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{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Ch-23, Thermal properties & materials"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"example-23.1 page no-681"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"#given\n",
"#length of glass rod and steel rod is equal at 273 K and differ by 1.2 mm at 373 K\n",
"T1=273 #K\n",
"T2=373 #K\n",
"#coefficients of linear expansion af glass and steel are\n",
"alphaG=8*10**-6 #per degree C\n",
"alphaS=12*10**-6 #per degrees C\n",
"#we know that\n",
"#lT2=lT1*(1+alpha(T2-T1))\n",
"#so for glass rod\n",
"#l100G=l0*(1+(alpha1)*(T2-T1))\n",
"#similarly for steel rod\n",
"#l100G=1.0008*l0 ----(1)\n",
"#l100S=lo*(1+(alpha2)*(T2-T1))\n",
"#l100S=1.0012*l0 ----------(2)\n",
"#we have given that\n",
"#l100S-l100G=1.2 mm ---(3)\n",
"#from 1 and 2 put in 3, we get\n",
"#1.0012*l0-1.0008*l0=1.2\n",
"#so\n",
"l0=1.2*10**-3/(0.0012-.0008) #m\n",
"print \" the length of rod at 0 degrees celcius is %.f m\"%(l0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" the length of rod at 0 degrees celcius is 3 m\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"example-23.2 page no-684"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#given\n",
"#coefficient of linear expansion of Cu and steel are\n",
"alphaCu=18*10**-6 #cm/cm/degree C\n",
"alphaSteel=14*10**-6 #cm/cm/degree C\n",
"#young's modulus of elasticity\n",
"ECu=106*10**9 #Pa\n",
"ESteel=200*10**9 #Pa\n",
"#part(a)\n",
"#since alphaCu>alphaSteel\n",
"#so steel will contract less. \n",
"print \" Hence strip will bend in the direction of copper\"\n",
"#part(b)\n",
"#annealing temp\n",
"T2=530 #degrees celcius\n",
"#room temp\n",
"T1=30 #degrees celcius\n",
"#difference in temp\n",
"T=T2-T1 #degrees celcius\n",
"#differnce in values of coefficient of linear expansion\n",
"alpha=alphaCu-alphaSteel #cm/cm/degrees celcius\n",
"#differential contraction\n",
"contraction=T*alpha #cm/cm\n",
"#since the two metals in the strip have equal dimension\n",
"#sigmaCu=sigmaSteel=sigma\n",
"#strain in copper\n",
"#eCu=sigma/Ecu -----(1)\n",
"#strain in steel\n",
"#eSteel=sigma/ESteel ---(2)\n",
"#sum of strains given by equation 1 and 2\n",
"sigma=contraction*ESteel*ECu/(ESteel+ECu)*10**-6 # MPa\n",
"print \" the stresses in each metal is %0.3f MPa\"%(sigma)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" Hence strip will bend in the direction of copper\n",
" the stresses in each metal is 138.562 MPa\n"
]
}
],
"prompt_number": 7
}
],
"metadata": {}
}
]
}
|
