{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Comparació propietats dels metalls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nom</th>\n",
       "      <th>Densitat</th>\n",
       "      <th>Punt de fusió</th>\n",
       "      <th>Conductivitat tèrmica</th>\n",
       "      <th>Dilatació tèrmica</th>\n",
       "      <th>Mòdul elàstic</th>\n",
       "      <th>Límit elàstic</th>\n",
       "      <th>Resistència al trencament</th>\n",
       "      <th>Allargament</th>\n",
       "      <th>Duresa</th>\n",
       "      <th>Resistivitat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cu</td>\n",
       "      <td>8.960</td>\n",
       "      <td>1084.62</td>\n",
       "      <td>401.0</td>\n",
       "      <td>16.5</td>\n",
       "      <td>110</td>\n",
       "      <td>69.00</td>\n",
       "      <td>220.0</td>\n",
       "      <td>45</td>\n",
       "      <td>874.0</td>\n",
       "      <td>16.78</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Al</td>\n",
       "      <td>2.700</td>\n",
       "      <td>660.32</td>\n",
       "      <td>237.0</td>\n",
       "      <td>23.1</td>\n",
       "      <td>70</td>\n",
       "      <td>17.00</td>\n",
       "      <td>55.0</td>\n",
       "      <td>25</td>\n",
       "      <td>245.0</td>\n",
       "      <td>28.20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Mg</td>\n",
       "      <td>1.738</td>\n",
       "      <td>650.00</td>\n",
       "      <td>156.0</td>\n",
       "      <td>24.8</td>\n",
       "      <td>45</td>\n",
       "      <td>41.00</td>\n",
       "      <td>165.0</td>\n",
       "      <td>6</td>\n",
       "      <td>260.0</td>\n",
       "      <td>43.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ti</td>\n",
       "      <td>4.506</td>\n",
       "      <td>1670.00</td>\n",
       "      <td>21.9</td>\n",
       "      <td>8.6</td>\n",
       "      <td>116</td>\n",
       "      <td>240.00</td>\n",
       "      <td>330.0</td>\n",
       "      <td>30</td>\n",
       "      <td>716.0</td>\n",
       "      <td>420.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pb</td>\n",
       "      <td>11.340</td>\n",
       "      <td>327.46</td>\n",
       "      <td>35.3</td>\n",
       "      <td>28.9</td>\n",
       "      <td>16</td>\n",
       "      <td>3.50</td>\n",
       "      <td>19.6</td>\n",
       "      <td>50</td>\n",
       "      <td>38.3</td>\n",
       "      <td>208.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Sn</td>\n",
       "      <td>7.365</td>\n",
       "      <td>231.93</td>\n",
       "      <td>66.8</td>\n",
       "      <td>22.0</td>\n",
       "      <td>50</td>\n",
       "      <td>2.55</td>\n",
       "      <td>34.3</td>\n",
       "      <td>40</td>\n",
       "      <td>350.0</td>\n",
       "      <td>115.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Zn</td>\n",
       "      <td>7.140</td>\n",
       "      <td>419.53</td>\n",
       "      <td>116.0</td>\n",
       "      <td>30.2</td>\n",
       "      <td>108</td>\n",
       "      <td>7.00</td>\n",
       "      <td>117.0</td>\n",
       "      <td>32</td>\n",
       "      <td>412.0</td>\n",
       "      <td>59.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Ni</td>\n",
       "      <td>8.908</td>\n",
       "      <td>1455.00</td>\n",
       "      <td>90.9</td>\n",
       "      <td>13.4</td>\n",
       "      <td>200</td>\n",
       "      <td>138.00</td>\n",
       "      <td>483.0</td>\n",
       "      <td>40</td>\n",
       "      <td>700.0</td>\n",
       "      <td>69.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Fe</td>\n",
       "      <td>7.874</td>\n",
       "      <td>1538.00</td>\n",
       "      <td>80.4</td>\n",
       "      <td>11.8</td>\n",
       "      <td>211</td>\n",
       "      <td>130.00</td>\n",
       "      <td>260.0</td>\n",
       "      <td>45</td>\n",
       "      <td>490.0</td>\n",
       "      <td>96.10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Nom  Densitat  Punt de fusió  Conductivitat tèrmica  Dilatació tèrmica  \\\n",
       "0  Cu     8.960        1084.62                  401.0               16.5   \n",
       "1  Al     2.700         660.32                  237.0               23.1   \n",
       "2  Mg     1.738         650.00                  156.0               24.8   \n",
       "3  Ti     4.506        1670.00                   21.9                8.6   \n",
       "4  Pb    11.340         327.46                   35.3               28.9   \n",
       "5  Sn     7.365         231.93                   66.8               22.0   \n",
       "6  Zn     7.140         419.53                  116.0               30.2   \n",
       "7  Ni     8.908        1455.00                   90.9               13.4   \n",
       "8  Fe     7.874        1538.00                   80.4               11.8   \n",
       "\n",
       "   Mòdul elàstic  Límit elàstic  Resistència al trencament  Allargament  \\\n",
       "0            110          69.00                      220.0           45   \n",
       "1             70          17.00                       55.0           25   \n",
       "2             45          41.00                      165.0            6   \n",
       "3            116         240.00                      330.0           30   \n",
       "4             16           3.50                       19.6           50   \n",
       "5             50           2.55                       34.3           40   \n",
       "6            108           7.00                      117.0           32   \n",
       "7            200         138.00                      483.0           40   \n",
       "8            211         130.00                      260.0           45   \n",
       "\n",
       "   Duresa  Resistivitat  \n",
       "0   874.0         16.78  \n",
       "1   245.0         28.20  \n",
       "2   260.0         43.90  \n",
       "3   716.0        420.00  \n",
       "4    38.3        208.00  \n",
       "5   350.0        115.00  \n",
       "6   412.0         59.00  \n",
       "7   700.0         69.30  \n",
       "8   490.0         96.10  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Dades de la Wikipèdia, excepte Límit elàstic, Resistència al trencament i Allargament.\n",
    "# Buscant una font més fiable que el llibre de McGraw-Hill, està ple d'errades\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'Nom':['Cu','Al','Mg','Ti','Pb','Sn','Zn','Ni','Fe'],\n",
    "# densitat ρ [10³·kg/m³]   \n",
    "    'Densitat':[8.96,2.70,1.738,4.506,11.34,7.365,7.14,8.908,7.874],\n",
    "# punt de fusió [⁰C]    \n",
    "    'Punt de fusió':[1084.62,660.32,650,1670,327.46,231.93,419.53,1455,1538],\n",
    "# conductivitat tèrmica ϰ [W/m·⁰C]    \n",
    "    'Conductivitat tèrmica':[401,237,156,21.9,35.3,66.8,116,90.9,80.4],\n",
    "# Dilatació tèrmica λ [10⁻⁶·K⁻¹]\n",
    "    'Dilatació tèrmica':[16.5,23.1,24.8,8.6,28.9,22,30.2,13.4,11.8],\n",
    "# mòdul elàstic E [GPa]    \n",
    "    'Mòdul elàstic':[110,70,45,116,16,50,108,200,211],\n",
    "# límit elàstic σe [MPa]    \n",
    "    'Límit elàstic':[69,17,41,240,3.5,2.55,7,138,130],\n",
    "# Resistència al trencament R [MPa]    \n",
    "    'Resistència al trencament':[220,55,165,330,19.6,34.3,117,483,260],\n",
    "# Allargament ε [%]    \n",
    "    'Allargament':[45,25,6,30,50,40,32,40,45],\n",
    "# Duresa HB  [MPa]  \n",
    "    'Duresa':[874,245,260,716,38.3,350,412,700,490],\n",
    "# Resistivitat elèctrica [10⁻⁹·Ω·m]    \n",
    "    'Resistivitat':[16.78,28.2,43.9,420,208,115,59,69.3,96.1]\n",
    "})\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Densitat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ρ  [10³·kg/m³]')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Densitat')\n",
    "plt.ylabel('ρ  [10³·kg/m³]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fixeu-vos en la baixa densitat de l'alumni i el magnesi. Els aliatges de l'alumini reben el nom d'*aliatges lleugers*, i els de magnesi d'*aliatges ultralleugers*.   \n",
    "Per altra banda fixeu-vos l'alta densitat del plom. D'aquí el seu ús a projectils, llastres per bussos o plomades."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Temperatura de fusió"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Tf  [⁰C]')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Punt de fusió')\n",
    "plt.ylabel('Tf  [⁰C]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La baixa temperatura de fusió de l'estany i el plom justifiquen el seu ús a soldadures i fusibles. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conductivitat tèrmica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ϰ  [W/m·⁰C]')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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gaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaDYNOwsXLlSLFi3k4eEhDw8PBQcHa926dZb9nTt3lslkslpefvllq2OcO3dOYWFhqlKlinx8fDRu3DjdvHmzvLsCAADslJMtT16rVi3NmjVLjRo1ktls1vLly9WrVy999913euCBByRJw4YNU2xsrOUzVapUsXydl5ensLAw+fn5adeuXUpJSVFERIScnZ01Y8aMcu8PAACwPzYNOz179rRanz59uhYuXKjdu3dbwk6VKlXk5+dX6Oe//vprHT16VJs2bZKvr69atWqladOmacKECXr99dfl4uJS5n0AAAD2zW7m7OTl5WnFihW6du2agoODLds//PBDVa9eXc2bN1dMTIx++eUXy77ExEQFBQXJ19fXsi00NFRZWVk6cuTIbc+Vk5OjrKwsqwUAABiTTUd2JOnQoUMKDg7W9evX5e7urlWrVikwMFCSNGDAANWpU0f+/v46ePCgJkyYoBMnTmjlypWSpNTUVKugI8mynpqaettzzpw5U1OnTi2jHgEAAHti87DTpEkTJScnKzMzU59++qkiIyOVkJCgwMBADR8+3NIuKChINWvWVJcuXXT69Gk1aNDgns8ZExOj6Ohoy3pWVpYCAgJK1A8AAGCfbH4Zy8XFRQ0bNlSbNm00c+ZMtWzZUu+8806hbdu3by9JOnXqlCTJz89PaWlpVm1urd9uno8kubq6Wu4Au7UAAABjsnnY+aP8/Hzl5OQUui85OVmSVLNmTUlScHCwDh06pPT0dEubjRs3ysPDw3IpDAAA/LnZ9DJWTEyMunfvrtq1a+vq1auKj4/X1q1btWHDBp0+fVrx8fHq0aOHqlWrpoMHD2rMmDHq1KmTWrRoIUnq2rWrAgMDNXDgQM2ZM0epqamaOHGioqKi5OrqasuuAQAAO2HTsJOenq6IiAilpKTI09NTLVq00IYNG/Tkk0/q/Pnz2rRpk+bNm6dr164pICBAffv21cSJEy2fd3R01Jo1azRixAgFBwfLzc1NkZGRVs/lAQAAf24ms9lstnURtpaVlSVPT09lZmYWa/5O3dfWlmFVBZ2dFVau5wMAwJ4V9fe33c3ZAQAAKE2EHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGiEHQAAYGg2DTsLFy5UixYt5OHhIQ8PDwUHB2vdunWW/devX1dUVJSqVasmd3d39e3bV2lpaVbHOHfunMLCwlSlShX5+Pho3LhxunnzZnl3BQAA2Cmbhp1atWpp1qxZSkpK0r59+/TEE0+oV69eOnLkiCRpzJgx+vLLL/XJJ58oISFBFy5cUJ8+fSyfz8vLU1hYmG7cuKFdu3Zp+fLlWrZsmSZPnmyrLgEAADtjMpvNZlsX8Xve3t5644039Oyzz6pGjRqKj4/Xs88+K0k6fvy4mjVrpsTERHXo0EHr1q3TU089pQsXLsjX11eStGjRIk2YMEEXL16Ui4tLkc6ZlZUlT09PZWZmysPDo8i11n1tbfE7WAJnZ4WV6/kAALBnRf39bTdzdvLy8rRixQpdu3ZNwcHBSkpKUm5urkJCQixtmjZtqtq1aysxMVGSlJiYqKCgIEvQkaTQ0FBlZWVZRocKk5OTo6ysLKsFAAAYk83DzqFDh+Tu7i5XV1e9/PLLWrVqlQIDA5WamioXFxd5eXlZtff19VVqaqokKTU11Sro3Np/a9/tzJw5U56enpYlICCgdDsFAADshs3DTpMmTZScnKxvv/1WI0aMUGRkpI4ePVqm54yJiVFmZqZlOX/+fJmeDwAA2I6TrQtwcXFRw4YNJUlt2rTR3r179c477+j555/XjRs3lJGRYTW6k5aWJj8/P0mSn5+f9uzZY3W8W3dr3WpTGFdXV7m6upZyTwAAgD2y+cjOH+Xn5ysnJ0dt2rSRs7OzNm/ebNl34sQJnTt3TsHBwZKk4OBgHTp0SOnp6ZY2GzdulIeHhwIDA8u9dgAAYH9sOrITExOj7t27q3bt2rp69ari4+O1detWbdiwQZ6enho6dKiio6Pl7e0tDw8PjRo1SsHBwerQoYMkqWvXrgoMDNTAgQM1Z84cpaamauLEiYqKimLkBgAASLJx2ElPT1dERIRSUlLk6empFi1aaMOGDXryySclSW+//bYcHBzUt29f5eTkKDQ0VO+++67l846OjlqzZo1GjBih4OBgubm5KTIyUrGxsbbqEgAAsDN295wdW+A5OwAAVDwV7jk7AAAAZYGwAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADM2pKI2++OKLYh/4ySefVOXKle/YZubMmVq5cqWOHz+uypUr6+GHH9bs2bPVpEkTS5vOnTsrISHB6nMvvfSSFi1aZFk/d+6cRowYoS1btsjd3V2RkZGaOXOmnJyK1D0AAGBgRUoDvXv3LtZBTSaTTp48qfr169+xXUJCgqKiotSuXTvdvHlTf/vb39S1a1cdPXpUbm5ulnbDhg1TbGysZb1KlSqWr/Py8hQWFiY/Pz/t2rVLKSkpioiIkLOzs2bMmFGsugEAgPEUeegjNTVVPj4+RWpbtWrVIrVbv3691fqyZcvk4+OjpKQkderUybK9SpUq8vPzK/QYX3/9tY4ePapNmzbJ19dXrVq10rRp0zRhwgS9/vrrcnFxKfCZnJwc5eTkWNazsrKKVC8AAKh4ijRnJzIy8q6XpH7vhRdekIeHR7GLyczMlCR5e3tbbf/www9VvXp1NW/eXDExMfrll18s+xITExUUFCRfX1/LttDQUGVlZenIkSOFnmfmzJny9PS0LAEBAcWuFQAAVAxFGtlZunRpsQ66cOHCYheSn5+v0aNHq2PHjmrevLll+4ABA1SnTh35+/vr4MGDmjBhgk6cOKGVK1dK+m3E6fdBR5JlPTU1tdBzxcTEKDo62rKelZVF4AEAwKCKfBkrLy9PR44cUaNGjQqM8vzyyy86deqUmjdvLgeHe7vBKyoqSocPH9aOHTustg8fPtzydVBQkGrWrKkuXbro9OnTatCgwT2dy9XVVa6urvf0WQAAULEUOZn8+9//1pAhQwqdA+Pi4qIhQ4YoPj7+nooYOXKk1qxZoy1btqhWrVp3bNu+fXtJ0qlTpyRJfn5+SktLs2pza/1283wAAMCfR5HDzuLFizV27Fg5OjoW2Ofk5KTx48frn//8Z7FObjabNXLkSK1atUrffPON6tWrd9fPJCcnS5Jq1qwpSQoODtahQ4eUnp5uabNx40Z5eHgoMDCwWPUAAADjKfJlrBMnTqhDhw633d+uXTsdO3asWCePiopSfHy8Pv/8c1WtWtUyx8bT01OVK1fW6dOnFR8frx49eqhatWo6ePCgxowZo06dOqlFixaSpK5duyowMFADBw7UnDlzlJqaqokTJyoqKopLVQAAoOgjO9euXbvjLdpXr161ukuqKBYuXKjMzEx17txZNWvWtCwff/yxpN8uj23atEldu3ZV06ZN9eqrr6pv37768ssvLcdwdHTUmjVr5OjoqODgYL3wwguKiIiwei4PAAD48yryyE6jRo20a9cuy4jKH+3YsUONGjUq1snNZvMd9wcEBBR4enJh6tSpo6+++qpY5wYAAH8ORR7ZGTBggCZOnKiDBw8W2HfgwAFNnjxZAwYMKNXiAAAASqrIIztjxozRunXr1KZNG4WEhKhp06aSpOPHj2vTpk3q2LGjxowZU2aFAgAA3Isihx1nZ2d9/fXXevvttxUfH69t27bJbDarcePGmj59ukaPHi1nZ+eyrBUAAKDYivVacGdnZ40fP17jx48vq3oAAABKVZHDzunTpzVp0iSdPn1aDRs2VGxs7D0/wRgVQ93X1pbbuc7OCiu3cwEA/lyKHHbGjRunKVOmqFmzZjp69KjGjh2rVatWlWVtAAAAJVbksOPt7a2WLVtKklq1aqVq1aqVWVEAAAClpchh59q1a1qyZIkCAwN15MgRZWdnl2VdAAAApaLIz9l57733dPnyZS1fvlwZGRnFfg8WAACALRR5ZMfDw0Njx44ty1oAAABKXZFHdv5o37592rZtW2nWAgAAUOqK9Zyd3xs4cKC+//575eXllWY9AAAApeqew87mzZuVm5tbmrUAAACUunsOO/7+/qVZBwAAQJm457CTnp6u9PR05efnW21v0aJFiYsCAAAoLcUOO0lJSYqMjNSxY8dkNpslSSaTSWazWSaTiTk8AADArhQ77AwZMkSNGzfW4sWL5evrK5PJVBZ1AQAAlIpih50ffvhBn332mRo2bFgW9QAAAJSqYj9np0uXLjpw4EBZ1AIAAFDqij2y869//UuRkZE6fPiwmjdvLmdnZ6v9Tz/9dKkVBwAAUFLFDjuJiYnauXOn1q1bV2AfE5QBAIC9KfZlrFGjRumFF15QSkqK8vPzrRaCDgAAsDfFDjuXLl3SmDFj5OvrWxb1AAAAlKpih50+ffpoy5YtZVELAABAqSv2nJ3GjRsrJiZGO3bsUFBQUIEJyn/5y19KrTgAAICSuqe7sdzd3ZWQkKCEhASrfSaTibADAADsSrHDzpkzZ8qiDgAAgDJR5Dk7jz76qN58802dPHmyLOsBAAAoVUUOO8OGDVNiYqIefPBBNWvWTBMmTNDOnTstLwMFAACwR0UOOxEREfrss8/0888/66233lJGRob+3//7f/Lz89OQIUO0evVq/frrr2VZKwAAQLEV+9ZzV1dX9ejRQ++9954uXLigL774QjVr1tSkSZNUrVo1PfXUU9q5c2dZ1AoAAFBsxQ47f9S+fXtNnz5dhw4d0qFDh9SlSxelpKSURm0AAAAlVuS7sSIjI9WlSxd17txZtWvXLrRNgwYNNGbMmFIrDgAAoKSKPLLz448/6qWXXlK9evXUoEEDvfjii/rwww9LNIozc+ZMtWvXTlWrVpWPj4969+6tEydOWLW5fv26oqKiVK1aNbm7u6tv375KS0uzanPu3DmFhYWpSpUq8vHx0bhx43Tz5s17rgsAABhHkcPO1q1blZGRoU2bNumFF17QyZMnNXToUNWqVUtNmzbViBEj9MknnxTr5AkJCYqKitLu3bu1ceNG5ebmqmvXrrp27ZqlzZgxY/Tll1/qk08+UUJCgi5cuKA+ffpY9ufl5SksLEw3btzQrl27tHz5ci1btkyTJ08uVi0AAMCYTOYS3Dt+/fp17dq1S+vWrdM///lPZWdnl+jN5xcvXpSPj48SEhLUqVMnZWZmqkaNGoqPj9ezzz4rSTp+/LiaNWumxMREdejQQevWrdNTTz2lCxcuWF5OumjRIk2YMEEXL16Ui4tLgfPk5OQoJyfHsp6VlaWAgABlZmbKw8OjyPXWfW3tPff1XpydFVau5yvP/pV33wAAFV9WVpY8PT3v+vv7niYo37hxQwkJCZo9e7ZiY2P1j3/8Q9WrV1dkZOQ9FyxJmZmZkiRvb29JUlJSknJzcxUSEmJp07RpU9WuXVuJiYmSpMTERAUFBVm9hT00NFRZWVk6cuRIoeeZOXOmPD09LUtAQECJ6gYAAParyBOUt23bpq1bt2rLli369ttvVbt2bT322GMaPny4/vOf/6hWrVolKiQ/P1+jR49Wx44d1bx5c0lSamqqXFxc5OXlZdXW19dXqamplja/Dzq39t/aV5iYmBhFR0db1m+N7AAAAOMpcti5dRfWhAkTtGLFigIBo6SioqJ0+PBh7dixo1SPWxhXV1e5urqW+XkAAIDtFfky1vjx4+Xn56fRo0frySef1KhRoyxPVC6pkSNHas2aNdqyZYvVCJGfn59u3LihjIwMq/ZpaWny8/OztPnj3Vm31m+1AQAAf15FDjuzZs3S7t27denSJc2ePVtVqlTRnDlz5O/vr+bNmysqKkqffvppsU5uNps1cuRIrVq1St98843q1atntb9NmzZydnbW5s2bLdtOnDihc+fOKTg4WJIUHBysQ4cOKT093dJm48aN8vDwUGBgYLHqAQAAxlPky1i3uLu7q3v37urevbsk6fLly5o7d64WLFigRYsWFeturKioKMXHx+vzzz9X1apVLXNsPD09VblyZXl6emro0KGKjo6Wt7e3PDw8NGrUKAUHB6tDhw6SpK5duyowMFADBw7UnDlzlJqaqokTJyoqKopLVQAAoPhhJz8/X3v37tXWrVu1detW7dy5U9nZ2apdu7bV82+KYuHChZJ+mw/0e0uXLtWgQYMkSW+//bYcHBzUt29f5eTkKDQ0VO+++66lraOjo9asWaMRI0YoODhYbm5uioyMVGxsbHG7BgAADKjIYWfOnDmWcHP16lXdf//96ty5s+bNm6fHH3+8wCWooijKI34qVaqkuLg4xcXF3bZNnTp19NVXXxX7/AAAwPiKHHbmzZunzp07680339Tjjz+uhg0blmVdAAAApaLIYefChQtlWQcAAECZKNLdWAcPHlR+fn6RD3rkyBFexAkAAOxCkcJO69atdenSpSIfNDg4WOfOnbvnogAAAEpLkS5jmc1mTZo0SVWqVCnSQW/cuFGiogAAAEpLkcJOp06ddOLEiSIfNDg4WJUrV77nogAAAEpLkcLO1q1by7gMAACAslHk10UAAABURIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaIQdAABgaMUOOzt37lRWVlaB7Wlpafr5559LpSgAAIDSUuywEx0drQYNGmj9+vVW23fu3KnmzZuXWmEAAAClodhhZ9WqVbrvvvvUq1cvLV68WLm5ub8dyMFBjo6OpV4gAABASRTpRaC/5+/vr8OHD2vRokV65ZVXNHLkSN133326cuWK5s2bVwYlAgAA3Ltihx1JysrK0sMPP6zw8HCZzWaNGDFCdevWlY+PT2nXBwAAUCLFDjvvvfee/vrXv1pGcySpYcOG+stf/lLqxQEAAJRUsefsTJs2TZ988olSUlKUlZWlBQsWaOrUqWrevLmOHz9eFjUCAADcs2KHnZs3b+r69euSJBcXFw0bNkxfffWVcnNz9dxzz5V6gQAAACVR7MtYx48fV35+vtW2kJAQ/fDDD/r+++9LrTAAAIDSUOyw4+XlVej2SpUqqUWLFiWtBwAAoFTxuggAAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBo9/S6CKCiq/va2nI719lZYeV2LgBAQTYd2dm2bZt69uwpf39/mUwmrV692mr/oEGDZDKZrJZu3bpZtbl8+bLCw8Pl4eEhLy8vDR06VNnZ2eXYCwAAYM9sGnauXbumli1bKi4u7rZtunXrppSUFMvy0UcfWe0PDw/XkSNHtHHjRq1Zs0bbtm3T8OHDy7p0AABQQdj0Mlb37t3VvXv3O7ZxdXWVn59fofuOHTum9evXa+/evWrbtq0kacGCBerRo4fefPNN+fv7l3rNAACgYrH7Ccpbt26Vj4+PmjRpohEjRujSpUuWfYmJifLy8rIEHem3V1c4ODjo22+/ve0xc3JylJWVZbUAAABjsuuw061bN33wwQfavHmzZs+erYSEBHXv3l15eXmSpNTUVPn4+Fh9xsnJSd7e3kpNTb3tcWfOnClPT0/LEhAQUKb9AAAAtmPXd2P169fP8nVQUJBatGihBg0aaOvWrerSpcs9HzcmJkbR0dGW9aysLAIPAAAGZdcjO39Uv359Va9eXadOnZIk+fn5KT093arNzZs3dfny5dvO85F+mwfk4eFhtQAAAGOqUGHnp59+0qVLl1SzZk1JUnBwsDIyMpSUlGRp88033yg/P1/t27e3VZkAAMCO2PQyVnZ2tmWURpLOnDmj5ORkeXt7y9vbW1OnTlXfvn3l5+en06dPa/z48WrYsKFCQ0MlSc2aNVO3bt00bNgwLVq0SLm5uRo5cqT69evHnVgAAECSjUd29u3bp9atW6t169aSpOjoaLVu3VqTJ0+Wo6OjDh48qKefflqNGzfW0KFD1aZNG23fvl2urq6WY3z44Ydq2rSpunTpoh49euiRRx7RP//5T1t1CQAA2Bmbjux07txZZrP5tvs3bNhw12N4e3srPj6+NMsCAAAGUqHm7AAAABQXYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABiak60LAAAYW93X1pbr+c7OCivX88H+MbIDAAAMjbADAAAMjbADAAAMjbADAAAMjbADAAAMjbADAAAMjbADAAAMjbADAAAMjbADAAAMzaZhZ9u2berZs6f8/f1lMpm0evVqq/1ms1mTJ09WzZo1VblyZYWEhOjkyZNWbS5fvqzw8HB5eHjIy8tLQ4cOVXZ2djn2AgAA2DObhp1r166pZcuWiouLK3T/nDlzNH/+fC1atEjffvut3NzcFBoaquvXr1vahIeH68iRI9q4caPWrFmjbdu2afjw4eXVBQAAYOds+m6s7t27q3v37oXuM5vNmjdvniZOnKhevXpJkj744AP5+vpq9erV6tevn44dO6b169dr7969atu2rSRpwYIF6tGjh9588035+/uXW18AAIB9sts5O2fOnFFqaqpCQkIs2zw9PdW+fXslJiZKkhITE+Xl5WUJOpIUEhIiBwcHffvtt7c9dk5OjrKysqwWAABgTHYbdlJTUyVJvr6+Vtt9fX0t+1JTU+Xj42O138nJSd7e3pY2hZk5c6Y8PT0tS0BAQClXDwAA7IXdhp2yFBMTo8zMTMty/vx5W5cEAADKiN2GHT8/P0lSWlqa1fa0tDTLPj8/P6Wnp1vtv3nzpi5fvmxpUxhXV1d5eHhYLQAAwJjsNuzUq1dPfn5+2rx5s2VbVlaWvv32WwUHB0uSgoODlZGRoaSkJEubb775Rvn5+Wrfvn251wwAAOyPTe/Gys7O1qlTpyzrZ86cUXJysry9vVW7dm2NHj1af//739WoUSPVq1dPkyZNkr+/v3r37i1Jatasmbp166Zhw4Zp0aJFys3N1ciRI9WvXz/uxAIAAJJsHHb27dunxx9/3LIeHR0tSYqMjNSyZcs0fvx4Xbt2TcOHD1dGRoYeeeQRrV+/XpUqVbJ85sMPP9TIkSPVpUsXOTg4qG/fvpo/f3659wUAANgnm4adzp07y2w233a/yWRSbGysYmNjb9vG29tb8fHxZVEeAAAwALudswMAAFAabDqyAwBARVb3tbXler6zs8LK9XxGwcgOAAAwNMIOAAAwNMIOAAAwNMIOAAAwNMIOAAAwNMIOAAAwNMIOAAAwNMIOAAAwNB4qCAAACjDSAxMZ2QEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIZG2AEAAIbGu7EAwA4Y6T1EgL1hZAcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABgaYQcAABiaXYed119/XSaTyWpp2rSpZf/169cVFRWlatWqyd3dXX379lVaWpoNKwYAAPbGrsOOJD3wwANKSUmxLDt27LDsGzNmjL788kt98sknSkhI0IULF9SnTx8bVgsAAOyN3b8I1MnJSX5+fgW2Z2ZmavHixYqPj9cTTzwhSVq6dKmaNWum3bt3q0OHDuVdKgAAsEN2P7Jz8uRJ+fv7q379+goPD9e5c+ckSUlJScrNzVVISIilbdOmTVW7dm0lJibe8Zg5OTnKysqyWgAAgDHZddhp3769li1bpvXr12vhwoU6c+aMHn30UV29elWpqalycXGRl5eX1Wd8fX2Vmpp6x+POnDlTnp6eliUgIKAMewEAAGzJri9jde/e3fJ1ixYt1L59e9WpU0f//e9/Vbly5Xs+bkxMjKKjoy3rWVlZBB4AAAzKrkd2/sjLy0uNGzfWqVOn5Ofnpxs3bigjI8OqTVpaWqFzfH7P1dVVHh4eVgsAADCmChV2srOzdfr0adWsWVNt2rSRs7OzNm/ebNl/4sQJnTt3TsHBwTasEgAA2BO7vow1duxY9ezZU3Xq1NGFCxc0ZcoUOTo6qn///vL09NTQoUMVHR0tb29veXh4aNSoUQoODuZOLAAAYGHXYeenn35S//79denSJdWoUUOPPPKIdu/erRo1akiS3n77bTk4OKhv377KyclRaGio3n33XRtXDQAA7Ildh50VK1bccX+lSpUUFxenuLi4cqoIAABUNBVqzg4AAEBxEXYAAIChEXYAAIChEXYAAIChEXYAAIChEXYAAICh2fWt5wDwe3VfW1tu5zo7K6zczgWgbDGyAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI2wAwAADI13YwEGw/ujAMAaIzsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQCDsAAMDQDBN24uLiVLduXVWqVEnt27fXnj17bF0SAACwA4YIOx9//LGio6M1ZcoU7d+/Xy1btlRoaKjS09NtXRoAALAxQ4SduXPnatiwYRo8eLACAwO1aNEiValSRUuWLLF1aQAAwMacbF1ASd24cUNJSUmKiYmxbHNwcFBISIgSExML/UxOTo5ycnIs65mZmZKkrKysYp07P+eXe6j43hW3vpIqz/7Rt9JD30qHkfsmlW//6FvpoW+Ff8ZsNt+5obmC+9///meWZN61a5fV9nHjxpkfeuihQj8zZcoUsyQWFhYWFhYWAyznz5+/Y1ao8CM79yImJkbR0dGW9fz8fF2+fFnVqlWTyWQq03NnZWUpICBA58+fl4eHR5meq7zRt4rLyP2jbxUTfauYyrtvZrNZV69elb+//x3bVfiwU716dTk6OiotLc1qe1pamvz8/Ar9jKurq1xdXa22eXl5lVWJhfLw8DDc/+S30LeKy8j9o28VE32rmMqzb56enndtU+EnKLu4uKhNmzbavHmzZVt+fr42b96s4OBgG1YGAADsQYUf2ZGk6OhoRUZGqm3btnrooYc0b948Xbt2TYMHD7Z1aQAAwMYMEXaef/55Xbx4UZMnT1ZqaqpatWql9evXy9fX19alFeDq6qopU6YUuIxmBPSt4jJy/+hbxUTfKiZ77ZvJbL7b/VoAAAAVV4WfswMAAHAnhB0AAGBohB0AAGBohB0AAGBohB0AAGBohrj1HMDd9enTR8uWLZOHh4f69Olzx7YrV64sp6oAoOwRdsrBtm3b7ri/U6dO5VRJyRXnrbRGfQx6ReXp6Wl591tRHq8O+5WRkaE9e/YoPT1d+fn5VvsiIiJsVFXpuHHjRqH9ql27to0qQnFcv35dlSpVsnUZBfCcnXLg4FDwauHvXzial5dXnuWUiIODw11flmo2m2UymSpUv27n9y+M/T2TyaRKlSqpYcOG6tWrl7y9vcu5snsTGxursWPHqkqVKrYupVzs27dPx44dkyQ1a9ZMbdu2tXFFJffll18qPDxc2dnZ8vDwsPp5NJlMunz5sg2ru3cnT57UkCFDtGvXLqvtRvr3xKjy8/M1ffp0LVq0SGlpafr+++9Vv359TZo0SXXr1tXQoUNtXSJhpzxkZmZarefm5uq7777TpEmTNH36dHXp0sVGlRVfQkJCkdodOnRII0eOLONqyt7jjz+u/fv3Ky8vT02aNJEkff/993J0dFTTpk114sQJmUwm7dixQ4GBgTau9u4cHR2VkpIiHx8fW5dSpn766Sf1799fO3futLzkNyMjQw8//LBWrFihWrVq2bbAEmjcuLF69OihGTNmGCq0duzYUU5OTnrttddUs2bNAn9UtWzZ0kaV3Ttvb299//33ql69uu677747/qFYUUOq9NsfUcuXL1dsbKyGDRumw4cPq379+vr44481b948JSYm2rpEwo4tJSQkKDo6WklJSbYupVRcvXpVH330kf71r38pKSnJEH+JzZs3T9u3b9fSpUstl+UyMzP14osv6pFHHtGwYcM0YMAA/frrr9qwYYONq707BwcHpaamGj7sdOvWTRkZGVq+fLklpJ44cUKDBw+Wh4eH1q9fb+MK752bm5sOHTqk+vXr27qUUuXm5qakpCQ1bdrU1qWUmuXLl6tfv35ydXXVsmXL7hh2IiMjy7Gy0tWwYUO999576tKli6pWraoDBw6ofv36On78uIKDg3XlyhVblyiZYTPHjh0zu7m52bqMEktISDBHRESY3dzczI0aNTJPmDDBvGfPHluXVSr8/f3NR44cKbD98OHDZn9/f7PZbDYnJSWZq1WrVt6l3ROTyWROT0+3dRllrlKlSub9+/cX2L5v3z5z5cqVbVBR6XnmmWfMH3/8sa3LKHVt27Y1b9++3dZl4B5UqlTJfPbsWbPZbDa7u7ubT58+bTabzeYjR47Yze84JiiXg4MHD1qtm81mpaSkaNasWWrVqpVtiiqh1NRULVu2TIsXL1ZWVpaee+455eTkaPXq1RXick5RZWZmKj09vUCfLl68aJms7eXlpRs3btiivHvSuHHju867qshD6pIUEBCg3NzcAtvz8vLk7+9vg4pKT1hYmMaNG6ejR48qKChIzs7OVvuffvppG1VWMrNnz9b48eM1Y8aMQvtVUW94KMo8R5PJpJs3b5ZTRaUvMDBQ27dvV506day2f/rpp2rdurWNqrJG2CkHrVq1kslkkvkPVww7dOigJUuW2Kiqe9ezZ09t27ZNYWFhmjdvnrp16yZHR0ctWrTI1qWVul69emnIkCF666231K5dO0nS3r17NXbsWPXu3VuStGfPHjVu3NiGVRbP1KlTDX831htvvKFRo0YpLi7OMil53759+utf/6o333zTxtWVzLBhwyT9Nk/ijyryRN6QkBBJKjCH0VzBJyivWrXqtvsSExM1f/78AneeVTSTJ09WZGSk/ve//yk/P18rV67UiRMn9MEHH2jNmjW2Lk8Sc3bKxY8//mi17uDgoBo1atjl7XlF4eTkpL/85S8aMWKEGjVqZNnu7OysAwcOGGpkJzs7W2PGjNEHH3ygmzdvymw2y9nZWZGRkZo7d67c3d2VnJwsSRVilM7Ic3b+OAH02rVrunnzppycfvub7tbXbm5uFX7kyojudvPDY489Vk6VlL0TJ07otddes9xZFxsbW2BUpCL44YcfVK9ePZlMJm3fvl2xsbE6cOCAsrOz9eCDD2ry5Mnq2rWrrcuUxMhOmfrmm280cuRI7d69u8AQbGZmptq0aaNFixbp0UcftVGF92bHjh1avHix2rRpo2bNmmngwIHq16+frcsqE+7u7nr//ff19ttv64cffpAk1a9fX+7u7pY2FSHk3HK34fSKbN68ebYuoUwlJibq0qVLeuqppyzbPvjgA02ZMkXXrl1T7969tWDBArm6utqwyuLr0qWLoqKibvugy59//lkPPfSQ5eevIrtw4YKmTJmi5cuXKzQ0VMnJyWrevLmty7pnjRo1stzd+eijj8rb21uHDh2Sr6+vrUsrgJGdMvT000/r8ccf15gxYwrdP3/+fG3ZsuWOw5z27Nq1a/r444+1ZMkS7dmzR3l5eZo7d66GDBmiqlWr2rq8EhkyZEiR2lW0y5BGHtmRfpuT8+abb+qLL77QjRs31KVLF02ZMkWVK1e2dWkl1r17d3Xu3FkTJkyQ9NvjHR588EENGjRIzZo10xtvvKGXXnpJr7/+um0LLSYHBwc5ODjo//7v/zR16tQC+9PS0uTv719hL2NJv/1xO2PGDC1YsECtWrXS7NmzK9wfuYX5478nHh4eSk5Otss7BXk3Vhk6cOCAunXrdtv9Xbt2rdC3nbu5uWnIkCHasWOHDh06pFdffVWzZs2Sj49PhZ0kecuyZcu0ZcsWZWRk6MqVK7ddKpr8/HzDBh1JmjFjhv72t7/J3d1d999/v9555x1FRUXZuqxSkZycbDWfZcWKFWrfvr3ef/99RUdHa/78+frvf/9rwwrv3cKFCzVv3jw988wzunbtmq3LKVVz5sxR/fr1tWbNGn300UfatWuXIYJOYex57ISRnTJUqVIlHT58WA0bNix0/6lTpxQUFKRff/21nCsrO3l5efryyy+1ZMkSffHFF7Yu555FRUXpo48+Up06dTR48GC98MILFeYpyX9mjRo10tixY/XSSy9JkjZt2qSwsDD9+uuvhT7JvCKpVKmSTp48qYCAAEnSI488ou7du+v//u//JElnz55VUFCQrl69assyi+3W6MClS5fUq1cvubq66vPPP7eMDlT0kR0HBwdVrlxZISEhcnR0vG27ivg+OkdHR6WmpqpGjRqSpKpVq+rgwYOqV6+ejSsriDk7Zej++++/Y9g5ePCgatasWc5VlS1HR0f17t3bcqdSRRUXF6e5c+dq5cqVWrJkiWJiYhQWFqahQ4eqa9euhp77UpGdO3dOPXr0sKyHhITIZDLpwoULFfqpyZLk6+urM2fOKCAgQDdu3ND+/futLvtcvXq1wO3aFUmzZs20d+9e9e/fX+3atdPHH39suUOrIouIiDDsvxdms1mDBg2yzBO7fv26Xn75Zbm5uVm1s4cgR9gpQz169NCkSZPUrVu3Ande/frrr5oyZYrVZEPYF1dXV/Xv31/9+/fXjz/+qGXLlumVV17RzZs3deTIEatJyrAPN2/eLPCz5uzsXOgzdyqaHj166LXXXtPs2bO1evVqValSxepyyMGDB9WgQQMbVlhynp6eWrt2rWJiYtSjRw/Nnj1bAwYMsHVZJbJs2TJbl1Bm/vjU5xdeeMFGldwdYacMTZw4UStXrlTjxo01cuRIy2Prjx8/rri4OOXl5VmGoGHfbj0YzGw2V9jh9D+DP/6lKRX+16Y9/KVZXNOmTVOfPn302GOPyd3dXcuXL5eLi4tl/5IlS+zmNt/i+OOoh8lksjxw9cUXX9Q333xjo8pwN0uXLrV1CUXGnJ0y9uOPP2rEiBHasGGDZfKWyWRSaGio4uLi7PLaJn6Tk5NjuYy1Y8cOPfXUUxo8eLC6detW4ed/GNXgwYOL1K4i/SP9R5mZmXJ3dy8w/+Py5ctyd3e3CkAVwZ3uEExOTlbv3r11/vx5/shAiRB2ysmVK1d06tQpmc1mNWrUSPfdd5+tS8IdvPLKK1qxYoUCAgI0ZMgQhYeHq3r16rYuCzCchIQEyxvPC3Pp0iWtXbtWERER5VwZjISwAxTCwcFBtWvXVuvWre84ubAiXg4BgD8b5uwAhTDyHRQA8GfDyA4AADA0ZlkCAABDI+wAAABDI+wAAABDI+wAAABDI+wAAABDI+wAqBAGDRpkeZXA761evZrHBAC4I8IOgAqjUqVKmj17tq5cuWLrUgBUIIQdABVGSEiI/Pz8NHPmzNu2+eyzz/TAAw/I1dVVdevW1VtvvWW1v27duvr73/+uiIgIubu7q06dOvriiy908eJF9erVS+7u7mrRooX27dtX1t0BUE4IOwAqDEdHR82YMUMLFizQTz/9VGB/UlKSnnvuOfXr10+HDh3S66+/rkmTJmnZsmVW7d5++2117NhR3333ncLCwjRw4EBFRETohRde0P79+9WgQQNFRESIZ64CxsATlAFUCIMGDVJGRoZWr16t4OBgBQYGavHixVq9erWeeeYZmc1mhYeH6+LFi/r6668tnxs/frzWrl2rI0eOSPptZOfRRx/Vv//9b0lSamqqatasqUmTJik2NlaStHv3bgUHByslJUV+fn7l31kApYqRHQAVzuzZs7V8+XIdO3bMavuxY8fUsWNHq20dO3bUyZMnlZeXZ9nWokULy9e+vr6SpKCgoALb0tPTS712AOWPsAOgwunUqZNCQ0MVExNzT593dna2fH3rTq7CtuXn55egSgD2greeA6iQZs2apVatWqlJkyaWbc2aNdPOnTut2u3cuVONGzeWo6NjeZcIwE4QdgBUSEFBQQoPD9f8+fMt21599VW1a9dO06ZN0/PPP6/ExET94x//0LvvvmvDSgHYGpexAFRYsbGxVpeaHnzwQf33v//VihUr1Lx5c02ePFmxsbEaNGiQ7YoEYHPcjQUAAAyNkR0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBohB0AAGBo/x8cHYxh+4t4mgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Conductivitat tèrmica')\n",
    "plt.ylabel('ϰ  [W/m·⁰C]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'alta conductivitat tèrmica del coure justifica el seu ús a recipients per a cuinar aliments."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dilatació tèrmica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'λ  [K⁻¹]')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Dilatació tèrmica')\n",
    "plt.ylabel('λ  [K⁻¹]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mòdul elàstic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'σ  [MPa]')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Mòdul elàstic')\n",
    "plt.ylabel('σ  [MPa]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Límit elàstic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'σe [MPa]')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Vp04d2xobPz8/eXl5yc/PTxMmTNDUqVMVEBAgX19fPfLIIwoPD1evXr0kSQMGDFC7du304IMPatGiRUpPT9ezzz6rKVOmyNPT057DAwAADsCuYecf//iHJKlfv37F2leuXKmxY8dKkl566SW5uLho5MiRysvLU2RkpJYvX27r6+rqqk2bNmny5MkKDw+Xt7e3xowZo/j4+JoaBgAAcGAOdZ8de+E+OzAJ99kB8GfhlPfZAQAAqGqEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACjEXYAAIDRCDsAAMBohB0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACjEXYAAIDRCDsAAMBohB0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACj2TXs7Ny5U0OGDFFwcLAsFos2bNhQbP/YsWNlsViKbVFRUcX6XLx4UTExMfL19ZW/v78mTJigy5cv1+AoAACAI7Nr2Lly5Yo6duyoZcuWXbNPVFSU0tLSbNtbb71VbH9MTIyOHj2qLVu2aNOmTdq5c6cmTZpU3aUDAAAn4WbPgw8cOFADBw68bh9PT08FBQWVuu/YsWPavHmz9u7dq27dukmSXn31VQ0aNEiLFy9WcHBwldcMAACci8Ov2dmxY4caNmyo1q1ba/Lkybpw4YJtX3Jysvz9/W1BR5IiIiLk4uKiPXv2XPMz8/LylJubW2wDAABmcuiwExUVpdWrV2vr1q1auHChkpKSNHDgQBUWFkqS0tPT1bBhw2LvcXNzU0BAgNLT06/5ufPnz5efn59ta9y4cbWOAwAA2I9dT2PdyKhRo2xfh4WFqUOHDmrRooV27Nih/v37V/hzZ8yYoalTp9pe5+bmEngAADCUQ8/s/FHz5s1Vv359nTp1SpIUFBSkzMzMYn2uXr2qixcvXnOdj/TrOiBfX99iGwAAMJNThZ3z58/rwoULatSokSQpPDxc2dnZ2r9/v63Ptm3bVFRUpJ49e9qrTAAA4EDsehrr8uXLtlkaSTpz5owOHjyogIAABQQEaO7cuRo5cqSCgoJ0+vRpTZ8+XS1btlRkZKQkqW3btoqKitLEiROVkJCggoICxcXFadSoUVyJBQAAJNl5Zmffvn3q3LmzOnfuLEmaOnWqOnfurFmzZsnV1VWHDx/WXXfdpdDQUE2YMEFdu3bVZ599Jk9PT9tnrFmzRm3atFH//v01aNAg9enTR//zP/9jryEBAAAHY9eZnX79+slqtV5z/8cff3zDzwgICNDatWursiwAAGCQMoWdLl26lOtDLRaLPvjgA910000VKgoAAKCqlCnsHDx4UE8++aR8fHxu2NdqtWrBggXKy8urdHEAAACVVebTWE899VSJG/hdy5IlSypcEAAAQFUqU9g5c+aMGjRoUOYP/eabb7gaCgAAOIQyhZ2QkJByfSh3IwYAAI6iwldj/fTTT0pJSVF+fn6x9g4dOlS6KAAAgKpS7rCTlZWlcePG6aOPPip1/28P6QQAAHAE5b6p4OOPP67s7Gzt2bNHXl5e2rx5s1atWqVWrVrpgw8+qI4aAQAAKqzcMzvbtm3T+++/r27dusnFxUUhISG688475evrq/nz5ys6Oro66gQAAKiQcs/sXLlyxXYJet26dZWVlSVJCgsL04EDB6q2OgAAgEoq98xO69atdeLECTVt2lQdO3bUa6+9pqZNmyohIcH2NHIAAP4Mmj7zYY0e7+wCzp5URLnDzmOPPabU1FRJ0uzZsxUVFaU1a9bIw8NDiYmJVV0fAABApZQ77DzwwAO2r7t27arvv/9ex48fV5MmTVS/fv0qLQ4AAKCyyrxm58qVK5o8ebJuuukmNWjQQKNGjVJWVpZq166tLl26EHQAAIBDKnPYmTlzpt58800NHjxY999/v7Zt26ZJkyZVZ20AAACVVubTWO+9955Wrlype+65R5IUGxurXr166erVq3Jzq/CNmAEAAKpVmWd2zp8/r969e9ted+3aVe7u7rbFygAAAI6ozGGnqKhI7u7uxdrc3Nx4PAQAAHBoZT7/ZLVa1b9//2KnrH766ScNGTJEHh4etjZuLAgAABxJmcPO7NmzS7QNHTq0SosBAACoapUKOwAAAI6u3M/GAgAAcCZlntm54447ytRv27ZtFS4GAAA4BpOe+1XmsLNjxw6FhIQoOjq6xFVZAAAAjqrMYWfhwoVauXKl3n33XcXExGj8+PFq3759ddYGAABQaWVes/PUU0/pm2++0YYNG3Tp0iX17t1bPXr0UEJCgnJzc6uzRgAAgAor9wLl8PBw/e///q/S0tI0ZcoUvfHGGwoODibwAAAAh1Thq7EOHDigpKQkHTt2TO3bt2cdDwAAcEjlCjupqamaN2+eQkNDdffddysgIEB79uzR7t275eXlVV01AgAAVFiZFygPGjRI27dv14ABA/TCCy8oOjqap50DAACHV+a0snnzZjVq1EgpKSmaO3eu5s6dW2o/no0FAAAcCY+LAAAARiPsAAAAo/FsLAAAYLQyhZ0uXbroxx9/LPOH9unTRz/88EOFiwIAAKgqZTqNdfDgQR06dEgBAQFl+tCDBw8qLy+vUoUBAABUhTKv2enfv7+sVmuZ+loslgoXBAAAUJXKFHbOnDlT7g+++eaby/0eAACAqlamsBMSElLddQAAAFQLrsYCAABGI+wAAACjEXYAAIDRCDsAAMBoFQo72dnZev311zVjxgxdvHhR0q8PAOVGggAAwNGU+T47vzl8+LAiIiLk5+ens2fPauLEiQoICND69euVkpKi1atXV0edAAAAFVLumZ2pU6dq7NixOnnypGrVqmVrHzRokHbu3FmlxQEAAFRWucPO3r179fDDD5dov+mmm5Senl4lRQEAAFSVcocdT09P5ebmlmj/9ttv1aBBgyopCgAAoKqUO+zcddddio+PV0FBgaRfn4OVkpKip59+WiNHjqzyAgEAACqj3GFnyZIlunz5sho2bKiff/5Z//Vf/6WWLVuqTp06ev7556ujRgAAgAor99VYfn5+2rJli3bt2qXDhw/r8uXL6tKliyIiIqqjPgAAgEopd9hZvXq1+vbtqz59+qhPnz7VURMAAECVKXfYGTdunP7+978rPz9fhw8flqurq9q1a6fx48fL19e3OmoEAACosHKv2bFarYqLi9PixYuVnZ2tzMxMLV68WC1atNBXX31VHTUCAABUWLlndiTpoYce0vLly+Xq6ipJKigo0MSJE/XYY49xY0EAAOBQKvRsrKlTp9qCjiS5u7tr+vTp2rdvX5UVBgAAUBXKHXb8/f11/vz5Eu3nzp1jzQ4AAHA45Q47d955pyZMmKB//etf+uGHH5SSkqK33npLDz30kGJiYqqjRgAAgAor95qd5cuX69FHH9V9991na/P09FRcXBw3FQQAAA6n3GGnXr16WrNmjf7xj3/ou+++k7u7u1q0aFHsCegAAACOokJXY0mSr6+vOnXqVIWlAAAAVL0KXY0FAADgLOwadnbu3KkhQ4YoODhYFotFGzZsKLbfarVq1qxZatSokby8vBQREaGTJ08W63Px4kXFxMTI19dX/v7+mjBhgi5fvlyDowAAAI7MrmHnypUr6tixo5YtW1bq/kWLFumVV15RQkKC9uzZI29vb0VGRuqXX36x9YmJidHRo0e1ZcsWbdq0STt37tSkSZNqaggAAMDBVXjNTlUYOHCgBg4cWOo+q9WqpUuX6tlnn9XQoUMl/foQ0sDAQG3YsEGjRo3SsWPHtHnzZu3du1fdunWTJL366qsaNGiQFi9erODg4BobCwAAcEwOu2bnzJkzSk9PV0REhK3Nz89PPXv2VHJysiQpOTlZ/v7+tqAjSREREXJxcdGePXuu+dl5eXnKzc0ttgEAADM5bNhJT0+XJAUGBhZrDwwMtO1LT09Xw4YNi+13c3NTQECArU9p5s+fLz8/P9vWuHHjKq4eAAA4CocNO9VpxowZysnJsW3nzp2zd0kAAKCaOGzYCQoKkiRlZGQUa8/IyLDtCwoKUmZmZrH9V69e1cWLF219SuPp6SlfX99iGwAAMJPDhp1mzZopKChIW7dutbXl5uZqz549Cg8PlySFh4crOztb+/fvt/XZtm2bioqK1LNnzxqvGQAAOB67Xo11+fJlnTp1yvb6zJkzOnjwoAICAtSkSRM9/vjj+tvf/qZWrVqpWbNmmjlzpoKDgzVs2DBJUtu2bRUVFaWJEycqISFBBQUFiouL06hRo7gSCwAASLJz2Nm3b59uv/122+upU6dKksaMGaPExERNnz5dV65c0aRJk5Sdna0+ffpo8+bNxZ7DtWbNGsXFxal///5ycXHRyJEj9corr9T4WAAAgGOya9jp16+frFbrNfdbLBbFx8crPj7+mn0CAgK0du3a6igPAAAYwGHX7AAAAFQFwg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACjEXYAAIDRCDsAAMBohB0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0dzsXYAza/rMhzV6vLMLomv0eAAAmICZHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACjEXYAAIDRCDsAAMBohB0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKM5dNiZM2eOLBZLsa1Nmza2/b/88oumTJmievXqycfHRyNHjlRGRoYdKwYAAI7GocOOJN1yyy1KS0uzbbt27bLte+KJJ7Rx40a9++67SkpKUmpqqkaMGGHHagEAgKNxs3cBN+Lm5qagoKAS7Tk5OVqxYoXWrl2rO+64Q5K0cuVKtW3bVrt371avXr1qulQAAOCAHH5m5+TJkwoODlbz5s0VExOjlJQUSdL+/ftVUFCgiIgIW982bdqoSZMmSk5Otle5AADAwTj0zE7Pnj2VmJio1q1bKy0tTXPnztVtt92mI0eOKD09XR4eHvL39y/2nsDAQKWnp1/3c/Py8pSXl2d7nZubWx3lAwAAB+DQYWfgwIG2rzt06KCePXsqJCRE77zzjry8vCr8ufPnz9fcuXOrokQAAODgHP401u/5+/srNDRUp06dUlBQkPLz85WdnV2sT0ZGRqlrfH5vxowZysnJsW3nzp2rxqoBAIA9OVXYuXz5sk6fPq1GjRqpa9eucnd319atW237T5w4oZSUFIWHh1/3czw9PeXr61tsAwAAZnLo01jTpk3TkCFDFBISotTUVM2ePVuurq4aPXq0/Pz8NGHCBE2dOlUBAQHy9fXVI488ovDwcK7EAgAANg4dds6fP6/Ro0frwoULatCggfr06aPdu3erQYMGkqSXXnpJLi4uGjlypPLy8hQZGanly5fbuWoAAOBIHDrsrFu37rr7a9WqpWXLlmnZsmU1VBEAAHA2TrVmBwAAoLwIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARnPo++wA1aXpMx/W2LHOLoiusWMBAEpiZgcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAoxF2AACA0Qg7AADAaIQdAABgNMIOAAAwGmEHAAAYjbADAACMRtgBAABGI+wAAACjEXYAAIDRCDsAAMBohB0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjOZm7wLguJo+82GNHevsgugaOxYA4M+FmR0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjEbYAQAARiPsAAAAo7nZuwAAgNmaPvNhjR7v7ILoGj0eHB8zOwAAwGiEHQAAYDTCDgAAMBphBwAAGI0FygCcRk0udGWRK2AOY8LOsmXL9MILLyg9PV0dO3bUq6++qh49eti7LAAoE65YAqqPEaex3n77bU2dOlWzZ8/WgQMH1LFjR0VGRiozM9PepQEAADszIuy8+OKLmjhxosaNG6d27dopISFBtWvX1htvvGHv0gAAgJ05/Wms/Px87d+/XzNmzLC1ubi4KCIiQsnJyaW+Jy8vT3l5ebbXOTk5kqTc3NxyHbso76cKVFxx5a2vsmpyfIyt6jC2qmHy2KSaHR9jqzqMrfT3WK3W63e0OrkffvjBKsn6xRdfFGt/6qmnrD169Cj1PbNnz7ZKYmNjY2NjYzNgO3fu3HWzgtPP7FTEjBkzNHXqVNvroqIiXbx4UfXq1ZPFYqnWY+fm5qpx48Y6d+6cfH19q/VYNY2xOS+Tx8fYnBNjc041PTar1apLly4pODj4uv2cPuzUr19frq6uysjIKNaekZGhoKCgUt/j6ekpT0/PYm3+/v7VVWKpfH19jftL/hvG5rxMHh9jc06MzTnV5Nj8/Pxu2MfpFyh7eHioa9eu2rp1q62tqKhIW7duVXh4uB0rAwAAjsDpZ3YkaerUqRozZoy6deumHj16aOnSpbpy5YrGjRtn79IAAICdGRF27rvvPmVlZWnWrFlKT09Xp06dtHnzZgUGBtq7tBI8PT01e/bsEqfRTMDYnJfJ42NszomxOSdHHZvFar3R9VoAAADOy+nX7AAAAFwPYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMZcem5o9u5c+d19/ft27eGKqm88jyozdQ7gzqrESNGKDExUb6+vhoxYsR1+65fv76GqkJFZGdn68svv1RmZqaKioqK7YuNjbVTVVUjPz+/1HE1adLEThXBBISdGtCvX78Sbb9/BldhYWENVlM5/v7+N3x+mNVqlcVicapx/Rn4+fnZvndlub26Cfbt26djx45Jktq2batu3brZuaLK27hxo2JiYnT58mX5+voW+/dosVicNuycPHlS48eP1xdffFGsnZ8nzuWXX35RrVq17F1GCdxnpwbk5OQUe11QUKCvvvpKM2fO1PPPP6/+/fvbqbLyS0pKKlO/r7/+WnFxcdVcTfX7/QNjf89isahWrVpq2bKlhg4dqoCAgBqurGLi4+M1bdo01a5d296lVKvz589r9OjR+vzzz23PvcvOztatt96qdevW6eabb7ZvgZUQGhqqQYMGad68eUZ9H3v37i03Nzc988wzatSoUYn/VHXs2NFOlVVcQECAvv32W9WvX19169a97n8UL168WIOVVa2ioiI9//zzSkhIUEZGhr799ls1b95cM2fOVNOmTTVhwgR7l0jYsaekpCRNnTpV+/fvt3cpVeLSpUt666239Prrr2v//v1G/E/s9ttv14EDB1RYWKjWrVtLkr799lu5urqqTZs2OnHihCwWi3bt2qV27drZudobc3V1VVpamho2bGjvUqpVVFSUsrOztWrVKtv37cSJExo3bpx8fX21efNmO1dYcd7e3vr666/VvHlze5dSpby9vbV//361adPG3qVUmVWrVmnUqFHy9PRUYmLidcPOmDFjarCyqhUfH69Vq1YpPj5eEydO1JEjR9S8eXO9/fbbWrp0qZKTk+1domSF3Rw7dszq7e1t7zIqLSkpyRobG2v19va2tmrVyvr0009bv/zyS3uXVSVeeukl64gRI6w5OTm2tuzsbOvdd99tXbp0qfXKlSvWoUOHWgcMGGDHKsvOYrFYMzIy7F1GtatVq5b1wIEDJdr37dtn9fLyskNFVWf48OHWt99+295lVLlu3bpZP/vsM3uXgQpo0aKF9dNPP7VarVarj4+P9fTp01ar9dffcf7+/vYszYY1OzXg8OHDxV5brValpaVpwYIF6tSpk32KqqT09HQlJiZqxYoVys3N1b333qu8vDxt2LDBKWY4yuqFF17Qli1bii229vPz05w5czRgwAA99thjmjVrlgYMGGDHKsvnRmuuTNC4cWMVFBSUaC8sLFRwcLAdKqo60dHReuqpp/TNN98oLCxM7u7uxfbfdddddqqschYuXKjp06dr3rx5pY7LWS94cHFxueG/OYvFoqtXr9ZQRVXvhx9+UMuWLUu0FxUVlfrv0B4IOzWgU6dOslgssv7hjGGvXr30xhtv2KmqihsyZIh27typ6OhoLV26VFFRUXJ1dVVCQoK9S6tyOTk5yszMLBHgsrKybFem+fv7Kz8/3x7lVUhoaOgNf/g68/oB6deQ+sgjj2jZsmW2Rcn79u3TY489psWLF9u5usqZOHGipF9PHfyRMy/kjYiIkKQSaxitTr5A+b333rvmvuTkZL3yyislrjxzNu3atdNnn32mkJCQYu3/+te/1LlzZztVVRxhpwacOXOm2GsXFxc1aNDAIVesl8VHH32kRx99VJMnT1arVq3sXU61Gjp0qMaPH68lS5aoe/fukqS9e/dq2rRpGjZsmCTpyy+/VGhoqB2rLJ+5c+caeTXWHxeAXrlyRT179pSb268/5q5evSo3NzeNHz/e9r1zRs7+i/Fatm/fbu8SqsXQoUNLtJ04cULPPPOM7cq60oKrM5k1a5bGjBmjH374QUVFRVq/fr1OnDih1atXa9OmTfYuTxJhp1pt27ZNcXFx2r17d4kp2JycHHXt2lUJCQm67bbb7FRhxezatUsrVqxQ165d1bZtWz344IMaNWqUvcuqFq+99pqeeOIJjRo1SlevXpXVapW7u7vGjBmjF198UZLUpk0bvf7663autOxGjRpl5ALlpUuX2ruEapWcnKwLFy5o8ODBtrbVq1dr9uzZunLlioYNG6ZXX31Vnp6edqyy/Pr3768pU6Zc895P//nPf9SjRw999913NVxZ1UtNTdXs2bO1atUqRUZG6uDBg2rfvr29y6qw7777Ts2aNdPQoUO1ceNGxcfHy9vbW7NmzVKXLl20ceNG3XnnnfYu81f2XTJktiFDhlhffPHFa+5/+eWXrcOGDavBiqrW5cuXrStWrLD27t3b6u7ubnVxcbEuXbrUmpuba+/SqtylS5eshw4dsh46dMh66dIle5dTYS4uLkYvUL569ap1wYIF1ltvvdXarVs369NPP2396aef7F1WlYiKirIuWLDA9vrw4cNWNzc360MPPWRdsmSJNSgoyDp79mz7FVhBFovF6urqap01a1ap+9PT060uLi41XFXVys7Otk6fPt3q5eVlDQ8Pt+7cudPeJVWJP/48uffee63p6el2rOjauPS8GoWEhGjz5s1q27ZtqfuPHz+uAQMGKCUlpYYrq3onTpzQihUr9Oabbyo7O1t33nmnPvjgA3uXVWHjx48vUz9nW3Pl4uKi9PR0I2d2JOm5557TnDlzFBERIS8vL3388ccaPXq0032fStOoUSNt3LjRtgbpr3/9q5KSkrRr1y5J0rvvvqvZs2frm2++sWeZ5ebi4qLXXntN06ZN0x133KF//vOf8vb2tu3PyMhQcHCw067ZWbRokRYuXKigoCDNmzev1NNazuqPP098fX118OBBh7wtAmGnGtWqVUtHjhwpdZW6JJ06dUphYWH6+eefa7iy6lNYWKiNGzfqjTfecOqw4+LiopCQEHXu3LnEwvLfu97iQ9S8Vq1aadq0aXr44YclSZ9++qmio6P1888/y8XFuR8FWKtWLZ08eVKNGzeWJPXp00cDBw7UX//6V0nS2bNnFRYWpkuXLtmzzHL77RfmhQsXNHToUHl6eur999+3/cJ09rDj4uIiLy8vRUREyNXV9Zr9nPERLX8MO3Xq1NGhQ4ccMuywZqca3XTTTdcNO4cPH1ajRo1quKrq5erqqmHDhjn1AlBJmjx5st566y2dOXNG48aN0wMPPOA0d0n+M0tJSdGgQYNsryMiImSxWJSamurUd02WpMDAQJ05c0aNGzdWfn6+Dhw4oLlz59r2X7p0qcTl2s6kbdu22rt3r0aPHq3u3bvr7bfftl2h5cxiY2ONvd2DxWIpMTZHHSszO9XokUce0Y4dO7R3794SV179/PPP6tGjh26//Xa98sordqoQ15OXl6f169frjTfe0BdffKHo6GhNmDBBAwYMcNh/0H92rq6uSk9PV4MGDWxtderU0eHDh9WsWTM7VlZ5kydP1qFDh7Rw4UJt2LBBq1atUmpqqjw8PCRJa9as0dKlS7V37147V1o+f5wdsFqtmjFjhl588UUtXLhQ999/v1PP7JjMxcVFAwcOtC2K37hxo+64445ipyElx5i1IuxUo4yMDHXp0kWurq6Ki4uz3bb++PHjWrZsmQoLC3XgwAEFBgbauVLcyPfff6/ExEStXr1aV69e1dGjR+Xj42PvsvAHf/zhK5X+A9gRfviW13/+8x+NGDFCu3btko+Pj1atWqXhw4fb9vfv31+9evXS888/b8cqy+9ajzBZt26dHnroId1+++3697//TdhxQOPGjStTv5UrV1ZzJTdG2Klm33//vSZPnqyPP/7YtvbDYrEoMjJSy5Ytc/r/bf5ZnDt3TitXrlRiYqLy8/N1/Phxwo4DcqYfvhWVk5MjHx+fEus/Ll68KB8fH9tMj7O43qL5gwcPatiwYTp37hxhB5VC2KkhP/74o06dOiWr1apWrVqpbt269i4JN/D701i7du3S4MGDNW7cOEVFRTn9YlfAUSQlJdmeeF6aCxcu6MMPP1RsbGwNVwaTEHaAUvzlL3/RunXr1LhxY40fP14xMTGqX7++vcsCAFQAYQcohYuLi5o0aaLOnTtfdzGyM679AIA/Gy49B0ph8uWiAPBnw8wOAAAwGqssAQCA0Qg7AADAaIQdAABgNMIOAAAwGmEHgFMYO3asLBaLFixYUKx9w4YNXDkH4LoIOwCcRq1atbRw4UL9+OOP9i4FgBMh7ABwGhEREQoKCtL8+fOv2ef//u//dMstt8jT01NNmzbVkiVLiu1v2rSp/va3vyk2NlY+Pj4KCQnRBx98oKysLA0dOlQ+Pj7q0KGD9u3bV93DAVBDCDsAnIarq6vmzZunV199VefPny+xf//+/br33ns1atQoff3115ozZ45mzpypxMTEYv1eeukl9e7dW1999ZWio6P14IMPKjY2Vg888IAOHDigFi1aKDY2VtyGDDADNxUE4BTGjh2r7OxsbdiwQeHh4WrXrp1WrFihDRs2aPjw4bJarYqJiVFWVpY++eQT2/umT5+uDz/8UEePHpX068zObbfdpjfffFOSlJ6erkaNGmnmzJmKj4+XJO3evVvh4eFKS0tTUFBQzQ8WQJViZgeA01m4cKFWrVqlY8eOFWs/duyYevfuXaytd+/eOnnypAoLC21tHTp0sH0dGBgoSQoLCyvRlpmZWeW1A6h5hB0ATqdv376KjIzUjBkzKvR+d3d329e/XclVWltRUVElqgTgKHgQKACntGDBAnXq1EmtW7e2tbVt21aff/55sX6ff/65QkND5erqWtMlAnAQhB0ATiksLEwxMTF65ZVXbG1PPvmkunfvrueee0733XefkpOT9fe//13Lly+3Y6UA7I3TWACcVnx8fLFTTV26dNE777yjdevWqX379po1a5bi4+M1duxY+xUJwO64GgsAABiNmR0AAGA0wg4AADAaYQcAABiNsAMAAIxG2AEAAEYj7AAAAKMRdgAAgNEIOwAAwGiEHQAAYDTCDgAAMBphBwAAGI2wAwAAjPb/AR3fQqJgwWPWAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Límit elàstic')\n",
    "plt.ylabel('σe [MPa]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El límit elàstic del titani, juntament amb la seva baixa densitat, justifiquen el seu ús a estructures aeroespacials, ulleres ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resistència al trencament"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'R  [MPa]')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Resistència al trencament')\n",
    "plt.ylabel('R  [MPa]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Allargament"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ε  [%]')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Allargament')\n",
    "plt.ylabel('ε  [%]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Molts d'aquest metalls són molt dúctils, degut a la possibilitat d'una alta deformàció plàstica"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Duresa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'HB  [MPa]')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Duresa')\n",
    "plt.ylabel('HB  [MPa]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resistivitat elèctrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'ρ  [10⁻⁹·Ω·m]')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='bar',x='Nom',y='Resistivitat')\n",
    "plt.ylabel('ρ  [10⁻⁹·Ω·m]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La baixa resistivitat del coure i l'alumini, juntament amb la seva ductibilitat, justifiquen el seu ús a cables elèctrics. L'alumini és molt més lleuger, per això s'utilitza a xarxes d'alta tensió, alleugerant la càrrega de l'estructura de la torre."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Efecte de la densitat en la propietat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Relació resistència mecànica / pes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nom</th>\n",
       "      <th>Densitat</th>\n",
       "      <th>Punt de fusió</th>\n",
       "      <th>Conductivitat tèrmica</th>\n",
       "      <th>Dilatació tèrmica</th>\n",
       "      <th>Mòdul elàstic</th>\n",
       "      <th>Límit elàstic</th>\n",
       "      <th>Resistència al trencament</th>\n",
       "      <th>Allargament</th>\n",
       "      <th>Duresa</th>\n",
       "      <th>Resistivitat</th>\n",
       "      <th>Relació Resistència/pes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cu</td>\n",
       "      <td>8.960</td>\n",
       "      <td>1084.62</td>\n",
       "      <td>401.0</td>\n",
       "      <td>16.5</td>\n",
       "      <td>110</td>\n",
       "      <td>69.00</td>\n",
       "      <td>220.0</td>\n",
       "      <td>45</td>\n",
       "      <td>874.0</td>\n",
       "      <td>16.78</td>\n",
       "      <td>7.700893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Al</td>\n",
       "      <td>2.700</td>\n",
       "      <td>660.32</td>\n",
       "      <td>237.0</td>\n",
       "      <td>23.1</td>\n",
       "      <td>70</td>\n",
       "      <td>17.00</td>\n",
       "      <td>55.0</td>\n",
       "      <td>25</td>\n",
       "      <td>245.0</td>\n",
       "      <td>28.20</td>\n",
       "      <td>6.296296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Mg</td>\n",
       "      <td>1.738</td>\n",
       "      <td>650.00</td>\n",
       "      <td>156.0</td>\n",
       "      <td>24.8</td>\n",
       "      <td>45</td>\n",
       "      <td>41.00</td>\n",
       "      <td>165.0</td>\n",
       "      <td>6</td>\n",
       "      <td>260.0</td>\n",
       "      <td>43.90</td>\n",
       "      <td>23.590334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ti</td>\n",
       "      <td>4.506</td>\n",
       "      <td>1670.00</td>\n",
       "      <td>21.9</td>\n",
       "      <td>8.6</td>\n",
       "      <td>116</td>\n",
       "      <td>240.00</td>\n",
       "      <td>330.0</td>\n",
       "      <td>30</td>\n",
       "      <td>716.0</td>\n",
       "      <td>420.00</td>\n",
       "      <td>53.262317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pb</td>\n",
       "      <td>11.340</td>\n",
       "      <td>327.46</td>\n",
       "      <td>35.3</td>\n",
       "      <td>28.9</td>\n",
       "      <td>16</td>\n",
       "      <td>3.50</td>\n",
       "      <td>19.6</td>\n",
       "      <td>50</td>\n",
       "      <td>38.3</td>\n",
       "      <td>208.00</td>\n",
       "      <td>0.308642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Sn</td>\n",
       "      <td>7.365</td>\n",
       "      <td>231.93</td>\n",
       "      <td>66.8</td>\n",
       "      <td>22.0</td>\n",
       "      <td>50</td>\n",
       "      <td>2.55</td>\n",
       "      <td>34.3</td>\n",
       "      <td>40</td>\n",
       "      <td>350.0</td>\n",
       "      <td>115.00</td>\n",
       "      <td>0.346232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Zn</td>\n",
       "      <td>7.140</td>\n",
       "      <td>419.53</td>\n",
       "      <td>116.0</td>\n",
       "      <td>30.2</td>\n",
       "      <td>108</td>\n",
       "      <td>7.00</td>\n",
       "      <td>117.0</td>\n",
       "      <td>32</td>\n",
       "      <td>412.0</td>\n",
       "      <td>59.00</td>\n",
       "      <td>0.980392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Ni</td>\n",
       "      <td>8.908</td>\n",
       "      <td>1455.00</td>\n",
       "      <td>90.9</td>\n",
       "      <td>13.4</td>\n",
       "      <td>200</td>\n",
       "      <td>138.00</td>\n",
       "      <td>483.0</td>\n",
       "      <td>40</td>\n",
       "      <td>700.0</td>\n",
       "      <td>69.30</td>\n",
       "      <td>15.491693</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Fe</td>\n",
       "      <td>7.874</td>\n",
       "      <td>1538.00</td>\n",
       "      <td>80.4</td>\n",
       "      <td>11.8</td>\n",
       "      <td>211</td>\n",
       "      <td>130.00</td>\n",
       "      <td>260.0</td>\n",
       "      <td>45</td>\n",
       "      <td>490.0</td>\n",
       "      <td>96.10</td>\n",
       "      <td>16.510033</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Nom  Densitat  Punt de fusió  Conductivitat tèrmica  Dilatació tèrmica  \\\n",
       "0  Cu     8.960        1084.62                  401.0               16.5   \n",
       "1  Al     2.700         660.32                  237.0               23.1   \n",
       "2  Mg     1.738         650.00                  156.0               24.8   \n",
       "3  Ti     4.506        1670.00                   21.9                8.6   \n",
       "4  Pb    11.340         327.46                   35.3               28.9   \n",
       "5  Sn     7.365         231.93                   66.8               22.0   \n",
       "6  Zn     7.140         419.53                  116.0               30.2   \n",
       "7  Ni     8.908        1455.00                   90.9               13.4   \n",
       "8  Fe     7.874        1538.00                   80.4               11.8   \n",
       "\n",
       "   Mòdul elàstic  Límit elàstic  Resistència al trencament  Allargament  \\\n",
       "0            110          69.00                      220.0           45   \n",
       "1             70          17.00                       55.0           25   \n",
       "2             45          41.00                      165.0            6   \n",
       "3            116         240.00                      330.0           30   \n",
       "4             16           3.50                       19.6           50   \n",
       "5             50           2.55                       34.3           40   \n",
       "6            108           7.00                      117.0           32   \n",
       "7            200         138.00                      483.0           40   \n",
       "8            211         130.00                      260.0           45   \n",
       "\n",
       "   Duresa  Resistivitat  Relació Resistència/pes  \n",
       "0   874.0         16.78                 7.700893  \n",
       "1   245.0         28.20                 6.296296  \n",
       "2   260.0         43.90                23.590334  \n",
       "3   716.0        420.00                53.262317  \n",
       "4    38.3        208.00                 0.308642  \n",
       "5   350.0        115.00                 0.346232  \n",
       "6   412.0         59.00                 0.980392  \n",
       "7   700.0         69.30                15.491693  \n",
       "8   490.0         96.10                16.510033  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho=df['Densitat']\n",
    "df[\"Relació Resistència/pes\"]= df[\"Límit elàstic\"].div(other = rho) \n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El titani és el que presenta de llarg la millor característica, com ja comentaven abans."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Producte resistivitat·densitat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Nom</th>\n",
       "      <th>Densitat</th>\n",
       "      <th>Punt de fusió</th>\n",
       "      <th>Conductivitat tèrmica</th>\n",
       "      <th>Dilatació tèrmica</th>\n",
       "      <th>Mòdul elàstic</th>\n",
       "      <th>Límit elàstic</th>\n",
       "      <th>Resistència al trencament</th>\n",
       "      <th>Allargament</th>\n",
       "      <th>Duresa</th>\n",
       "      <th>Resistivitat</th>\n",
       "      <th>Relació Resistència/pes</th>\n",
       "      <th>Producte Resistivitat·densitat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Cu</td>\n",
       "      <td>8.960</td>\n",
       "      <td>1084.62</td>\n",
       "      <td>401.0</td>\n",
       "      <td>16.5</td>\n",
       "      <td>110</td>\n",
       "      <td>69.00</td>\n",
       "      <td>220.0</td>\n",
       "      <td>45</td>\n",
       "      <td>874.0</td>\n",
       "      <td>16.78</td>\n",
       "      <td>7.700893</td>\n",
       "      <td>150.3488</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Al</td>\n",
       "      <td>2.700</td>\n",
       "      <td>660.32</td>\n",
       "      <td>237.0</td>\n",
       "      <td>23.1</td>\n",
       "      <td>70</td>\n",
       "      <td>17.00</td>\n",
       "      <td>55.0</td>\n",
       "      <td>25</td>\n",
       "      <td>245.0</td>\n",
       "      <td>28.20</td>\n",
       "      <td>6.296296</td>\n",
       "      <td>76.1400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Mg</td>\n",
       "      <td>1.738</td>\n",
       "      <td>650.00</td>\n",
       "      <td>156.0</td>\n",
       "      <td>24.8</td>\n",
       "      <td>45</td>\n",
       "      <td>41.00</td>\n",
       "      <td>165.0</td>\n",
       "      <td>6</td>\n",
       "      <td>260.0</td>\n",
       "      <td>43.90</td>\n",
       "      <td>23.590334</td>\n",
       "      <td>76.2982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Ti</td>\n",
       "      <td>4.506</td>\n",
       "      <td>1670.00</td>\n",
       "      <td>21.9</td>\n",
       "      <td>8.6</td>\n",
       "      <td>116</td>\n",
       "      <td>240.00</td>\n",
       "      <td>330.0</td>\n",
       "      <td>30</td>\n",
       "      <td>716.0</td>\n",
       "      <td>420.00</td>\n",
       "      <td>53.262317</td>\n",
       "      <td>1892.5200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Pb</td>\n",
       "      <td>11.340</td>\n",
       "      <td>327.46</td>\n",
       "      <td>35.3</td>\n",
       "      <td>28.9</td>\n",
       "      <td>16</td>\n",
       "      <td>3.50</td>\n",
       "      <td>19.6</td>\n",
       "      <td>50</td>\n",
       "      <td>38.3</td>\n",
       "      <td>208.00</td>\n",
       "      <td>0.308642</td>\n",
       "      <td>2358.7200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Sn</td>\n",
       "      <td>7.365</td>\n",
       "      <td>231.93</td>\n",
       "      <td>66.8</td>\n",
       "      <td>22.0</td>\n",
       "      <td>50</td>\n",
       "      <td>2.55</td>\n",
       "      <td>34.3</td>\n",
       "      <td>40</td>\n",
       "      <td>350.0</td>\n",
       "      <td>115.00</td>\n",
       "      <td>0.346232</td>\n",
       "      <td>846.9750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Zn</td>\n",
       "      <td>7.140</td>\n",
       "      <td>419.53</td>\n",
       "      <td>116.0</td>\n",
       "      <td>30.2</td>\n",
       "      <td>108</td>\n",
       "      <td>7.00</td>\n",
       "      <td>117.0</td>\n",
       "      <td>32</td>\n",
       "      <td>412.0</td>\n",
       "      <td>59.00</td>\n",
       "      <td>0.980392</td>\n",
       "      <td>421.2600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Ni</td>\n",
       "      <td>8.908</td>\n",
       "      <td>1455.00</td>\n",
       "      <td>90.9</td>\n",
       "      <td>13.4</td>\n",
       "      <td>200</td>\n",
       "      <td>138.00</td>\n",
       "      <td>483.0</td>\n",
       "      <td>40</td>\n",
       "      <td>700.0</td>\n",
       "      <td>69.30</td>\n",
       "      <td>15.491693</td>\n",
       "      <td>617.3244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Fe</td>\n",
       "      <td>7.874</td>\n",
       "      <td>1538.00</td>\n",
       "      <td>80.4</td>\n",
       "      <td>11.8</td>\n",
       "      <td>211</td>\n",
       "      <td>130.00</td>\n",
       "      <td>260.0</td>\n",
       "      <td>45</td>\n",
       "      <td>490.0</td>\n",
       "      <td>96.10</td>\n",
       "      <td>16.510033</td>\n",
       "      <td>756.6914</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Nom  Densitat  Punt de fusió  Conductivitat tèrmica  Dilatació tèrmica  \\\n",
       "0  Cu     8.960        1084.62                  401.0               16.5   \n",
       "1  Al     2.700         660.32                  237.0               23.1   \n",
       "2  Mg     1.738         650.00                  156.0               24.8   \n",
       "3  Ti     4.506        1670.00                   21.9                8.6   \n",
       "4  Pb    11.340         327.46                   35.3               28.9   \n",
       "5  Sn     7.365         231.93                   66.8               22.0   \n",
       "6  Zn     7.140         419.53                  116.0               30.2   \n",
       "7  Ni     8.908        1455.00                   90.9               13.4   \n",
       "8  Fe     7.874        1538.00                   80.4               11.8   \n",
       "\n",
       "   Mòdul elàstic  Límit elàstic  Resistència al trencament  Allargament  \\\n",
       "0            110          69.00                      220.0           45   \n",
       "1             70          17.00                       55.0           25   \n",
       "2             45          41.00                      165.0            6   \n",
       "3            116         240.00                      330.0           30   \n",
       "4             16           3.50                       19.6           50   \n",
       "5             50           2.55                       34.3           40   \n",
       "6            108           7.00                      117.0           32   \n",
       "7            200         138.00                      483.0           40   \n",
       "8            211         130.00                      260.0           45   \n",
       "\n",
       "   Duresa  Resistivitat  Relació Resistència/pes  \\\n",
       "0   874.0         16.78                 7.700893   \n",
       "1   245.0         28.20                 6.296296   \n",
       "2   260.0         43.90                23.590334   \n",
       "3   716.0        420.00                53.262317   \n",
       "4    38.3        208.00                 0.308642   \n",
       "5   350.0        115.00                 0.346232   \n",
       "6   412.0         59.00                 0.980392   \n",
       "7   700.0         69.30                15.491693   \n",
       "8   490.0         96.10                16.510033   \n",
       "\n",
       "   Producte Resistivitat·densitat  \n",
       "0                        150.3488  \n",
       "1                         76.1400  \n",
       "2                         76.2982  \n",
       "3                       1892.5200  \n",
       "4                       2358.7200  \n",
       "5                        846.9750  \n",
       "6                        421.2600  \n",
       "7                        617.3244  \n",
       "8                        756.6914  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"Producte Resistivitat·densitat\"]= df[\"Resistivitat\"].mul(other = rho) \n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per a un cable de resistència $R$, llargada $L$ i secció fixades, la massa del cable té l'expressió, en funció de la resistivitat $\\rho$ i densitat $d$ del material amb que està fet:   \n",
    "$M = \\frac{\\rho}{R} · L^2·d$   \n",
    "Per tant, quan més baix el producte $\\rho · d$ més lleuger el cable i menys esforç ha de suportar l'estructura que manté elevat el cable. Com veieu, l'alumni és millor candidat que el coure en aquest cas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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