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{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter14-Thermionic Generation"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14.4.1-pg738"
]
},
{
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"input": [
"##Ex.14.4.1.;Calculate the efficiency of the generator and also compare with the carnot efficiency\n",
"import math\n",
"##cathode work funtion \n",
"flux_c=2.5;##unit=volts\n",
"##anode work funtion \n",
"flux_a=2.;##unit=volts\n",
"##Temp. of cathode\n",
"Tc=2000.;##unit=degree k\n",
"##Temp. of surrounding\n",
"Ts=1000.;##unit=degree k\n",
"##plasma potentail drop\n",
"flux_p=0.1;##unit=volts\n",
"##Net output voltage\n",
"V=flux_c-flux_a-flux_p\n",
"print'%s %.2f %s'%(\" V=\",V,\" volt\");\n",
"##charge of an electron\n",
"e=1.6*10**-19.;##unit=coulomb\n",
"##boltzmann constant\n",
"k=1.38*10**-23.;##unit=joule/degree kelvin\n",
"A=1.20*10**6;\n",
"##one electron volt=1.6*10**-19 joule\n",
"##The net current in the generator J=J_cathode-J_anode\n",
"##let EC=e**(-flux_c/k*Tc)\n",
"EC=math.e**(-(1.6*10**-19*flux_c)/(k*Tc));\n",
"J_cathode=A*(Tc*Tc)*EC##J_cathode=A*Tc**2*e**(-flux_c/k*Tc)\n",
"print'%s %.2f %s'%(\"\\n J_cathode=\",J_cathode,\" amp/m^2\");\n",
"##let EA=e**(-flux_c/k*Ts)\n",
"EA=math.e**(-(1.6*10**-19*flux_a)/(k*Ts));\n",
"J_anode=A*(Ts**2)*EA;##J_cathode=A*Ts**2*e**(-flux_c/k*Ts)\n",
"print'%s %.2f %s'%(\"\\n J_anode=\",J_anode,\" amp/m^2\");\n",
"##The net current can be taken =Jc,as Ja can be neglected in comparison with Jc\n",
"J=J_cathode;\n",
"print'%s %.2f %s'%(\"\\n J=\",J,\" amp/m^2\");\n",
"##The heat supplied to the cathode Qc/Ac=J(flux_c+((2*k*Tc)/e))+samestion of sigma*(Tc**4-Ts**4)\n",
"##let QA=Qc/Ac; and\n",
"a=2.5+((2*1.38*10**-23*2000.)/(1.6*10**-19));\n",
"b=J*a;\n",
"c=(0.2*5.67*(10**-12.)*(10**-4.)*((2000**4)-(1000**4)));\n",
"##therefore\n",
"QA=b+c; ##since: QA=(J*(2.5+((2*(1.38*10**-23)*2000*)/(1.6*10**-19))))+(0.2*5.67*(10**-12)*(10**-4)*((2000**4)-(1000**4)))\n",
"print'%s %.2f %s'%(\"\\n The heat supplied to the cathode Qc/Ac=\",QA,\" watt/m^2\");\n",
"##efficiency of the generator\n",
"ng=((J*V)/(7.026*10**6))*100.;\n",
"print'%s %.2f %s'%(\"\\n ng=\",ng,\" persent\");\n",
"##carnot efficiency this device\n",
"T1=2000.;\n",
"T2=1000.;\n",
"T=2000.;\n",
"nc=((T1-T2)/T)*100.;\n",
"print'%s %.2f %s'%(\"\\n nc=\",nc,\" persent\");\n",
"\n",
"\n",
"##Value of \"The heat supplied to the cathode Qc/Ac\" is given wrong\n",
"##value of charge e is taken wrong;corrected by giving value 1.6*10**-19\n",
"##value of J anode is differ from calculated value. \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" V= 0.40 volt\n",
"\n",
" J_cathode= 2438475.02 amp/m^2\n",
"\n",
" J_anode= 102.00 amp/m^2\n",
"\n",
" J= 2438475.02 amp/m^2\n",
"\n",
" The heat supplied to the cathode Qc/Ac= 6937461.44 watt/m^2\n",
"\n",
" ng= 13.88 persent\n",
"\n",
" nc= 50.00 persent\n"
]
}
],
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}
],
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}
]
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