Lab 6 Black Body Radiation and Stefan-Boltzmann Law.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 6: Black Body Radiation and Stefan-Boltzmann Law"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Physics 202\n",
    "\n",
    "Shreya Parjan + Alex G.\n",
    "\n",
    "10/22/18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "import scipy.optimize\n",
    "import math as m\n",
    "%matplotlib inline\n",
    "import scipy.interpolate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The array of experimentally determined resistances is: \n",
      "[ 8.62068966  7.92079208  8.20895522  9.52380952 10.71428571 10.89108911\n",
      " 11.25541126 12.15686275 13.18681319 13.88888889 15.         12.78772379\n",
      " 13.59223301 14.21911422 14.86486486 15.40130152 15.96638655 16.56565657\n",
      " 17.02544031 17.58034026 18.16513761 18.24817518 20.66772655 22.56699577\n",
      " 24.42159383 26.12826603 27.59381898 28.92561983 30.42198234 31.71641791\n",
      " 32.88888889 34.04255319 36.86635945 39.52011291 41.85742315 44.14469651\n",
      " 46.2962963  48.298573   50.23547881 52.05205205 53.82027871 55.50416281\n",
      " 57.21949039 58.84898312 60.42803189 61.70300288 62.52570958 65.07413509\n",
      " 66.44655386 67.82464847 69.29460581 70.83333333 72.96499367 75.43934848]\n",
      "The interpolated temps are: \n",
      "[ 320.88051078  300.          308.60343716  347.72431877  382.86267211\n",
      "  388.05138299  398.71523394  424.92099995  454.49902578  474.40448887\n",
      "  505.41994731  443.08816063  466.02086477  483.68758155  501.68201903\n",
      "  516.46254251  531.86506934  548.01061563  560.26561761  574.90172745\n",
      "  590.14295354  592.29178103  653.43920237  700.25204556  745.7770729\n",
      "  787.5819464   823.36312282  855.74217556  891.91506272  922.99376046\n",
      "  950.99468356  978.45132527 1045.48081834 1108.2869856  1163.29742741\n",
      " 1216.51908741 1266.01486126 1311.98691822 1356.52400522 1398.06714124\n",
      " 1438.06887654 1475.87606983 1514.30247946 1550.79708574 1586.07553623\n",
      " 1614.44108991 1632.67722459 1688.86515167 1718.96039305 1749.07604752\n",
      " 1781.08662012 1814.47342656 1860.56543425 1913.97350894]\n",
      "The power radiated by the filament is: \n",
      "[2.90000e-04 8.08000e-04 1.47400e-03 2.05800e-03 3.02400e-03 4.44400e-03\n",
      " 6.00600e-03 7.90500e-03 9.82800e-03 1.15200e-02 1.35000e-02 1.95500e-02\n",
      " 2.30720e-02 2.61690e-02 2.93040e-02 3.27310e-02 3.61760e-02 4.05900e-02\n",
      " 4.44570e-02 4.91970e-02 5.39550e-02 5.48000e-02 8.17700e-02 1.13440e-01\n",
      " 1.47820e-01 1.85240e-01 2.26500e-01 2.71040e-01 3.15890e-01 3.64480e-01\n",
      " 4.16250e-01 4.70000e-01 6.24960e-01 7.93520e-01 9.78560e-01 1.17432e+00\n",
      " 1.38240e+00 1.60336e+00 1.83456e+00 2.07792e+00 2.33072e+00 2.59440e+00\n",
      " 2.86336e+00 3.14296e+00 3.43152e+00 3.64650e+00 3.69512e+00 3.83624e+00\n",
      " 3.90103e+00 3.96552e+00 4.02470e+00 4.08000e+00 4.10183e+00 4.10608e+00]\n"
     ]
    }
   ],
   "source": [
    "#calculate array of resistances\n",
    "data = np.loadtxt('TungstenExperimental.txt')\n",
    "V = data[:,0] #volts\n",
    "I = data[:,1] #amps\n",
    "R = V/I\n",
    "print(\"The array of experimentally determined resistances is: \")\n",
    "print(R)\n",
    "\n",
    "#determine temps of tungsten filaments\n",
    "data = np.loadtxt('Tungsten.txt')\n",
    "rho = data[:,0] #rho\n",
    "t = data[:,1] #kelvin\n",
    "#our equation is R/Rmin = rho/rho[0]\n",
    "rhoMin = data[0,0]\n",
    "rhoNorm = rho/rhoMin\n",
    "Rnorm = R/R.min()\n",
    "\n",
    "from scipy.interpolate import interp1d #interpolate in 1 dimension\n",
    "func = interp1d(rhoNorm, t, kind = 'cubic')\n",
    "interpolatedTemps = func(Rnorm)\n",
    "print(\"The interpolated temps are: \")\n",
    "print(interpolatedTemps)\n",
    "\n",
    "#find power radiated by tungsten filament (equation: P = IV)\n",
    "P = I*V #watts\n",
    "print(\"The power radiated by the filament is: \")\n",
    "print(P)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y-intercept =  249.4350536493489\n",
      "slope =  169.2056220126674\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#REPLICATION OF GRAPH FROM HANDOUT FIGURE 1\n",
    "fig = plt.figure(figsize=(15,10))\n",
    "plt.grid(True)\n",
    "def straight_line_model(x, A, B):\n",
    "    return A + B * x\n",
    "\n",
    "popt, pcov = scipy.optimize.curve_fit(straight_line_model, rhoNorm, t)\n",
    "yIntercept = popt[0]\n",
    "slope = popt[1]\n",
    "print('y-intercept = ',yIntercept)\n",
    "print('slope = ',slope)\n",
    "\n",
    "rhoNorm_for_plot = np.linspace(rhoNorm.min(), rhoNorm.max(), 50)\n",
    "best_fit_line = straight_line_model(rhoNorm_for_plot, popt[0], popt[1])\n",
    "\n",
    "#calculates uncertainties for both variables\n",
    "popt_uncertainties = np.sqrt(np.diag(pcov)) # get the diagonal elements then take sqrt\n",
    "\n",
    "plt.plot(rhoNorm, t, 'bo') #without '-' after bo, plots points alone\n",
    "\n",
    "plt.xlabel('Tungsten Resistivity Normalized to 300K') # label the x-axis\n",
    "plt.ylabel('Temperature (K)', size=12) # label the y-axis\n",
    "\n",
    "plt.title('Temperature vs. Normalized Resistivity of Tungsten') # title\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Log of pPower (W)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.log(interpolatedTemps), np.log(P), 'bo')\n",
    "plt.title ('Log of Power vs. Log of Interpolated Temperatures')\n",
    "plt.xlabel ('Log of Interpolated Temperature (K)')\n",
    "plt.ylabel ('Log of pPower (W)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y-intercept =  -29.389922546348007\n",
      "slope =  4.157435710706198\n",
      "[0.10226572 0.01511838]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "popt, pcov = scipy.optimize.curve_fit(straight_line_model, (np.log(interpolatedTemps))[11:45], (np.log(P))[11:45])\n",
    "yIntercept2 = popt[0]\n",
    "slope2 = popt[1]\n",
    "print('y-intercept = ',yIntercept2)\n",
    "print('slope = ',slope2)\n",
    "\n",
    "lntemps_for_plot = np.linspace(6, 7.5, 50)\n",
    "best_fit_line = straight_line_model(lntemps_for_plot, popt[0], popt[1])\n",
    "\n",
    "plt.plot((np.log(interpolatedTemps))[11:45], (np.log(P))[11:45], 'bo')\n",
    "plt.plot(lntemps_for_plot, best_fit_line, 'b')\n",
    "plt.title ('Log of Interpolated Temps vs. Log of Power for Restricted Data')\n",
    "plt.xlabel ('Log of Interpolated Temperature (K)')\n",
    "plt.ylabel ('Log of pPower (W)')\n",
    "popt_uncertainties2 = np.sqrt(np.diag(pcov))\n",
    "print(popt_uncertainties2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The slope is 4.16 +/- 0.02 which is slightly off from the expected value of 4."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of D 59.125\n",
      "Mean of d 3.1333333333333334e-05\n",
      "Mean of N 0.00017987500000000002\n"
     ]
    }
   ],
   "source": [
    "D = np.array([0.264, 0.138, 0.231, 0.215,0.139,0.153,0.152, 0.147])\n",
    "D = D*0.001\n",
    "d = np.array([.021,.052,.029,.048,0.021,.048, .021,.017,.025])\n",
    "d = d*0.001\n",
    "N = np.array([60,61,65,57,52,58,63,57])\n",
    "\n",
    "meanN = np.mean(D)\n",
    "meand = np.mean(d)\n",
    "meanD = np.mean(N)\n",
    "\n",
    "print ('Mean of D', meanD)\n",
    "print ('Mean of d', meand)\n",
    "print ('Mean of N', meanN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "surface area =  3.2888820985317563e-06\n"
     ]
    }
   ],
   "source": [
    "SA = meanD*meand*meanN*(np.pi**2)\n",
    "print('surface area = ', SA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "emissivity =  0.9236074996390992  which is significantly smaller than the accepted value but is still between 0 and 1\n"
     ]
    }
   ],
   "source": [
    "sigma = 5.67e-8 #W/m2K4\n",
    "E = np.exp(popt[0])/(sigma*SA)\n",
    "print(\"emissivity = \", E,\" which is between 0 and 1, as it should be\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At low temps:\n",
    "\n",
    "1. By the Stefan Boltzmann law, the black body's temperature should be low because a low power is radiated and temperature and power are directly proportional.\n",
    "\n",
    "2. The temperature should equal room temp without any power. The equation should be modified to include a change in temperature from room temperature variable, delta T, in place of just temperature so that delta T = 0 when power is 0. Similarly, the power should be modified to a delta power because the filament radiates power even at room temperature.\n",
    "\n",
    "3. Heat loss due to conduction means that power is also being conducted away. This would result in falsely inflated interpolated temperatures. The values for epsilon would thus be higher than expected.\n",
    "\n",
    "4. Heat loss due to conduction has more of an impact at lower temperatures when the filament is not completely heated. Because the filmament heats up from the middle, it conducts at the middle more than it radiates so loss due to conduction has more of an impact.\n",
    "\n",
    "\n",
    "At high temps:\n",
    "\n",
    "1. Because the area of the filament decreases at higher temperatures, the temperature would need to increase to satisfy our equation. The power levels off as the filament disintegrates, according to our results. Power is near constant because resistance and voltage increase while current decreases. This results in low values of power, as evidenced by the graph.\n",
    "\n",
    "2. We assumed that the length/area of the filament are unchanged at higher temperatures but we know that the area decreases as the filament breaks down at higher temperatures, so we cannot neglect the change in dimension of the filament. "
   ]
  }
 ],
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