01-handling_numbers.ipynb

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   "source": [
    "# Handling Numbers"
   ]
  },
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   "source": [
    "## Information\n",
    "Taylor, *An Introduction to Error Analysis*, Ch 1, 2\n",
    "\n",
    "Some of these questions do not have a right or wrong answer, but all require a justification."
   ]
  },
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   "source": [
    "\n",
    "1) Below are listed physical properties that have been measured by an experienced scientist who gives us no explicit indication of the uncertainty in each measurement.  Estimate a reasonable range of values for each measurement, using Taylor's notation (sec 1.5, 1.6, 2.1).\n",
    "\n",
    "mass of crystal = 1.64 g\n",
    "\n",
    "boiling point = 169.1$^\\circ$C\n",
    "\n",
    "height of GC peak = 8.3 inches\n",
    " \n",
    "Explain any assumptions you make about the instruments or method of the measurement."
   ]
  },
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    "2) Criticize the following ways of reporting an experimental result (Taylor, 2.2).  Rewrite each in a more acceptable form.\n",
    "\n",
    "a) Our measurements determined R to be $8.3 \\pm 0.1168$ J/(K$\\cdot$mol) \n",
    "\n",
    "b) Our measurements determined R to be $8.31478 \\pm 0.1$\n",
    "    J/(K$\\cdot$mol)\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "3) Mary and Joe measured R in the lab with the following results: \n",
    "\n",
    "Mary's R:  $8.3 \\pm 0.2$ J/(K$\\cdot$mol)\n",
    "\n",
    "Joe's R: $8.5 \\pm 0.2$    J/(K$\\cdot$mol)\n",
    "\n",
    "Would you judge the discrepancy in their results *significant* or *insignificant*? Explain. (Taylor 2.3)"
   ]
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   "source": [
    "4) When Mg metal is treated with HCl to generate dihydrogen gas, the ideal gas law predicts\n",
    "\n",
    "$$ V_{\\text{H}_2}=\\frac{RT}{\\text{AW}_{\\text{Mg}} P}\\;\n",
    "  \\text{g}_{_{\\text{Mg}}}$$\n",
    "\n",
    "Do the data listed below verify the relation between $V_{\\text{H}_2}$ and $\\text{g}_{_{\\text{Mg}}}$?  Use a graphical or ratio argument to support your answer. \\marginlabel{Taylor: 2.6} You may wish to include estimated uncertainties in your account.\n"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [],
   "source": [
    "V_H2 = np.array([\n",
    "12.7, 14.0, 15.2, 16.5, 17.8, 19.0])\n",
    "\n",
    "g_Mg = np.array([\n",
    "0.0101, 0.0110, 0.0120, 0.0129, 0.0140, 0.0150])"
   ]
  },
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KTFXVnUkOAS8E/qZ/mk9U1fWLnNtXK0jL8NUK0vqxmlcrrOiljEleB3wjcHdV/Z8V9nda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\nHEiSpIbhQJIkNQwHkiSp8f8BYS5C2OM9VREAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7c6f783cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.ylim(0.008, 0.016)\n",
    "plt.plot(V_H2, g_Mg, 'o', mfc='none')\n",
    "plt.xlabel('g Mg')\n",
    "plt.ylabel(r'$V_{H_2}$')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1257.42574257\n",
      "1272.72727273\n",
      "1266.66666667\n",
      "1279.06976744\n",
      "1271.42857143\n",
      "1266.66666667\n"
     ]
    }
   ],
   "source": [
    "ratios = V_H2 / g_Mg\n",
    "for r in ratios:\n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1268.9974479175492, 6.6588665485425897)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(ratios), np.std(ratios)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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