelHeatingValue;//KJ/s or KW\n", "Eta=Wdot/Q1dot*100;//%\n", "disp(Eta,'Actual Efficiency of Engine in % : ');\n", "Eta_c=(1-T2/T1)*100;//%\n", "disp(Eta_c,'Carnot Efficiency of Engine in % : ');\n", "disp('Claim of inventor is wrong as actual efficiency is greater than carnot efficiency.');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.12: Power_required_to_run_the_heat_pump.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.12\n", "clc;\n", "clear;\n", "close;\n", "format('v',5);\n", "\n", "//Given Data :\n", "T1=24+273;//K\n", "T2=10+273;//K\n", "Q1=1500;//kJ/min\n", "Q1=Q1/60;//kW\n", "COP_ideal=T1/(T1-T2);\n", "ActualCOP=COP_ideal*30/100;\n", "W=Q1/ActualCOP;//kW\n", "disp(W,'Power required in kW : ');\n", "//Answer is wromg in the book as calculation for Q1 is wrong." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.13: Patent_of_engine.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.13\n", "clc;\n", "clear;\n", "close;\n", "format('v',5);\n", "\n", "//Given Data :\n", "T1=450;//K\n", "T2=280;//K\n", "Q1=1200;//KJ\n", "W=0.15;//KWh\n", "W=W*3600;//KJ\n", "Eta_a=W/Q1*100;//%\n", "disp(Eta_a,'Actual Efficiency of Engine in % : ');\n", "Eta_c=(1-T2/T1)*100;//%\n", "disp(Eta_c,'Carnot Efficiency of Engine in % : ');\n", "disp('We would not issue a patent as actual efficiency is greater than carnot efficiency.');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.14: Heat_rejected_Work_done_and_Efficiency.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.14\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=1000;//K\n", "T3=100;//K\n", "Q1=1680;//KJ\n", "//Eta_a=Eta_b : 1-T2/T1=1-T3/T2\n", "T2=sqrt(T1*T3);//K\n", "Eta_a=1-T2/T1;\n", "Eta_b=Eta_a;\n", "W1=Eta_a*Q1;//KJ\n", "Q2=Q1-W1;//KJ\n", "Q3=(1-Eta_b)*Q2;//KJ\n", "disp(Q3,'Heat rejected by engine B in KJ : ');\n", "disp(T2,'Temperature at which heat is rejected by engine A in K : ');\n", "disp(W1,'Workdone by engine A in KJ ; ');\n", "W2=Eta_b*Q2;//KJ\n", "disp(W2,'Workdone by engine B in KJ ; ');\n", "//If W1=W2\n", "//Q/T=constant\n", "T2=(T1+T3)/2;//K\n", "Eta_a=(1-T2/T1)*100;//%\n", "Eta_b=(1-T3/T2)*100;//%\n", "disp('If Engine A & B deliver equal work.')\n", "disp(Eta_a,'Efficiency of Engine A in % : ');\n", "disp(Eta_b,'Efficiency of Engine B in % : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.15: Heat_absorbed_by_the_refrigerant.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.15\n", "clc;\n", "clear;\n", "close;\n", "format('v',8);\n", "\n", "//Given Data :\n", "T1=800+273;//K\n", "T2=30+273;//K\n", "T3=30+273;//K\n", "T4=-15+273;//K\n", "Q1=1900;//KJ\n", "W2=290;//KJ\n", "//Eta=1-T2/T1=W1/Q1\n", "W1=(1-T2/T1)*Q1;//KJ\n", "Q2=Q1-W1;//KJ\n", "W3=W1-W2;//KJ\n", "//COP=T4/(T3-T4)=Q4/W3\n", "Q4=T4/(T3-T4)*W3;//KJ\n", "disp(Q4,'Heat absorbed by refrigerant in KJ : ');\n", "Q3=W3+Q4;//KJ\n", "TotalHeat=Q2+Q3;//KJ\n", "disp(TotalHeat,'Total Heat transferred to reservoir at 30 degree centigrade in KJ : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.16: Rate_of_heat_supply_and_heat_rejection.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.16\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "T1=840+273;//K\n", "T2=60+273;//K\n", "T3=5+273;//K\n", "W3=30;//KW\n", "Q3=17;//KJ/s\n", "//Q3/T3=Q4/T4\n", "T4=T2;//K\n", "Q4=Q3/T3*T4;//KJ/s\n", "W2=Q4-Q3;//KJ/s\n", "W1=W2+W3;//KJ/s\n", "Q1subQ2=W1;//KJ/s\n", "//Q1/T1=Q2/T2\n", "Q1ByQ2=T1/T2;\n", "//Q1subQ2=Q1subQ2*Q2-Q2\n", "Q2=Q1subQ2/(Q1ByQ2-1);//KW\n", "Q1=Q1ByQ2*Q2;//KW\n", "disp(Q1,'Rate of heat supply from 800 degree C source in KW : ');\n", "disp(Q2+Q4,'Rate of heat rejection to sink in KW : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.17: Inventors_Claim.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.17\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "T1=27+273;//K\n", "T2=-23+273;//K\n", "W=1;//KW\n", "Q2=20000;//KJ/hr\n", "Q2=Q2/3600;//KJ/s\n", "ActualCOP=Q2/W;\n", "disp(ActualCOP,'Actual COP of machine : ');\n", "IdealCOP=T2/(T1-T2);\n", "disp(IdealCOP,'Ideal COP of machine : ');\n", "disp('ActualCOP>IdealCOP, Inventor claim is wrong.');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.18: Max_Power_and_Max_Temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.18\n", "clc;\n", "clear;\n", "close;\n", "format('v',8);\n", "\n", "//Given Data :\n", "//Heat Pump in winter\n", "Q1=2400;//KJ/hr/degree temperature difference\n", "t1=20;//degreeC\n", "t2=0;//degreeC\n", "Q1=Q1*(t1-t2)/3600;//KJ/s\n", "T1=t1+273;//K\n", "T2=t2+273;//K\n", "COP=T1/(T1-T2);\n", "W=Q1/COP;//KW\n", "disp(W,'Power required to drive heat pump in KW : ');\n", "//Refrigerating unit in summer\n", "T4=20+273;//K\n", "//Q4=2400*(T3-T4)/3600;//KJ/s\n", "Q3subQ4=W;//KJ\n", "//COP=Q4/(Q3subQ4)=T4/(T3-T4);\n", "//T3^2-2*T3*T4+T4^2-T4*3600/2400*(Q3subQ4)=0\n", "P=[1 -2*T4 T4^2-T4*3600/2400*(Q3subQ4)]\n", "T3=roots(P);\n", "T3=T3(1);//K(Maximum outside temperature)\n", "disp(T3,'Maximum outside temperature in K : ');\n", "disp(T3-273,'or in degree C :');\n", "" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.1: Determine_COP.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.1\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "Q2=1800;//KJ/hr\n", "Q2=Q2/3600;//KJ/sec or KW\n", "W=0.35;//KW\n", "COP=Q2/W;\n", "disp(COP,'COP is : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.20: Expansion_Ratio.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.20\n", "clc;\n", "clear;\n", "close;\n", "format('v',5);\n", "\n", "//Given Data :\n", "VcByVa=14;//Overall expansion ratio\n", "T1=257+273;//K\n", "T2=27+273;//K\n", "Gamma=1.4;\n", "Ta=T1;//K\n", "Tb=T1;//K\n", "Tc=T2;//K\n", "Td=T2;//K\n", "VcByVb=(Tb/Tc)^(1/(Gamma-1));//Expansion ratio for Adiabatic Process : \n", "disp(VcByVb,'Expansion ratio for adiabatic process : ');\n", "VbByVa=VcByVa/VcByVb;//Expansion ratio for Isothermal Process : \n", "disp(VbByVa,'Expansion ratio for Isothermal process : ');\n", "Eta=(1-T2/T1)*100;//%\n", "disp(Eta,'Thermal Efficiency of carnot cycle in % : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.21: Minimum_Theoretical_area.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.21\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "W=10;//KW\n", "//For flat plate collector\n", "T1=90+273;//K\n", "T2=27+273;//K\n", "Tmax=T1;//K\n", "IE=1;//KW/m^2 incident energy\n", "EtaCollection=60/100;\n", "//Eta=1-T2/T1=W/Q1\n", "Q1=W/(1-T2/T1);//KJ/s\n", "A1=Q1/IE/EtaCollection;//m^2\n", "disp(A1,'Solar Collector Area required in m^2 : ');\n", "//For parabolic collector\n", "T3=250+273;//K\n", "T4=27+273;//K\n", "Tmax=T3;//K\n", "IE=1;//KW/m^2 incident energy\n", "EtaCollection=50/100;\n", "//Eta=1-T2/T1=W/Q1\n", "Q3=W/(1-T4/T3);//KJ/s\n", "A2=Q3/IE/EtaCollection;//m^2\n", "disp(A2,'Parabolic Solar Collector Area required in m^2 : ');\n", "//Answer of 2nd part is wrong in the book." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.24: COP_and_Work_input.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.24\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=40+273;//K\n", "T2=5+273;//K\n", "T3=400+273;//K\n", "T4=T1;//K\n", "Q2=1500;//KJ/min\n", "COP_R=T2/(T1-T2);\n", "disp(COP_R,'COP of refrigerator is : ');\n", "Q2dot=Q2/60;//KJ/s\n", "Wdot=Q2dot/COP_R;//KW\n", "disp(Wdot,'Work Input to refrigerator in KW : ');\n", "Eta=(1-T4/T3);//%\n", "Q3dot=Wdot/Eta;//KW\n", "OverallCOP=Q2dot/Q3dot;//\n", "disp(OverallCOP,'Overall COP of refrigerator : ');\n", "//Ans of overall COP is wrong in the book." ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.25: Determine_the_COP.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.25\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=1500;//K\n", "T2=450;//K\n", "T3=150;//K\n", "Q3=250;//KJ\n", "COP_CR=T3/(T2-T3);\n", "disp(COP_CR,'COP of cold refrigerator is : ');\n", "COP_HR=T2/(T1-T2);\n", "disp(COP_HR,'COP of hotter refrigerator is : ');\n", "COP=T3/(T1-T3);\n", "disp(COP,'COP of composite system is : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.26: Heat_Supplied_and_efficiency.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.26\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=870;//K\n", "T2=580;//K\n", "T3=290;//K\n", "Wdot=85;//KW\n", "Q3=3000;//KJmin\n", "Q3=Q3/60;//KJ/s\n", "Q1plusQ2=Wdot+Q3;//KJ\n", "//sigma(Q/T)=0\n", "//Q1/T1+Q2/T2=Q3/T3\n", "//Q1/T1+(Q1plusQ2-Q1)/T2-Q3/T3=0\n", "Q1=(-Q3*T1*T2/T3+Q1plusQ2*T1)/(T1-T2);//KW\n", "disp(Q1,'Heat Supplied by source1 in KW : ');\n", "Q2=Q1plusQ2-Q1;//KW\n", "disp(Q2,'Heat Supplied by source2 in KW : ');\n", "Eta=Wdot/(Q1+Q2)*100;//%\n", "disp(Eta,'Efficiency of engine in % :');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.2: COP_Temperature_and_Heat_Rejected.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.2\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "Q2=1;//KJ/sec or KW\n", "W=0.4;//KW\n", "T2=-30+273;//K\n", "COP=Q2/W;\n", "disp(COP,'COP of refrigerator is : ');\n", "T1=T2*(1+COP)/COP;//K\n", "disp(T1,'Temperature at which heat is rejected in K : ');\n", "Q1=Q2*(1+COP)/COP;//KW\n", "disp(Q1,'Heat rejected per KW of cooling(KW) : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.3: Power_Input_COP.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.3\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "Q2=100;//KJ/sec or KW\n", "T2=-20+273;//K\n", "T1=35+273;//K\n", "COP=T2/(T1-T2);\n", "disp(COP,'COP is : ');\n", "W=Q2/COP;//KW\n", "disp(W,'Power input in KJ/s or KW : ');\n", "COPheatpump=T1/(T1-T2);//\n", "disp(COPheatpump,'COP as heat pump : ');\n", "Eta_engine=(1-T2/T1)*100;\n", "disp(Eta_engine,'Efficiency as an engine in % : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.4: COP_and_Heat_transfer_rate.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.4\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "Q2dot=12000;//KJ/hr\n", "Wdot=0.75;//KW\n", "Wdot=Wdot*3600;//KJ/hr\n", "COP=Q2dot/Wdot;\n", "disp(COP,'Coefficient of Performance is : ');\n", "Q1dot=Q2dot+Wdot;//KJ/hr\n", "disp(Q1dot,'Heat transfer rate in condenser in KJ/hr : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.5: Source_and_sink_temperature.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.5\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "Eta1=25/100;//efficiency\n", "deltaT=20;//degree centigrade\n", "//T2dash=T2-20;//K\n", "//T1dash=T1;//K\n", "deltaEta1=30/100;\n", "Eta_dash=30/100;//efficiency\n", "//Eta1/Eta_dash=(1-T2dash/T1dash)/(1-T2/T1)\n", "//T1-T2=100;\n", "//0.75*T1-T2=0;\n", "A=[1 -1;0.75 -1];\n", "B=[100;0];\n", "X=A^-1*B;\n", "//Solution for T1 and T2 by matrix\n", "T1=X(1);//K\n", "T2=X(2);//K\n", "disp(T1,'Source temperature in K : ');\n", "disp(T2,'Sink temperature in K : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.6: Power_required_to_heat_pump.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.6\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "T1=23+273;//K\n", "COP_HP=2.5;\n", "HeatLost=60000;//KJ/hr\n", "HeatGenerated=4000;//KJ/hr\n", "Q1=HeatLost-HeatGenerated;//KJ/hr\n", "W=Q1/COP_HP;//KJ/hr\n", "W=W/3600;//KJ/s or KW\n", "disp(W,'Power input in KW : ');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.7: Operation_in_which_engine_delivers_more_power.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.7\n", "clc;\n", "clear;\n", "close;\n", "format('v',7);\n", "\n", "//Given Data :\n", "T1=400+273;//K\n", "T2=20+273;//K\n", "T3=100+273;//K\n", "T4=T2;//K\n", "Q1=12000;//KW\n", "Q3=25000;//KW\n", "Eta1=1-T2/T1;//Efficiency\n", "W1=Eta1*Q1;//KW\n", "disp(W1,'Power of Engine 1, W1 in KW : ');\n", "Eta2=1-T4/T3;//Efficiency\n", "W2=Eta2*Q3;//KW\n", "disp(W2,'Power of Engine 2, W2 in KW : ');\n", "disp('W1>W2, The engine 1 delivers more power.');" ] } , { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 3.8: Temperature_of_cold_space.sce" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "//Exa 3.8\n", "clc;\n", "clear;\n", "close;\n", "format('v',6);\n", "\n", "//Given Data :\n", "Wdot=200;//W\n", "t1=40;//degree centigrade\n", "//Q2dot=20*(t1-t2);//W\n", "//COP=Q2dot/W2dot=T2/(T1-T2)\n", "//(t1-t2)/(W2dot/20)=(t1+273)/(t1-t2)\n", "//20*t1^2+20*t2^2-20*2*t1*t2-t1*Wdot-273*Wdot\n", "//(t2+273)/(t1-t2)=(t1-t2)/(Wdot/20)\n", "//t2^2-(2*t1+(Wdot/20))*t2-273*(Wdot/20)+t1^2\n", "P=[1 -(2*t1+(Wdot/20)) -273*(Wdot/20)+t1^2];\n", "t2=roots(P);\n", "t2=t2(2);//degree C\n", "//Taken only -ve value as t2 cant be greater than t1\n", "disp(t2,'Temperature of cold space(degree C)');" ] } ], "metadata": { "kernelspec": { "display_name": "Scilab", "language": "scilab", "name": "scilab" }, "language_info": { "file_extension": ".sce", "help_links": [ { "text": "MetaKernel Magics", "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" } ], "mimetype": "text/x-octave", "name": "scilab", "version": "0.7.1" } }, "nbformat": 4, "nbformat_minor": 0 }