{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3: First Law of Thermodynyamics"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, page no. 76"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Variable Declaration: \n",
"#Pressure in the gas cylinder(in kPa):\n",
"p=689\n",
"#Final volume(in m**3):\n",
"v2=0.045\n",
"#Initial volume(in m**3):\n",
"v1=0.04\n",
"#Work done by the paddle(in kJ):\n",
"Pw=-4.88\n",
"\n",
"#Calculation:\n",
"#Work done by the system on the piston(in kJ):\n",
"w=p*(v2-v1)\n",
"#Net Work of the system(in kJ):\n",
"wn=w+Pw\n",
"\n",
"#Results:\n",
"print \"Work done on the piston in kJ: \",w\n",
"print \"Work done on the system in kJ: \",-wn"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done on the piston in kJ: 3.445\n",
"Work done on the system in kJ: 1.435\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, page no. 76"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Variable Declaration: \n",
"#Mass of the gas(in kg):\n",
"m=0.5\n",
"#Initial internal energy(in kJ/kg):\n",
"u1=26.6\n",
"#Final internal energy(in kJ/kg):\n",
"u2=37.8\n",
"\n",
"#Calculation:\n",
"#Heat required(in kJ):\n",
"Q=(u2-u1)*m\n",
"\n",
"#Results: \n",
"print \"Heat required (kJ): \",Q"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat required (kJ): 5.6\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, page no. 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Variable Declaration: \n",
"#Mass flow rate(in kg/hr):\n",
"m=50\n",
"#Initial temp(in C):\n",
"t1=800\n",
"#Final temp(in C):\n",
"t2=50\n",
"#Heat capacity at const pressure(in kJ/kg.K):\n",
"Cp=1.08\n",
"\n",
"#Calculation:\n",
"#Heat to be removed(in kJ/hr):\n",
"Q=m*Cp*(t2-t1)\n",
"\n",
"#Results: \n",
"print \"Heat should be removed at (kJ/hr): \",-Q"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat should be removed at (kJ/hr): 40500.0\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, page no. 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Variable Declaration: \n",
"#Volume of the cylinnder(in m**3):\n",
"v=0.78\n",
"#Atmospheric pressure(in kPa):\n",
"p=101.325\n",
"\n",
"#Calculation:\n",
"#Work done(in kJ):\n",
"w=round(p*v,2)\n",
"\n",
"#Results: \n",
"print \"Work done by air (KJ): \",-w\n",
"print \"Work done by surroundings (KJ): \",w"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done by air (KJ): -79.03\n",
"Work done by surroundings (KJ): 79.03\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, page no. 77"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"#Mass of the gas(in kg):\n",
"m=5\n",
"#Value of n in P*(V**n)=const:\n",
"n=1.3\n",
"#Initial pressure(in MPa):\n",
"p1=1\n",
"#Initial volume(in m**3):\n",
"v1=0.5\n",
"#Final pressure(in MPa):\n",
"p2=0.5\n",
"\n",
"#Calculation:\n",
"#Final volume(in m**3):\n",
"v2=round(v1*((p1/p2)**(1/n)),3)\n",
"#Work done(in kJ):\n",
"w=(p2*v2-p1*v1)*10**3/(1-n)\n",
"#Change in internal energy(in kJ/kg):\n",
"du=1.8*(p2*v2-p1*v1)*10**3\n",
"#Heat interaction(in kJ):\n",
"Q=du+w\n",
"\n",
"#Results: \n",
"print \"Heat interaction (kJ): \",round(Q,1)\n",
"print \"Work interaction (kJ): \",round(w,1)\n",
"print \"Change in internal energy (kJ): \",round(du,1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat interaction (kJ): 113.5\n",
"Work interaction (kJ): 246.7\n",
"Change in internal energy (kJ): -133.2\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6, page no. 78"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"#Initial pressure(in MPa):\n",
"p1=1.0\n",
"#Final pressure(in MPa):\n",
"p2=2.0\n",
"#Initial volume(in m**3):\n",
"v1=0.05\n",
"#Value of n:\n",
"n=1.4\n",
"\n",
"#Calculation:\n",
"#Final volume(in m**3):\n",
"v2=round(v1*((p1/p2)**(1/n)),2)\n",
"\n",
"#Change in internal energy(in kJ/kg):\n",
"du=7.5*(p2*v2-p1*v1)*10**3\n",
"#Work done(in kJ):\n",
"w=(p2*v2-p1*v1)*10**3/(1-n)\n",
"#Heat interaction(in kJ):\n",
"Q=du+w\n",
"\n",
"#Results: \n",
"print \"Heat interaction (kJ): \",Q\n",
"print \"Work interaction (kJ): \",w\n",
"print \"Change in internal energy (kJ): \",du\n",
"\n",
"#If 180 kJ heat transfer takes place:\n",
"#Work done(in kJ):\n",
"w2=180-du\n",
"print \"New work (kJ): \",w2"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat interaction (kJ): 50.0\n",
"Work interaction (kJ): -25.0\n",
"Change in internal energy (kJ): 75.0\n",
"New work (kJ): 105.0\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7, page no. 79"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration:\n",
"#Universal Gas Constant (in KJ.mol/Kg.K):\n",
"r=8.3143\n",
"#Molecular weight of perfect gas:\n",
"M=16\n",
"#Molar specific heat at constant pressure for perfect gas(KJ/Kg.K):\n",
"Cp=1.7\n",
"#Initial pressure (Kpa):\n",
"p1=101.3\n",
"#Final pressure (Kpa):\n",
"p2 = 600\n",
"#Initial tempreture (K):\n",
"T1 = 273+20\n",
"#Polytripic index from PV^1.3 = const\n",
"n = 1.3\n",
"\n",
"#Calculations:\n",
"#Characterstic Gas Constant (KJ/Kg.K):\n",
"R=r/M\n",
"#Molar specific heat at constant volume for perfect gas(KJ/Kg.K):\n",
"Cv=Cp-R\n",
"#Specific heat ratio:\n",
"y = Cp/Cv\n",
"#Final Tempreture (K):\n",
"T2 = T1*(p2/p1)**((n-1)/n)\n",
"#Polytropic work (KJ/Kg):\n",
"W = R*(T1-T2)/(n-1)\n",
"#Polytropic process heat (KJ/Kg):\n",
"Q = W*(y-n)/(y-1)\n",
"\n",
"#Results:\n",
"print \"Heat transfered (KJ/Kg): \",round(Q,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat transfered (KJ/Kg): -82.06\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8, page no. 80"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math as m\n",
"\n",
"#Variable Declaration: \n",
"#Initial temperature(in K):\n",
"t1=627+273\n",
"#Final temperature(in K):\n",
"t2=27+273\n",
"#Specific heat at const pressure(in kJ/kg.K):\n",
"Cp=1.005\n",
"\n",
"#Calculation\n",
"#Exit velocity(in m/s):\n",
"c2=m.sqrt(2*Cp*10**3*(t1-t2))\n",
"\n",
"#Results: \n",
"print \"Exit Velocity (m/s): \" ,round(c2,1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Exit Velocity (m/s): 1098.2\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9, page no. 80"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"#Work interaction(in kJ):\n",
"w=-200\n",
"#Increase in enthalpy(in kJ/kg):\n",
"dh=100\n",
"#Heat picked up by the cooling water(in kJ/kg):\n",
"qc=-90\n",
"\n",
"#Calculation:\n",
"#Heat flow(in kJ/kg):\n",
"Q=dh+w\n",
"#Heat transferred to atmosphere(in kJ/kg):\n",
"Qa=Q-qc\n",
"\n",
"#Results: \n",
"print \"Heat transferred to atmosphere (kJ/kg): \",Qa"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat transferred to atmosphere (kJ/kg): -10\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10, page no. 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"#Variable Declaration: \n",
"c=500 #Seating capacity:\n",
"q=50 #Heat requirement per person(in kcal/hr):\n",
"h1=80 #Enthalpy of water entering the pipe(in kcal/kg):\n",
"h2=45 #Enthalpy of water leaving the pipe(in kcal/kg):\n",
"z=10 #Difference in elevation of inlet and exit pipe(in m):\n",
"g=9.81 #Acceleration due to gravity(in m/s**2):\n",
"\n",
"#Calculation:\n",
"Q=c*q #Heat to be supplied(in kcal/hr):\n",
"Ql=-Q #Heat lost by water(in kcal/kg):\n",
"m=(Ql*10**3*4.18)/(g*z+(h2-h1)*10**3*4.18) #Quantity of water circulated(in kg/hr):\n",
"\n",
"\n",
"#Results: \n",
"print \"Water circulation rate (kg/min):\",round(m/60,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Water circulation rate (kg/min): 11.91\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11, page no. 81"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"h1=720.0 #Enthalpy of steam entering the injector(in kcal/kg):\n",
"h2=24.6 #Enthalpy of water entering(in kcal/kg):\n",
"h3=100.0 #Enthalpy of water and steam mixture leaving the injector(in kcal/kg):\n",
"z=2.0 #Depth of water injector from steam injector(in m):\n",
"v1=50.0 #Velocity of steam entering the injector(in m/s):\n",
"v3=25.0 #Velocity of mixture leaving the injector(in m/s):\n",
"q=12.0 #Heat loss from injector to surroundings(in kcal/kg):\n",
"g=9.8 #Acceleration due to gravity (m/s^2):\n",
"\n",
"\n",
"#Calculation:\n",
"m=(((v3**2)/2+h3*10**3*4.18)-(h2*10**3*4.18+g*z))/(((v1**2)/2+h1*10**3*4.18)-((v3**2)/2+h3*10**3*4.18)-(q*10**3*4.18))\n",
"\n",
"#Results: \n",
"print \"Steam supply rate (kg/s): \",round(m,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Steam supply rate (kg/s): 0.124\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12, page no. 82"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"#Variable Declaration: \n",
"p=1.013 #Atmospheric pressure(in bar):\n",
"v=0.4 #Volume to which the baloon is inflated(in m**3):\n",
"w1=0 #Work done by cylinder(in kJ):\n",
"\n",
"#Calculation:\n",
"w2=p*10**5*v #Work done by the balloon(in kJ):\n",
"w=w1+w2 #Total work(in kJ):\n",
"\n",
"\n",
"#Results: \n",
"print \"Work done by the system upon atmoshere (KJ): \",w/(10**3)\n",
"print \"Work done by the atmoshere (KJ): \",-w/(10**3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done by the system upon atmoshere (KJ): 40.52\n",
"Work done by the atmoshere (KJ): -40.52\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 13, page no. 82"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"Qa=5000 #Heat added(in J/s):\n",
"\n",
"#Calculation:\n",
"Wt=0.25*Qa #Turbine work(in J/s):\n",
"Qr=0.75*Qa #Heat rejected(in J/s):\n",
"Wp=0.002*Qa #Work by feed pump(in J/s):\n",
"C=Wt-Wp #Capacity of generator(in W):\n",
"\n",
"#Results: \n",
"print \"Capacity of generator (KW): \",C/(10**3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacity of generator (KW): 1.24\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14, page no. 83"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math as m\n",
"\n",
"#Variable Declaration: \n",
"T1=27+273 #Ambient temperature(in K):\n",
"T2=750+273 #Temperature of air inside heat exchanger(in K):\n",
"T3=600+273 #Temperature of air leaving turbine(in K):\n",
"T4=500+273 #Temperature of air leaving turbine(in K):\n",
"c2=50 #Velocity of air entering turbine(in m/s):\n",
"c3=60 #Velocity of air entering the nozzle(in m/s):\n",
"Cp=1.005#Specific heat at constant pressure(in kj?kg.K):\n",
"\n",
"\n",
"#Calculation:\n",
"Q12=Cp*(T2-T1) #Heat transfer to air in heat exchanger(in kJ):\n",
"Wt=Cp*(T2-T3)+(c2**2-c3**2)*10**(-3)/2 #Power output from turbine(in kJ/s):\n",
"c4=m.sqrt(2*(Cp*(T3-T4)+(c3**2)*10**(-3)/2))#Velocity at exit of the nozzle(in m/s):\n",
"\n",
"#Results: \n",
"print \"Heat transfer to air in heat exchanger (KJ): \",round(Q12,2)\n",
"print \"Power output from turbine (KJ/s): \",Wt\n",
"print \"Velocity at exit of the nozzle (m/s): \",round(c4,1)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat transfer to air in heat exchanger (KJ): 726.61\n",
"Power output from turbine (KJ/s): 150.2\n",
"Velocity at exit of the nozzle (m/s): 14.3\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 15, page no. 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math as m\n",
"\n",
"#Variable Declaration: \n",
"p1=0.5 #Initial pressure(in MPa):\n",
"T1=400 #Initial temperature(in K):\n",
"r1=2 #Ratio of v2 to v1:\n",
"r2=6 #Ratio of v3 to v1:\n",
"R=8.314 #Universal gas constant(in kJ/kg):\n",
"\n",
"#Calculation:\n",
"Wa=R*T1 #Work from state 1 to 2(in kJ):\n",
"T2=2*T1 #Temperature at point 2(in K):\n",
"Wb=R*T2*m.log(r2/r1) #Work done from state 2 to 3(in kJ):\n",
"W=Wa+Wb#Total work done by air(in kJ):\n",
"\n",
"#Results: \n",
"print \"Work done (KJ): \",round(W,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done (KJ): 10632.69\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16, page no. 85"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"pi=0.5*10**6 #Initial pressure(in Pa):\n",
"vi=0.5 #Initial volume(in m**3):\n",
"pf=1*10**6 #Final pressure(in Pa):\n",
"patm=1.013*10**5 #Atmospheric pressure(in Pa):\n",
"\n",
"#Calculation:\n",
"vf=3*vi #Final volume(in m**3):\n",
"W=(vf-vi)*(pi+pf)/2 #Work done(in J):\n",
"\n",
"#Results: \n",
"print \"Work done (MJ): \",W/10**6"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work done (MJ): 0.75\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17, page no. 87"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"p1=0.5*10**6 #Initial pressure(in Pa):\n",
"pf=1*10**6 #Final pressure(in Pa):\n",
"v1=0.5 #Initial volume(in m**3):\n",
"v2=0.25 #Final volume(in m**3):\n",
"vN2=0.75#Final Nitrogen volume(in m**3):\n",
"T1=273+27#Initial Tempereature (K):\n",
"patm=1.013*10**5 #Atmospheric pressure(in Pa):\n",
"CpH2=14.307 #Cp of hydrogen (KJ/Kg)\n",
"CpN2=1.039 #Cp of hydrogen (KJ/Kg)\n",
"RN2=0.2968\n",
"RH2=4.1240 \n",
"\n",
"#Calculations:\n",
"rH2=CpH2/(CpH2-RH2) #Adiabatic index of compression for H2:\n",
"rN2=CpN2/(CpN2-RN2) #Adiabatic index of compression for N2:\n",
"p2=p1*(v1/v2)**rH2 #Final pressure of hydrogen(in Pa):\n",
"Pw=0 #Partition work:\n",
"WH2=(p1*v1-p2*v2)/(rH2-1) #Work done upon H2(in J):\n",
"WN2=-WH2 #Work done by nitrogen(in J):\n",
"mN2=round(p1*v1/(RN2*10**3*T1),1) #Mass of N2(in kg):\n",
"T2=p2*vN2*T1/(p1*v1) #Final temperature of N2(in K):\n",
"CvN2=CpN2-RN2 #Cv of N2(in kJ/kg):\n",
"QN2=mN2*CvN2*10**3*(T2-T1)+WN2 #Heat added to N2(in kJ):\n",
"\n",
"#Results: \n",
"print \"Final pressure of hydrogen (MPa): \",round(p2/(10**6),3)\n",
"print \"Partition work (KJ): \",Pw\n",
"print \"Work done by hyrogen (10^5 J): \",round(WH2/10**5)\n",
"print \"Work done by nitrogen (10^5 J): \",round(WN2/10**5)\n",
"print \"Heat added to nitrogen (kJ): \",round(QN2/(10**3),2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final pressure of hydrogen (MPa): 1.324\n",
"Partition work (KJ): 0\n",
"Work done by hyrogen (10^5 J): -2.0\n",
"Work done by nitrogen (10^5 J): 2.0\n",
"Heat added to nitrogen (kJ): 2053.09\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 18, page no. 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"v1=2 #Volume of the cylinder(in m**3):\n",
"p1=0.5*10**6 #Pressure in the cylinder(in Pa):\n",
"T1=375 #Temperature of the cylinder(in K):\n",
"Cp=1.003 #Specific heat at const pressure(in kJ/kg.K):\n",
"Cv=0.716 #Specific heat at const volume(in kJ/kg.K):\n",
"Ra=0.287 #Gas constant for air(in kJ/kg.K):\n",
"patm=1.013*10**5 #Atmospheric pressure(in Pa):\n",
"r=1.4 #Compression ratio:\n",
"\n",
"#Calculation:\n",
"m1=p1*v1/(Ra*T1) #Initial mass of air(in kg):\n",
"T2=T1*(patm/p1)**((r-1)/r) #Final temperature(in K):\n",
"m2=patm*v1/(Ra*T2) #Final mass of air left in tank(in kg):\n",
"KE=m1*Cv*T1-m2*Cv*T2-(m1-m2)*Cp*T2 #Kinetic energy available(in kJ):\n",
"\n",
"#Results: \n",
"print \"Amount of work available (KJ): \",round(KE/10**3,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Amount of work available (KJ): 482.67\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19, page no. 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"p1=0.5*10**6 #Pressure in the vessel(in Pa):\n",
"v1=0.5 #Volume of 1st chamber(in m**3):\n",
"T1=300 #Temperature in the vessel(in K):\n",
"p2=10**6 #Final pressure(in Pa):\n",
"v2=0.5 #Volume of 2nd chamber(in m**3):\n",
"T2=500 #Final temperature(in K):\n",
"R=8314 #Universal gas constant(in J/kg.K):\n",
"\n",
"#Calculation:\n",
"n1=p1*v1/(R*T1) #Moles in chamber 1:\n",
"n2=p2*v2/(R*T2) #Moles in chamber 2:\n",
"T3=(n1*T1+n2*T2)/(n1+n2) #Temperature of the mixture(in K):\n",
"p3=(n1+n2)*R*T3/(v1+v2) #Final pressure(in MPa):\n",
"\n",
"\n",
"#Results: \n",
"print \"Final pressure (MPa): \",p3/(10**6)\n",
"print \"Final temperature (K): \",round(T3,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Final pressure (MPa): 0.75\n",
"Final temperature (K): 409.09\n"
]
}
],
"prompt_number": 20
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 20, page no. 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"\n",
"#Variable Declaration: \n",
"v=0.5 #Volume of the bottle(in m**3):\n",
"p=1.0135 #Pressure in the bottle(in Bar):\n",
"\n",
"#Calculation:\n",
"W=p*10**5*(0-v) #Displacement work(in N-m):\n",
"Q=-W #Heat transfer(in N-m):\n",
"\n",
"#Results: \n",
"print \"Heat transferred (N-m): \",Q"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat transferred (N-m): 50675.0\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21, page no. 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"v1=0.3 #Volume of bottle(in m**3):\n",
"p1=35.0 #Pressure in the bottle(in bar):\n",
"T1=40.0+273.0 #Temperature in the bottle(in K):\n",
"w1=5.0 #Turbo generator's actual output(in kJ/s):\n",
"p2=1.0 #Final prssure(in bar):\n",
"v2=v1 #Final volume(in m**3):\n",
"Ra=0.287 #Gas constant for air(in kJ/kg.K):\n",
"r=1.4 #Compression ratio:\n",
"Cv=0.718 #Specific heat at const volume(in kJ/kg):\n",
"Cp=1.005 #Specific heat at const pressure(in kJ/kg):\n",
"\n",
"#Calculation:\n",
"T2=T1*(p2/p1)**((r-1)/r) #Final temperature(in K):\n",
"m1=p1*10**2*v1/(Ra*T1) #Initial mass in the bottle(in kg):\n",
"m2=p2*10**2*v2/(Ra*T2) #Final mass in the bottle(in kg):\n",
"W=(m1*Cv*T1-m2*Cv*T2)-(m1-m2)*Cp*T2 #Maximum work that can be obtained(in kJ):\n",
"i=w1/0.6 #Input to the turbo generator(in kJ/s):\n",
"t=W/round(i,2) #Time duration(in s):\n",
"\n",
"#Results: \n",
"print \"Duration (Seconds): \",round(t,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Duration (Seconds): 159.11\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 22, page no. 91"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math as M\n",
"#Variable Declaration: \n",
"p1=1.5 #Pressure at state 1(in bar):\n",
"T1=77+273 #Temperature at state 1(in K):\n",
"p2=7.5 #Pressure at state 2(in bar):\n",
"m=3 #Mass of the air(in kg):\n",
"n=1.2 #Value of n:\n",
"Ra=0.287 \n",
"\n",
"#Calculation:\n",
"T2=T1*(p2/p1)**((n-1)/n) #Temperature at state 2(in K):\n",
"v1=m*Ra*T1/(p1*10**2) #Initial volume(in m**3):\n",
"v2=(p1*(v1**n)/p2)**(1/n) #Volume at state 2(in m**3):\n",
"T3=T1 #Temperature at state 3(in K):\n",
"v3=v2*T3/T2 #Volume at state 3(in m**3):\n",
"p3=7.5 #Pressure at state 3(in bar):\n",
"W12=m*Ra*(T2-T1)/(1-n) #Compression work during process 1-2(in kJ):\n",
"W23=p2*(10**2)*(v3-v2) #Work during process 2-3(in kJ):\n",
"W31=p3*10**2*v3*M.log(v1/v3) #Work during process 3-1(in kJ):\n",
"Wn=W12+W23+W31 #Net work(in kJ):\n",
"\n",
"#Results: \n",
"print \"Heat transferred from the system (kJ): \",round(-Wn,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Heat transferred from the system (kJ): 71.28\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 23, page no. 93"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#Variable Declaration: \n",
"v1=0.15 #Volume of air bottle(in m**3):\n",
"p1=40 #Initial pressure(in bar):\n",
"T1=27+273 #Initial temperature(in K):\n",
"p2=2.0 #Final presure(in bar):\n",
"Ra=0.287 #Gas constant for air(in kJ/kg):\n",
"Cp=1.005 #Specific heat at const pressure(in kJ/kg):\n",
"Cv=0.718 #Specific heat at const volume(in kJ/kg):\n",
"r=1.4 #Compression ratio:\n",
"\n",
"#Calculation:\n",
"v2=v1 #Final volume(in m**3):\n",
"m1=p1*10**2*v1/(Ra*T1) #Initial mass of air in bottle(in kg):\n",
"T2=T1*(p2/p1)**((r-1)/r) #Final temperature(in K):\n",
"m2=p2*10**2*v2/(Ra*T2) #Final mass of air in bottle(in kg):\n",
"E=m1*Cv*T1-m2*Cv*T2-(m1-m2)*Cp*T2 #Energy available for running of turbine due to emptying of bottle(in kJ):\n",
"\n",
"#Results: \n",
"print \"Work available from turbine(KJ):\",round(E,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Work available from turbine(KJ): 638.33\n"
]
}
],
"prompt_number": 24
}
],
"metadata": {}
}
]
}