thermohub/preliminaries/First_Notebook_HW1_CHEG231.ipynb
2024-08-29 16:45:31 -04:00

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Text

{
"cells": [
{
"cell_type": "markdown",
"id": "dfad842a-3891-400f-bbec-1959db1f0ded",
"metadata": {},
"source": [
"# My first Jupyter Notebook\n",
"\n",
"The goal of this notebook is to calcuate the molar volume of a gas using the van der Waals equation of state.\n",
"\n",
"$$ (P + a/V^2)(V-b) = RT$$\n",
"\n",
"$$ f(V) = RT - (P +a/V^2)(V-b) $$\n",
"\n",
"$ V $ is the molar volume (m^3/mol)"
]
},
{
"cell_type": "code",
"execution_count": 81,
"id": "3517ba18-e223-47d5-bc9a-d97f4dde4843",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.00488274]\n"
]
}
],
"source": [
"import scipy.optimize as opt\n",
"\n",
"\"\"\"\n",
"Constants for the vdW equation for CO2\n",
"\"\"\"\n",
"\n",
"a = 0.3658 # Pa m^6/mol^2\n",
"b = 4.286e-5 # m^3/mol\n",
"\n",
"\"\"\"\n",
"Other parameters\n",
"\"\"\"\n",
"\n",
"R = 8.314 # J/mol.K R = the ideal gas constant\n",
"\n",
"P = 5e5 # Pa, pressure\n",
"T = 300 # K, temperature\n",
"\n",
"def vdW(V):\n",
" x = R*T - (P + a/V**2)*(V-b)\n",
" return x\n",
"\n",
"V_vdw = opt.fsolve(vdW, R*T/P)\n",
"\n",
"print(V_vdw)\n",
"# has units of mol/m3"
]
},
{
"cell_type": "markdown",
"id": "0036f5cc-4c1b-4ac2-bd9c-fbd501ec8850",
"metadata": {},
"source": [
"We are going to compare the vdW volume to the one predicted by the ideal gas"
]
},
{
"cell_type": "code",
"execution_count": 82,
"id": "86b52e50-7e13-4f9c-866a-84fc1cb6e673",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0049884\n",
"[-0.02118087]\n"
]
}
],
"source": [
"V_ideal = R*T/P\n",
"print(V_ideal)\n",
"print((V_vdw-V_ideal)/V_ideal)"
]
},
{
"cell_type": "markdown",
"id": "75391bd7-7390-4ffc-9c1b-c7425f92fb76",
"metadata": {},
"source": [
"---\n",
"# Additional calculations for the homework:\n",
"\n",
"1. What is the molar volume of CO2 for 150K, 200K, 250K, and 350K calculated using the van der Waals equation?\n",
"2. Make a plot of the molar volume of CO2 using the van der Waals equation between 150K and 350K"
]
},
{
"cell_type": "code",
"execution_count": 83,
"id": "ca417379-e444-4ae2-99e4-048319282dfc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.00221285 0.00313854 0.0040198 0.00488274 0.00573607]\n",
"[0.0024942 0.0033256 0.004157 0.0049884 0.0058198]\n",
"[-0.11280207 -0.0562481 -0.03300422 -0.02118087 -0.01438723]\n"
]
}
],
"source": [
"# First, we'll need numpy\n",
"\n",
"import numpy as np\n",
"\n",
"# then make an array of temperatures\n",
"\n",
"T = np.array([150, 200, 250, 300, 350])\n",
"\n",
"# and caculate (now an array) of molar volumes\n",
"\n",
"V_ideal = R*T/P\n",
"V_vdw = opt.fsolve(vdW, R*T/P)\n",
"\n",
"print(V_vdw)\n",
"print(V_ideal)\n",
"print((V_vdw-V_ideal)/V_ideal)"
]
},
{
"cell_type": "markdown",
"id": "0e365e83-d431-4ab3-b0a3-f80b78658952",
"metadata": {},
"source": [
"We can make a table of the results:"
]
},
{
"cell_type": "code",
"execution_count": 84,
"id": "a717f6d6-4a99-46d0-af7c-d99e3d996177",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[ 1.50000000e+02 2.21284907e-03 2.49420000e-03 -1.12802074e-01]\n",
" [ 2.00000000e+02 3.13854133e-03 3.32560000e-03 -5.62480969e-02]\n",
" [ 2.50000000e+02 4.01980148e-03 4.15700000e-03 -3.30042156e-02]\n",
" [ 3.00000000e+02 4.88274136e-03 4.98840000e-03 -2.11808682e-02]\n",
" [ 3.50000000e+02 5.73606922e-03 5.81980000e-03 -1.43872263e-02]]\n"
]
}
],
"source": [
"# Transpose and stack the arrays\n",
"\n",
"# First I have to reshape the array into a 1x5 array:\n",
"T = T.reshape(1,5)\n",
"V_vdw = V_vdw.reshape(1,5)\n",
"V_ideal = V_ideal.reshape(1,5)\n",
"\n",
"# I'll also include the differences\n",
"V_diff = (V_vdw-V_ideal)/V_ideal\n",
"V_diff = V_diff.reshape(1,5)\n",
"\n",
"# Now we're ready to transpose the array\n",
"table = np.hstack((T.T, V_vdw.T, V_ideal.T, V_diff.T))\n",
"\n",
"# and print the table\n",
"print(table)"
]
},
{
"cell_type": "markdown",
"id": "92fad8ed-b458-4c89-80f9-31da065969ac",
"metadata": {},
"source": [
"What would happen if we printed the table without transposed arrays?"
]
},
{
"cell_type": "code",
"execution_count": 85,
"id": "0d689b0e-f0c9-4f4e-96ce-5c6224374430",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[150 200 250 300 350]] [[0.00221285 0.00313854 0.0040198 0.00488274 0.00573607]] [[0.0024942 0.0033256 0.004157 0.0049884 0.0058198]] [[-0.11280207 -0.0562481 -0.03300422 -0.02118087 -0.01438723]]\n",
"\n",
"[[ 1.50000000e+02 2.00000000e+02 2.50000000e+02 3.00000000e+02\n",
" 3.50000000e+02 2.21284907e-03 3.13854133e-03 4.01980148e-03\n",
" 4.88274136e-03 5.73606922e-03 2.49420000e-03 3.32560000e-03\n",
" 4.15700000e-03 4.98840000e-03 5.81980000e-03 -1.12802074e-01\n",
" -5.62480969e-02 -3.30042156e-02 -2.11808682e-02 -1.43872263e-02]]\n"
]
}
],
"source": [
"print(T, V_vdw, V_ideal, V_diff)\n",
"print()\n",
"print(np.hstack((T, V_vdw, V_ideal, V_diff)))"
]
},
{
"cell_type": "markdown",
"id": "520b17ef-813f-4ace-b2c7-416c3d205164",
"metadata": {},
"source": [
"This makes one long row array!\n",
"\n",
"Next, we'll make a plot."
]
},
{
"cell_type": "code",
"execution_count": 86,
"id": "2c33c8eb-3eb2-49b1-99a1-0249d216efa8",
"metadata": {},
"outputs": [],
"source": [
"# Make many more points for T\n",
"\n",
"T = np.arange(150, 450, 1)\n",
"\n",
"# Recalculate V_vdw and V_ideal for those points\n",
"\n",
"V_vdw = opt.fsolve(vdW, R*T/P)\n",
"V_ideal = R*T/P\n"
]
},
{
"cell_type": "code",
"execution_count": 87,
"id": "15bf663f-0c1f-4870-87b9-bbaf9b2f38b5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10843f500>"
]
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Create a figure. We need to load matplotlib\n",
"\n",
"import matplotlib.pyplot as plt\n",
"\n",
"fig, ax = plt.subplots()\n",
"plt.title('Molar volume versus temperature of CO2, van der Waals EOS')\n",
"ax.plot(T,V_vdw, label='V_vdw')\n",
"ax.plot(T,V_ideal, label='V_ideal')\n",
"ax.set(xlabel='Temperature, K',ylabel='Molar volume, m^3/mol')\n",
"ax.legend(loc='best')\n",
"#plt.show()"
]
},
{
"cell_type": "markdown",
"id": "fd7a68ed-ba69-4eb0-ae59-e949f57645bb",
"metadata": {},
"source": [
"Let's plot the difference between the vdw and ideal equations of state?"
]
},
{
"cell_type": "code",
"execution_count": 88,
"id": "a501cef5-3fb4-4c0f-a162-67028ff898aa",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0.5, 0, 'Temperature, K'), Text(0, 0.5, 'Molar volume, m^3/mol')]"
]
},
"execution_count": 88,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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U1tbWolWrVkKj0RS7zedJ7p5W0E46dOggXn31Ve3ykn6Ln4777t27wszMrNA/QBISEoSJiYlO2yn4/p5u4127dhX16tXTvh8xYoSoVq1asXEbYtWqVQKAmD9/vl7lC05QPPkPkqdt2bJFABCzZs0qtsy2bduEkZFRod/BZ+Fl2VISQpTp9jZt2oRq1arhlVdeQV5envbVuHFjODk5FbrU0LBhw0Knejdt2oR27drBxcVFZxsvv/wyACAyMlKnfLdu3WBsbKyzTQDay0kXL17ElStX8O6778LU1LTIuLOysrBz5068+uqrMDc319lv165dkZWVVeSl3qd16NBBe/8iABgbG6Nv3764fPmy9lS0ocdX3H7i4uIQHx+PrKws7N+/H126dEG7du0QEREBANixYwdMTEy0p9e3bduGvLw8DBo0SGe/pqamCAkJ0X43ly9fxvnz57X3Uj5dF0lJSbhw4YJOPD169NB5//R38CyvvfaazntD2lFcXBzefPNNODk5wdjYGCqVCiEhIQBQ6DKIPu7fv49x48ahTp06UCqVUCqVsLS0xIMHD4rc3rOOfffu3QBQ6N7UPn36QKks3e3Cu3fvLratPUnf77w0x62v7t2767z39fUF8Pjv9unlT7aXXbt2wcLCAq+//rpOuYLLYTt37ixxv2vXrkXLli1haWkJpVIJlUqFxYsXF3ks7du3h62t7TOPRalUYsCAAVi3bh3S09MBPL4n6ffff0fPnj1RvXp1bexPxlrgjTfegIWFxTNjN4RCoUDXrl11YqxTpw6cnZ3h7++vXW5nZ4caNWro1PHz/BZFREQgPz8fH3zwQYnxpaSkYNiwYXB3d9d+Dx4eHgBK/vs8ePAgMjIy8P7775frKPf58+cjICAApqam2vh27txZ6jYfFRWFR48eFfru3d3d0b59+0LfvUKhwCuvvKKzrGHDhjrfU9OmTXHv3j30798fGzdu1PuS9otSkEcU9z2dOHECffr0QfPmzXUuqeuDAypK4cGDB0hLS0ODBg3KbJu3bt3CvXv3oFari/z86UZZ1AijW7du4Z9//inymn1R2yj4QS1gYmIC4PHgDADae7RKGm2YlpaGvLw8/Pzzz/j555/12m9RnJycil2WlpYGNzc3g4+vKAUjnHfs2AEvLy/k5uaiffv2uHXrFqZPn679rGXLltobw2/dugUAaNKkSZHbNDIy0ik3duxYjB07Vq8Yn/UdlKRgWP2T9G1H9+/fR+vWrWFqaoovvvgC3t7eMDc3R2JiInr37q3X/p/25ptvYufOnZg8eTKaNGkCa2trbQda1PaedexpaWkACrcNpVJZaF19paWlldjWCuj7nQOGH7e+nh5FX/CdFrU8KytL+77gGJ/uMGrUqAGlUqmt16KsW7cOffr0wRtvvIFPPvkETk5OUCqVmDdvXpEj9QwZ6fjOO+/gu+++w6pVqzB06FBs27YNSUlJePvtt3ViVyqVhW60VygUcHJyKjF2Q5mbmxf6R2vBtBZPe7qOn+e3SJ/fVY1Gg9DQUNy8eROTJ09GgwYNYGFhAY1Gg+bNm5fYrvTZ/vOaPXs2xowZg2HDhmH69Omwt7eHsbExJk+eXOrkruC7LapNubi4aP/xXaCo78/ExETnexo4cCDy8vLw66+/4rXXXoNGo0GTJk3wxRdfoFOnTgbFV7NmTQBAfHy8weV9fHyKLFNwv2FRgySio6PRqVMn1K1bF5s3b9b+PuqLyV0p/Pvvv8jPzy/TaTYKbirfunVrkZ9bWVnpvC8q07e3t0fDhg3x5ZdfFrkNFxcXg2Iq+IEt6SZOW1tbGBsbY+DAgcX+S9TLy+uZ+yq4obSoZQUdeVkcn5ubG7y9vbFjxw54enoiKCgI1apVQ4cOHfD+++/j8OHDOHTokHaASsF+AeCvv/7S/su5KAXlJkyYgN69exdZpl69es+MUV/FtQF92tGuXbtw8+ZN7NmzR3u2DsAzb1ovTnp6OjZt2oQpU6Zg/Pjx2uXZ2dm4c+dOqbZZ8L0nJyfD1dVVuzwvL6/UnXz16tVLbGsF9P3Oy+O4n1f16tVx+PBhCCF02khKSgry8vK0x1aUP/74A15eXli9erXOusUNxDDkzJCfnx+aNm2KpUuXYujQoVi6dClcXFwQGhqqE3teXh5u376tk+AJIZCcnFxssg1A29E/HWt5nK15nt+iJ39Xixv5ePbsWZw6dQrLli1DWFiYdnnBSMyS6PO7DTyur4KzqE/Sp77++OMPtG3bFvPmzdNZnpmZ+cx1i1Pw956UlFTos5s3b5bYbkvy9ttv4+2338aDBw+wd+9eTJkyBd27d8fFixdL/Nt+WlBQEOzs7LBx40bMmDHjmW2/U6dOWLhwITZs2KDz2/CkDRs2QKlUFsoloqOj0bFjR3h4eGD79u2wsbHRO84CTO4MlJCQgLFjx8LGxgZDhw4ts+12794dq1atQn5+Ppo1a1bqbWzevBm1a9fW61LJs3h7e6N27dpYsmQJPv744yL/5WBubo527dohOjoaDRs2LPaM0bPs3LkTt27d0l4uy8/Px+rVq1G7dm3tv0D1Pb5nnf3q2LEj1qxZA3d3d+0lLm9vb9SsWROff/45cnNzdeYw7Ny5M5RKJa5cuVLoMuiT6tWrh7p16+LUqVP46quvDKuAMqJvOyr4YXr6O31yBLghFAoFhBCFtrdo0SKDJ98sUPCDt2LFCp2Ry2vWrNF7ROLT2rVrh7///rvItvYkfb/z8jju59WhQwesWbMGGzZswKuvvqpdvnz5cu3nxVEoFFCr1TodV3JycpGjZUvj7bffxvDhw7F//378888/+Pjjj3VuDenQoQO+/vpr/PHHHxg9erR2eXh4OB48eFBi7AUjPE+fPo3OnTtrl//9999lEvuTnue3NjQ0FMbGxpg3bx6Cg4OLLPM8f58tWrSAjY0N5s+fj379+hWbhHh6emLt2rXIzs7W7ictLQ0HDx4sdEWgqPieju306dOIiorSSVgNuRIRHBwMMzMz/PHHH3jjjTe0y69fv45du3YVus3AUBYWFnj55ZeRk5ODXr164dy5cwYldyqVCuPGjcO4ceMwffr0QlOhAI//AXXp0iW0bNkSr776Kvz8/DBz5kz07t270G1Uq1evxvbt2zFs2DCdKwcnT55Ex44d4ebmhoiIiFL35UzuSnD27FntvRQpKSnYt28fli5dCmNjY6xfv75M5+jp168fVqxYga5du+Kjjz5C06ZNoVKpcP36dezevRs9e/bU+aEuyn//+19ERESgRYsWGDlyJOrVq4esrCxcvXoVmzdvxvz58w0+VT9nzhy88soraN68OUaPHo2aNWsiISEB27Ztw4oVKwAAP/74I1q1aoXWrVtj+PDh8PT0RGZmJi5fvox//vlHex9NSezt7dG+fXtMnjwZFhYWmDt3Ls6fP68zHYq+x2dlZQUPDw9s3LgRHTp0gJ2dHezt7bU//h06dMDcuXORmpqKH374Qbv9Dh06YOnSpbC1tdVJJjw9PfHf//4XkyZNQlxcHLp06QJbW1vcunULR44cgYWFhfZM34IFC/Dyyy+jc+fOGDx4MFxdXXHnzh3ExsbixIkTOtOwlAd921GLFi1ga2uLYcOGYcqUKVCpVFixYgVOnTpVqv1aW1ujTZs2+Oabb7R1HRkZicWLF6NatWql2qavry8GDBiAH374ASqVCh07dsTZs2fx7bffPrPzKc5nn32Gv//+G+3bt8fnn38Oc3NzzJkzp9D0L/p+5+Vx3M9r0KBBmDNnDsLCwnD16lU0aNAA+/fvx1dffYWuXbvq/MPlaQVTLL3//vt4/fXXkZiYiOnTp8PZ2RmXLl167tj69++Pjz/+GP3790d2dnah+6s6deqEzp07Y9y4ccjIyEDLli1x+vRpTJkyBf7+/hg4cGCx23ZyckLHjh0xY8YM2NrawsPDAzt37sS6deueO+6nPc9vraenJyZOnIjp06fj0aNH6N+/P2xsbBATE4PU1FRMmzYNPj4+qF27NsaPHw8hBOzs7PDPP/8UujRZFEtLS3z33Xd477330LFjRwwZMgSOjo64fPkyTp06hV9++QXA40uWCxYswIABAzBkyBCkpaXh66+/1utvq3v37pg+fTqmTJmCkJAQXLhwAf/973/h5eWl8w+vZ/0WP6latWqYPHkyJk6ciEGDBqF///5IS0vDtGnTYGpqiilTpjwzrqcNGTIEZmZmaNmyJZydnZGcnIwZM2bAxsZG5yxwQTzPelrGJ598gtjYWEyZMgVHjhzBm2++qZ3EeO/evVi4cCGmTZuGli1bwtjYGOHh4ejUqROCg4MxZswYBAcHIzs7G//88w8WLlyIkJAQfPfdd9rtX7hwQfv3+eWXX+LSpUs6f3e1a9fWP+8waPhFFVEwiqfgpVarRY0aNURISIj46quvREpKSqF1nne0rBCPR2t9++23olGjRsLU1FRYWloKHx8fMXToUHHp0iVtOQ8PD9GtW7ciY799+7YYOXKk8PLyEiqVStjZ2YnAwEAxadIkcf/+fSHE/48e++abbwqtjyJGNkVFRYmXX35Z2NjYCBMTE1G7du1CI3fi4+PFO++8I1xdXYVKpRIODg6iRYsW4osvvigyzqf3+cEHH4i5c+eK2rVrC5VKJXx8fMSKFStKdXxCCLFjxw7h7+8vTExMCo2svHv3rjAyMhIWFhY6UwoUjMLs3bt3kXFu2LBBtGvXTlhbWwsTExPh4eEhXn/9dbFjxw6dcqdOnRJ9+vQRNWrUECqVSjg5OYn27dvrjLIqbkS2viMqi2tbQujfjg4ePCiCg4OFubm5cHBwEO+99544ceJEoZGF+o6WvX79unjttdeEra2tsLKyEl26dBFnz54tNCLTkGPPzs4WY8aMETVq1BCmpqaiefPmIioq6pmjPAsU1Z4PHDggmjdvLkxMTISTk5P45JNPxMKFCwtNyyCEft+5vsdt6GjZp+un4Ht4cnoVIYpuC2lpaWLYsGHC2dlZKJVK4eHhISZMmFBo5F5R9Thz5kzh6ekpTExMhK+vr/j111+LbAMFf7eGevPNNwUA0bJlyyI/f/TokRg3bpzw8PAQKpVKODs7i+HDh4u7d+/qlCtqtGdSUpJ4/fXXhZ2dnbCxsREDBgwQx44dK3K0rCG/zUX95ur7W1Sc5cuXiyZNmmj/Rv39/XVijImJEZ06dRJWVlbC1tZWvPHGGyIhIaFQmy5qShEhhNi8ebMICQkRFhYW2ul/nh6V+dtvvwlfX19hamoq/Pz8xOrVq/UaLZudnS3Gjh0rXF1dhampqQgICBAbNmwoct3ifouLi3vRokWiYcOGQq1WCxsbG9GzZ89Co4+L+/6ebqe//fabaNeunXB0dBRqtVq4uLiIPn36iNOnT+usZ29vL5o3b15oe8XZuHGj6Natm3BwcBBKpVI7jdP8+fNFdna2TtnU1FQxfvx44ePjo/2umzZtKn755Red/ufJOinu9WT7eBaFEGU87JOIiIioAoiJicFLL72ETZs2FRqJXpFxKhQiIiKqknbv3o3g4OBKldgBAM/cEREREVUiPHNHREREVIkwuSMiIiKqRJjcEREREVUiTO6IiIiIKhFOYiwxjUaDmzdvwsrKqlwf8kxERERlRwiBzMxMuLi46DxvWg6Y3Ens5s2bxT5fkIiIiOQtMTHR4Kc/lTcmdxIreJB7YmJiqR+pRERERC9WRkYG3N3dtf24nDC5k1jBpVhra2smd0RERBWMHG+pktdFYiIiIiJ6LkzuiIiIiCoRJndERERElQiTOyIiIqJKhMkdERERUSXC5I6IiIioEmFyR0RERFSJMLkjIiIiqkSY3BERERFVIkzuiIiIiCoRJndERERElQiTOyIiIqJKhMldJSWEwMnEe8jIypU6FCIiInqBmNxVUsP+OI5ecw7gn1M3pQ6FiIiIXiAmd5VUoIctAOCv49cljoSIiIheJCZ3lVSvxq4wNlIgOuEerty+L3U4RERE9IIwuaukalibIsTbAQAQzrN3REREVQaTu0rs9UA3AMC6EzeQrxESR0NEREQvApO7SqyDbw3YmKmQnJGFA5dTpQ6HiIiIXgAmd5WYidIYPRu7AODACiIioqqCyV0lV3Bpdtu5ZKQ/4px3RERElR2Tu0qugasNvB0tkZ2nwb+nk6QOh4iIiMoZk7tKTqFQaM/e/XU8UeJoiIiIqLwxuasCCua8O8E574iIiCo9JndVAOe8IyIiqjqY3FURnPOOiIioamByV0V08K2BauaP57yLvJgidThERERUTpjcVREmSmO8FvD47N2fhzmwgoiIqLJicleF9G/qDgDYfSEFyelZEkdDRERE5YHJXRVSp4YVmnjaIl8jsPYYz94RERFVRkzuqpj+TWsCAFYdTYSGAyuIiIgqHSZ3VUzXBs6wNlXixr1H2Hc5VepwiIiIqIwxuatiTFXG6P2/gRUrDydIHA0RERGVNSZ3VVC//w2s2BF7CymZHFhBRERUmTC5q4J8nKwRULMa8jQCf/GJFURERJUKk7sqql/BwIojHFhBRERUmTC5q6K6N3SGlYkSCXce4uCVNKnDISIiojLC5K6KMlcr0cvfFQCw4vA1iaMhIiKissLkrgob0NwDALA95haS0h9JHA0RERGVBSZ3VVg9Jys087JDvkbgT06LQkREVCkwuaviBgV7AgBWHklAdl6+tMEQERHRc2NyV8WFvuQIR2sTpN7PwdazyVKHQ0RERM+JyV0VpzI2wptNH997tzyKAyuIiIgqOiZ3hP7N3KEyVuD4tbs4eyNd6nCIiIjoOTC5I9SwMkWX+s4AgN959o6IiKhCY3JHAICw4MeXZjecvIF7D3MkjoaIiIhKi8kdAQACPWzh62yN7DwN1h7j82aJiIgqKiZ3BABQKBQY9L+zd78fuoZ8Pm+WiIioQmJyR1o9G7vA2vTx82Z3nU+ROhwiIiIqBSZ3pGWuVuLNZo/P3i3aFydxNERERFQaTO5IR1gLDyiNFDgcf4fTohAREVVATO5Ih7ONGbo1fDwtypL98RJHQ0RERIZickeFvNvKCwDw96mbuJWRJXE0REREZAgmd1RIQ7dqaOJpizyNwPKoq1KHQ0RERAZgckdFerdVLQDAisMJeJSTL3E0REREpC8md1SkTn6OqGlnjnsPcxF+gpMaExERVRSSJ3dz586Fl5cXTE1NERgYiH379pVYPjIyEoGBgTA1NUWtWrUwf/78QmXCw8Ph5+cHExMT+Pn5Yf369QbtNzc3F+PGjUODBg1gYWEBFxcXDBo0CDdv3tTZRtu2baFQKHRe/fr1K2VNyIuxkQJvt/QEACw5EA8NJzUmIiKqECRN7lavXo1Ro0Zh0qRJiI6ORuvWrfHyyy8jISGhyPLx8fHo2rUrWrdujejoaEycOBEjR45EeHi4tkxUVBT69u2LgQMH4tSpUxg4cCD69OmDw4cP673fhw8f4sSJE5g8eTJOnDiBdevW4eLFi+jRo0ehmIYMGYKkpCTta8GCBWVcS9J5I8gdViZKxN1+gD0XOakxERFRRaAQQkh2SqZZs2YICAjAvHnztMt8fX3Rq1cvzJgxo1D5cePG4e+//0ZsbKx22bBhw3Dq1ClERUUBAPr27YuMjAxs2bJFW6ZLly6wtbXFypUrS7VfADh69CiaNm2Ka9euoWbNmgAen7lr3Lgxfvjhh1LXQUZGBmxsbJCeng5ra+tSb6e8fPlvDH7dF4/mteyw6j/BUodDREQkC3LuvyU7c5eTk4Pjx48jNDRUZ3loaCgOHjxY5DpRUVGFynfu3BnHjh1Dbm5uiWUKtlma/QJAeno6FAoFqlWrprN8xYoVsLe3x0svvYSxY8ciMzOz+IOugN5p5QWVsQKH4u4gOuGu1OEQERHRM0iW3KWmpiI/Px+Ojo46yx0dHZGcnFzkOsnJyUWWz8vLQ2pqaollCrZZmv1mZWVh/PjxePPNN3Wy87feegsrV67Enj17MHnyZISHh6N3794lHnd2djYyMjJ0XnLmbGOGno1dAQDzI69IHA0RERE9i1LqABQKhc57IUShZc8q//Ryfbap735zc3PRr18/aDQazJ07V+ezIUOGaP+/fv36qFu3LoKCgnDixAkEBAQUGf+MGTMwbdq04g5PloaF1MJfx69je8wtXE65jzo1LKUOiYiIiIoh2Zk7e3t7GBsbFzpblpKSUuisWgEnJ6ciyyuVSlSvXr3EMgXbNGS/ubm56NOnD+Lj4xEREfHMa+oBAQFQqVS4dOlSsWUmTJiA9PR07SsxMbHEbcpBnRpW6OTnCCGAhXt59o6IiEjOJEvu1Go1AgMDERERobM8IiICLVq0KHKd4ODgQuW3b9+OoKAgqFSqEssUbFPf/RYkdpcuXcKOHTu0yWNJzp07h9zcXDg7OxdbxsTEBNbW1jqvimBYSG0AwProG0hO5yPJiIiIZEtIaNWqVUKlUonFixeLmJgYMWrUKGFhYSGuXr0qhBBi/PjxYuDAgdrycXFxwtzcXIwePVrExMSIxYsXC5VKJf766y9tmQMHDghjY2Mxc+ZMERsbK2bOnCmUSqU4dOiQ3vvNzc0VPXr0EG5ubuLkyZMiKSlJ+8rOzhZCCHH58mUxbdo0cfToUREfHy/+/fdf4ePjI/z9/UVeXp7edZCeni4AiPT09OeqyxfhjfkHhce4TeLLf2OkDoWIiEhScu6/JU3uhBBizpw5wsPDQ6jVahEQECAiIyO1n4WFhYmQkBCd8nv27BH+/v5CrVYLT09PMW/evELbXLt2rahXr55QqVTCx8dHhIeHG7Tf+Ph4AaDI1+7du4UQQiQkJIg2bdoIOzs7oVarRe3atcXIkSNFWlqaQccv58bxtF2xt4THuE3Cb/IWce9BjtThEBERSUbO/bek89yRvOfJeZoQAi//uA/nkzPxSed6+KBdHalDIiIikoSc+2/JHz9GFYdCodDee7f0QDyycvMljoiIiIiexuSODNK9oTPcbM2Qej8HK48U/Zg4IiIikg6TOzKI0tgIw9s+Pns3P/IKz94RERHJDJM7MtjrgW5wtjHFrYxsrD1+XepwiIiI6AlM7shgJkpj7b138/dcQU6eRuKIiIiIqACTOyqVvk3cUcPKBDfuPcK6Ezx7R0REJBdM7qhUTFXG+E+bWgCAOXsuIzefZ++IiIjkgMkdldpbzTxgb6lG4p1H2HjyptThEBEREZjc0XMwUxvjvdb/O3u3+zLyNZwPm4iISGpM7ui5DGzuAVtzFeJTH2DTaZ69IyIikhqTO3ouFiZK7dm7H3deQh7vvSMiIpIUkzt6bmEtPGFrrkLc7QfYwHvviIiIJMXkjp6bpYlSO+/djzsvcuQsERGRhJjcUZkYFOwJe0sTJN55hLXHOO8dERGRVJjcUZkwUxvjg3aPz979vOsSnzlLREQkESZ3VGb6N60JZxtTJKVnYeWRBKnDISIiqpKY3FGZMVUZY0T7OgCAObuv4FEOz94RERG9aEzuqEy9EegOdzszpN7PxvKoq1KHQ0REVOUwuaMypVYaYWT7ugCA+ZFXkJmVK3FEREREVQuTOypzr/q7opaDBe4+zMWve+OkDoeIiKhKYXJHZU5pbIRPO9cDAPy6Lx4pmVkSR0RERFR1MLmjctH5JSc0dq+GR7n5+GnnJanDISIiqjKY3FG5UCgUGP+yDwBg5ZFExN2+L3FEREREVQOTOyo3zWtVR3ufGsjXCHy3/aLU4RAREVUJTO6oXH3apR4UCuDfM0k4mXhP6nCIiIgqPSZ3VK58nKzR298NADBzSyyEEBJHREREVLkxuaNy93GoN9RKIxyKu4PIi7elDoeIiKhSY3JH5c61mhnCgj0AADM2n0e+hmfviIiIyguTO3ohPmhXBzZmKly4lYnVRxOlDoeIiKjSYnJHL0Q1czU+6vD4sWSzIy7wsWRERETlhMkdvTADmnvAy94CqfdzMG/PFanDISIiqpSY3NELo1YaYWJXXwDAov3xuH73ocQRERERVT5M7uiF6uhbA8G1qiMnT4NZWy9IHQ4REVGlo9Sn0E8//aT3BkeOHFnqYKjyUygU+Ky7L7r/vB//nLqJwS08EehhK3VYRERElYZC6DGrrJeXl34bUygQFxf33EFVJRkZGbCxsUF6ejqsra2lDueF+fSvU1hz7Dr8a1bDuuEtoFAopA6JiIhIb3Luv/U6cxcfH1/ecVAVMya0HjadTkJ0wj1sPHkTvfxdpQ6JiIioUniue+6EEHycFJWKo7UpPmhXBwDw1eZY3M/OkzgiIiKiyqFUyd3y5cvRoEEDmJmZwczMDA0bNsTvv/9e1rFRJfdeay94VDdHSmY2ft51SepwiIiIKgWDk7vZs2dj+PDh6Nq1K9asWYPVq1ejS5cuGDZsGL7//vvyiJEqKROlMT7v7gcAWLI/Hldu35c4IiIioopPrwEVT/Ly8sK0adMwaNAgneW//fYbpk6dyvvzDCTnGzJflLeXHsHuC7cR4u2AZW834eAKIiKSPTn33wafuUtKSkKLFi0KLW/RogWSkpLKJCiqWj5/5SWojY0QefE2dsSmSB0OERFRhWZwclenTh2sWbOm0PLVq1ejbt26ZRIUVS1e9hZ4t/Xj6Xamb4pBVm6+xBERERFVXHpNhfKkadOmoW/fvti7dy9atmwJhUKB/fv3Y+fOnUUmfUT6GNGuDtaduI6EOw+xcG8cRnbgPxSIiIhKw+Azd6+99hoOHz4Me3t7bNiwAevWrYO9vT2OHDmCV199tTxipCrAwkSpfe7snN2XcS3tgcQRERERVUwGD6igsiXnGzJfNCEEBiw+jAOX09DG2wG/cXAFERHJlJz7b4MvyxZISUlBSkoKNBqNzvKGDRs+d1BUNSkUCkzvWR9dftiHvRdvY9PpJLzSyEXqsIiIiCoUg5O748ePIywsDLGxsYWeTqFQKJCfz5vhqfRqOVji/Xa18cOOS/jvphiE1HOAtalK6rCIiIgqDIPvuXv77bfh7e2NgwcPIi4uDvHx8dpXXFxcecRIVcywkNrwsrfA7cxsfLvtgtThEBERVSgG33NnZWWF6Oho1KlTp7xiqlLkfM1eSgcvp+LNRYehUADr32+Jxu7VpA6JiIhIS879t8Fn7jp06IBTp06VRyxEWi3q2ONVf1cIAUxafwZ5+Zpnr0RERESG33O3aNEihIWF4ezZs6hfvz5UKt37oXr06FFmwVHVNrGrL3bG3sK5mxn4Leoa3m3lJXVIREREsmdwcnfw4EHs378fW7ZsKfQZB1RQWXKwMsH4l30xcf0ZzN5+AV0bOMHZxkzqsIiIiGTN4MuyI0eOxMCBA5GUlASNRqPzYmJHZa1fE3cE1KyGBzn5mLLxXKER2kRERKTL4OQuLS0No0ePhqOjY3nEQ6TDyEiBr3o3gNJIge0xt/DvmSSpQyIiIpI1g5O73r17Y/fu3eURC1GRfJys8X67x6Ozp2w8hzsPciSOiIiISL4MvufO29sbEyZMwP79+9GgQYNCAypGjhxZZsERFRjRrg62nU3GhVuZmPbPOfzYz1/qkIiIiGTJ4HnuvLyKH7GoUCg4kbGB5DxPjtycSryHV+cegEYAiwYFoaMfbw0gIiJpyLn/NvjMXXx8fHnEQfRMjdyrYUjrWliwNw6TNpxBEy872Jjx0WRERERP0vueu+DgYMyaNQvnz58vz3iISjS6kze87C1wKyMbMzbHSh0OERGR7Oid3A0bNgxHjhxBkyZN4O3tjU8++QT79u3j1BT0QpmqjDHrtYYAgFVHE7H/UqrEEREREcmL3sldWFgYwsPDkZqaih9++AEZGRno27cvatSogcGDB2P9+vV4+PBhecZKBABo6mWHsGAPAMD4dafxIDtP4oiIiIjkw+CpUExMTNC1a1csWLAAN2/exKZNm+Dq6orPP/8c9vb26N69Ow4cOFAesRJpfdrFB67VzHD97iN8vZW3ChARERUwOLl7WrNmzfDll1/izJkzOHPmDDp06ICkJE40S+XLwkSJma81AAD8FnWNl2eJiIj+x+CpUJ4mhIAQAkZGz50nVklyHkpdEXy24Qz+OJQAZxtTbB3VhqNniYjohZBz/613RpaXl4fPPvsMISEhmDJlCgDgm2++gaWlJczMzBAWFoacHMOfHDB37lx4eXnB1NQUgYGB2LdvX4nlIyMjERgYCFNTU9SqVQvz588vVCY8PBx+fn4wMTGBn58f1q9fb9B+c3NzMW7cODRo0AAWFhZwcXHBoEGDcPPmTZ1tZGdn48MPP4S9vT0sLCzQo0cPXL9+3eA6oNKb2NUXXvYWSErPwpSNZ6UOh4iISHJ6J3fTpk3DokWLEBQUhL/++gvDhw/Hzz//jIULF2LRokXYtWsXfvjhB4N2vnr1aowaNQqTJk1CdHQ0WrdujZdffhkJCQlFlo+Pj0fXrl3RunVrREdHY+LEiRg5ciTCw8O1ZaKiotC3b18MHDgQp06dwsCBA9GnTx8cPnxY7/0+fPgQJ06cwOTJk3HixAmsW7cOFy9eRI8ePXTiGTVqFNavX49Vq1Zh//79uH//Prp37478/HyD6oFKz1ytxHd9GsFIAWw4eRP/nuYtAUREVMUJPdWqVUv8888/QgghLl26JIyMjMSqVau0n69Zs0bUr19f380JIYRo2rSpGDZsmM4yHx8fMX78+CLLf/rpp8LHx0dn2dChQ0Xz5s217/v06SO6dOmiU6Zz586iX79+pd6vEEIcOXJEABDXrl0TQghx7949oVKpdOrgxo0bwsjISGzdurXY7TwtPT1dABDp6el6r0OFfbvtvPAYt0k0mrZN3Ep/JHU4RERUycm5/9b7zN3NmzfRqFEjAECdOnWgVqu17wEgKCgI165d0zupzMnJwfHjxxEaGqqzPDQ0FAcPHixynaioqELlO3fujGPHjiE3N7fEMgXbLM1+ASA9PR0KhQLVqlUDABw/fhy5ubk623FxcUH9+vVL3E52djYyMjJ0XvT8Rnaoi/qu1rj3MBefhp/m/ItERFRl6Z3c2djY4N69e9r3AQEBsLKy0r7Pzs6GQqHQe8epqanIz8+Ho6Pu80EdHR2RnJxc5DrJyclFls/Ly0NqamqJZQq2WZr9ZmVlYfz48XjzzTe1N00mJydDrVbD1tZW7+0AwIwZM2BjY6N9ubu7F1uW9KcyNsL3fRpDrTTCngu38eeRoi/tExERVXZ6J3d+fn44ceKE9v2BAwfg6uqqfX/mzBnUrVvX4ACeTgiFECUmiUWVf3q5PtvUd7+5ubno168fNBoN5s6dW8KR6Bf/hAkTkJ6ern0lJiY+c5ukn7qOVvi0cz0AwBebYnE19YHEEREREb14eid38+fPR5s2bYr9PDc3F59++qneO7a3t4exsXGhs1wpKSmFzqoVcHJyKrK8UqlE9erVSyxTsE1D9pubm4s+ffogPj4eEREROkOdnZyckJOTg7t37+odP/B4Emhra2udF5Wdd1p6IbhWdTzKzceo1SeRm6+ROiQiIqIXSu/kztvbG15eXsV+/uabb6JPnz5671itViMwMBARERE6yyMiItCiRYsi1wkODi5Ufvv27QgKCoJKpSqxTME29d1vQWJ36dIl7NixQ5s8FggMDIRKpdLZTlJSEs6ePVts/FT+jIwU+LZPI1iZKnEy8R5+2HFR6pCIiIheLClHc6xatUqoVCqxePFiERMTI0aNGiUsLCzE1atXhRBCjB8/XgwcOFBbPi4uTpibm4vRo0eLmJgYsXjxYqFSqcRff/2lLXPgwAFhbGwsZs6cKWJjY8XMmTOFUqkUhw4d0nu/ubm5okePHsLNzU2cPHlSJCUlaV/Z2dna7QwbNky4ubmJHTt2iBMnToj27duLRo0aiby8PL3rQM6jbSqyTaduCo9xm4Tn+E3iwKXbUodDRESVjJz7b4OTu2+++aZMA5gzZ47w8PAQarVaBAQEiMjISO1nYWFhIiQkRKf8nj17hL+/v1Cr1cLT01PMmzev0DbXrl0r6tWrJ1QqlfDx8RHh4eEG7Tc+Pl4AKPK1e/dubblHjx6JESNGCDs7O2FmZia6d+8uEhISDDp+OTeOim58+CnhMW6TaPJFhEi7n/3sFYiIiPQk5/7boMePjR8/HuvXr8eFCxfK/hRiFSXnx5dUdI9y8vHKL/txOeU+OvjUwKKwIINGdBMRERVHzv23XvfcCSEwZMgQrF69Gjt27CjvmIjKhJnaGD/184daaYSd51Pw28GrUodERERU7vRK7l5//XVs3rwZERERnJeNKhQ/F2tM6uoLAPhq83nE3OSk0UREVLnpldytX78e06ZNQ506dco7HqIyNyjYAx19HZGTr8GIlSfwMCdP6pCIiIjKjV7J3ahRozBmzBgcPXq0vOMhKnMKhQLfvN4QTtamiLv9AFP/Pid1SEREROVGr+Ru9uzZ+PTTT/Hyyy/jzJkz5R0TUZmztVDj+76NoVAAa45dx9pjfDIIERFVTnpPYjxp0iR89dVX6NKlS3nGQ1RugmtXx+iO3gCAyRvP4nwy778jIqLKR+/kDgD+85//4KeffiqvWIjK3Yh2ddDG2wFZuRoM/+MEMrNypQ6JiIioTBmU3AHAa6+9Vh5xEL0QRkYK/NC3MVxsTBGf+gDjw8/AgKkeiYiIZM/g5I6oorOzUOOXtwKgMlbg3zNJWMb574iIqBJRlmalI0eOYM+ePUhJSYFGo9H5bPbs2WUSGFF5Cqhpi4ldfTHtnxh8+W8sGrpVQ6CHrdRhERERPTeDk7uvvvoKn332GerVqwdHR0edxznx0U5UkQxu4YljV+/i3zNJGPHnCfw7sjXsLNRSh0VERPRcDHq2LAA4Ojpi1qxZGDx4cDmFVLXI+dl0VUFmVi56/nIAcakP0LquPZa93RTGRvxHChERlUzO/bfB99wZGRmhZcuW5REL0QtnZarC3AEBMFUZYd+lVHyz7YLUIRERET0Xg5O70aNHY86cOeURC5EkfJys8fXrjQAA8yOvYNPpmxJHREREVHoGX5bVaDTo1q0bLl68CD8/P6hUKp3P161bV6YBVnZyPq1b1czYHIsFe+NgpjJG+PAW8HPh90FEREWTc/9t8Jm7Dz/8ELt374a3tzeqV68OGxsbnRdRRfVpFx+0rmuPR7n5GPrHMdx9kCN1SERERAYz+MydlZUVVq1ahW7dupVXTFWKnDP/qujewxz0+OUAEu48ROu69lg6uAmUxpwOkoiIdMm5/za417Kzs0Pt2rXLIxYiyVUzV2PhoECYqYyx71IqvuYACyIiqmAMTu6mTp2KKVOm4OHDh+URD5HkfJys8e0bjwdYLNwbh40nb0gcERERkf4MnsT4p59+wpUrV+Do6AhPT89CAypOnDhRZsERSaVbQ2ecvVkb8/Zcwad/nYZndQs0cq8mdVhERETPZHBy16tXr3IIg0h+xobWw4XkTOw6n4L3lh/Dxg9awqWamdRhERERlcjgARVUtuR8QyY9foLF6/OicOFWJvycrbF2WDAsTEr1SGYiIqpE5Nx/cxggUQmsTFVYFBYEe0s1YpIyMGr1SWg0/PcQERHJF5M7omdwtzPHgoFBUCuNEBFzC7O2nZc6JCIiomIxuSPSQ6CHLb55vSEAYEFkHNYeS5Q4IiIioqIxuSPSU8/GrhjZvg4AYOL6MzgclyZxRERERIUxuSMywKiO3ujWwBm5+QJD/ziOK7fvSx0SERGRjjJN7v773/9i7969ZblJIlkxMlLg2zcaoZF7Ndx7mIvBS4/gdma21GERERFplWlyt3TpUnTp0gWvvPJKWW6WSFbM1MZYHBYEj+rmSLzzCO8sO4oH2XlSh0VERASgjJO7+Ph43LlzByNGjCjLzRLJjr2lCZa93RR2FmqcuZGOEX+eQF6+RuqwiIiIyv6eO1NTU3Tu3LmsN0skO172FlgUFgQTpRF2X7iNyRvPgnOCExGR1EqV3O3btw8DBgxAcHAwbtx4/FD133//Hfv37y/T4IjkLqCmLX7u7w8jBbDySCLm7L4sdUhERFTFGZzchYeHo3PnzjAzM0N0dDSysx/fTJ6ZmYmvvvqqzAMkkrvQl5wwtcdLAIBvt1/EX8evSxwRERFVZQYnd1988QXmz5+PX3/9FSqVSru8RYsWOHHiRJkGR1RRDAr2xNCQWgCA8eGnsft8isQRERFRVWVwcnfhwgW0adOm0HJra2vcu3evLGIiqpDGdfZBr8YuyNMIDF9xHMeu3pE6JCIiqoIMTu6cnZ1x+XLh+4r279+PWrVqlUlQRBWRkZEC37zRCG3rOSArV4N3lh1FbFKG1GEREVEVY3ByN3ToUHz00Uc4fPgwFAoFbt68iRUrVmDs2LF4//33yyNGogpDZWyEeW8FIsjDFhlZeRi05AgS0h5KHRYREVUhClGKuRsmTZqE77//HllZWQAAExMTjB07FtOnTy/zACu7jIwM2NjYID09HdbW1lKHQ2Uk/WEu+i6MwvnkTHhUN8faYcGoYWUqdVhERFRG5Nx/lyq5A4CHDx8iJiYGGo0Gfn5+sLS0LOvYqgQ5Nw56PikZWXht/kEk3nkEX2drrPpPc9iYqZ69IhERyZ6c++9ST2Jsbm6OoKAgNG3alIkdURFqWJvij3ebwd7SBLFJGXjvt6N4mMPHlBERUfky+MxdVlYWfv75Z+zevRspKSnQaHQfucTpUAwj58yfykbMzQz0XRiFzKw8tKpjj0VhQTBVGUsdFhERPQc5999KQ1d45513EBERgddffx1NmzaFQqEoj7iIKg0/F2sse7spBi4+jP2XU/H+ihOYPyAQamWZP/2PiIjI8DN3NjY22Lx5M1q2bFleMVUpcs78qWxFXUnD4KVHkJ2nQdcGTvipnz+UxkzwiIgqIjn33wb3LK6urrCysiqPWIgqteDa1bFwUBDUxkbYfCYZn/x1GvmaUo1nIiIiKpbByd13332HcePG4dq1a+URD1GlFuLtgDlvBUBppMD66BuYtP4MSjlgnYiIqEgGJ3dBQUHIyspCrVq1YGVlBTs7O50XEZWsk58jvu/bGEYKYNXRREz7J4YJHhERlRmDB1T0798fN27cwFdffQVHR0cOqCAqhVcauSA7T4Oxa09h2cGrAIApr/jx74mIiJ6bwcndwYMHERUVhUaNGpVHPERVxuuBbsjN12DCujNYdvAqhBCY2uMlJnhERPRcDL4s6+Pjg0ePHpVHLERVTv+mNTHrtQZQKIDfoq5h8saz0HCQBRERPQeDk7uZM2dizJgx2LNnD9LS0pCRkaHzIiLD9G1SE7NeawiFAvjjUAITPCIiei4Gz3NnZPQ4H3z60pEQAgqFAvn5+WUXXRUg53ly6MX66/h1fPLXKQgB9G/qji97NYCRES/REhHJkZz7b4Pvudu9e3d5xEFU5b0e6AYjBTBm7SmsPJIIjQaY0ZsJHhERGcbg5C4kJKQ84iAiAL0D3GCkUODjNSex+lgiNEJg1msNmeAREZHeDE7u9u7dW+Lnbdq0KXUwRAT08neFQgGMXn0Sa49fR55G4JvXG/JRZUREpBeDk7u2bdsWWvbk/Xe8547o+fVs7AojhQKjVp/E+ugbuJ+dh5/7+8NUZSx1aEREJHMGnwq4e/euzislJQVbt25FkyZNsH379vKIkahKeqWRCxYMCIRaaYSImFt497ejeJCdJ3VYREQkcwaPli3O3r17MXr0aBw/frwsNldlyHm0DcnDwcupeG/5MTzMyUdAzWpY+nZT2JippA6LiKhKk3P/XWY38Tg4OODChQtltTki+p8Wdeyx4r1msDFT4UTCPfRbeAip97OlDouIiGTK4DN3p0+f1nkvhEBSUhJmzpyJ3NxcHDhwoEwDrOzknPmTvMQmZWDg4iNIvZ+NWvYW+OO9ZnCpZiZ1WEREVZKc++9STWKsUCjw9GrNmzfHkiVL4OPjU6YBVnZybhwkP/GpDzBg0WHcuPcIrtXM8Md7zeBlbyF1WEREVY6c+2+Dk7tr167pvDcyMoKDgwNMTU3LNLCqQs6Ng+Tpxr1HGLjoMOJSH8DeUo1lbzdFfVcbqcMiIqpS5Nx/l9mACiodOTcOkq/bmdkIW3IEMUkZsFAbY/7AQLSu6yB1WEREVYac+2+9kruffvpJ7w2OHDnyuQKqauTcOEjeMrJyMez34zh4JQ1KIwW+eaMhXvV3kzosIqIqQdb9t9CDp6enXi8vLy99Nqdjzpw5wtPTU5iYmIiAgACxd+/eEsvv2bNHBAQECBMTE+Hl5SXmzZtXqMxff/0lfH19hVqtFr6+vmLdunUG7zc8PFyEhoaK6tWrCwAiOjq60DZCQkIEAJ1X3759DTr+9PR0AUCkp6cbtB6REEJk5eaJEX+eEB7jNgmPcZvE/D2XhUajkTosIqJKT879t15TocTHx+v1iouLMyixXL16NUaNGoVJkyYhOjoarVu3xssvv4yEhIRi4+jatStat26N6OhoTJw4ESNHjkR4eLi2TFRUFPr27YuBAwfi1KlTGDhwIPr06YPDhw8btN8HDx6gZcuWmDlzZonHMGTIECQlJWlfCxYsMKgOiJ6HidIYP/ZtjHdbeQEAZmw5j/9uioFGw7stiIiqque6565g1ScfP2aIZs2aISAgAPPmzdMu8/X1Ra9evTBjxoxC5ceNG4e///4bsbGx2mXDhg3DqVOnEBUVBQDo27cvMjIysGXLFm2ZLl26wNbWFitXrjR4v1evXoWXlxeio6PRuHFjnc/atm2Lxo0b44cffijV8QMyP61LFcqve+Pw5ebHfxvdGjpjdp9GMFHycWVEROVBzv13qSYxXr58ORo0aAAzMzOYmZmhYcOG+P333w3aRk5ODo4fP47Q0FCd5aGhoTh48GCR60RFRRUq37lzZxw7dgy5ubkllinYZmn2W5IVK1bA3t4eL730EsaOHYvMzMwSy2dnZyMjI0PnRVQWhrSphR/6NobKWIF/TychbMkRZGTlSh0WERG9YAYnd7Nnz8bw4cPRtWtXrFmzBqtXr0aXLl0wbNgwfP/993pvJzU1Ffn5+XB0dNRZ7ujoiOTk5CLXSU5OLrJ8Xl4eUlNTSyxTsM3S7Lc4b731FlauXIk9e/Zg8uTJCA8PR+/evUtcZ8aMGbCxsdG+3N3dDdonUUl6+bti6eCmsFAb41DcHbw+7yAS7zyUOiwiInqBlIau8PPPP2PevHkYNGiQdlnPnj3x0ksvYerUqRg9erRB23v6kq4QosTLvEWVf3q5Pts0dL9FGTJkiPb/69evj7p16yIoKAgnTpxAQEBAketMmDABH3/8sfZ9RkYGEzwqU63q2mP10GC8s+woLt66j1fnHsCvg4LgX9NW6tCIiOgFMPjMXVJSElq0aFFoeYsWLZCUlKT3duzt7WFsbFzobFlKSkqhs2oFnJyciiyvVCpRvXr1EssUbLM0+9VXQEAAVCoVLl26VGwZExMTWFtb67yIylp9VxtsHNESvs7WSL2fg34LD2HzGf3/PomIqOIyOLmrU6cO1qxZU2j56tWrUbduXb23o1arERgYiIiICJ3lERERRSaPABAcHFyo/Pbt2xEUFASVSlVimYJtlma/+jp37hxyc3Ph7Oz8XNshKgvONmZYOywY7X1qIDtPg/dXnMDcPZcLPTqQiIgqF4Mvy06bNg19+/bF3r170bJlSygUCuzfvx87d+4sMukryccff4yBAwciKCgIwcHBWLhwIRISEjBs2DAAjy9h3rhxA8uXLwfweGTsL7/8go8//hhDhgxBVFQUFi9erB0FCwAfffQR2rRpg1mzZqFnz57YuHEjduzYgf379+u9XwC4c+cOEhIScPPmTQDAhQsXADw+M+jk5IQrV65gxYoV6Nq1K+zt7RETE4MxY8bA398fLVu2NLRaicqFpYkSvw4KwvRNMVh28Cq+3noBV1Mf4IteDaBWlmo8FRERyV1pJsc7duyYeOutt0RAQIDw9/cXb731ljhx4kSpJtqbM2eO8PDwEGq1WgQEBIjIyEjtZ2FhYSIkJESn/J49e4S/v79Qq9XC09OzyEmM165dK+rVqydUKpXw8fER4eHhBu1XCCGWLl1aaIJiAGLKlClCCCESEhJEmzZthJ2dnVCr1aJ27dpi5MiRIi0tzaDjl/MkiFS5LDsQL7zGP57suN+CKHHvQY7UIRERVVhy7r/5bFmJyXmeHKp8dp9PwYg/T+BBTj5qOVhg0aAg1HKwlDosIqIKR879t8HXZdq1a4fFixcjPT29POIhonLUzqcG/hreAi42poi7/QA95xzAngspUodFRERlyODkrkGDBvjss8/g5OSE1157DRs2bEBOTk55xEZE5cDX2RobRrREoIctMrPy8M6yo1i49woHWhARVRIGJ3c//fQTbty4gY0bN8LKygphYWFwcnLCf/7zH0RGRpZHjERUxmpYmeLPIc3QN8gdGgF8tfk8Rq8+iazcfKlDIyKi5/Tc99xlZWXhn3/+wZdffokzZ84gP5+dgyHkfM2eKj8hBJZHXcN/N8UgXyPQ0M0GCwYGwtnGTOrQiIhkTc7993PNhZCcnIz58+dj1qxZOH36NIKCgsoqLiJ6ARQKBcJaeOL3d5vC1lyF09fT8crPB3D82h2pQyMiolIyOLnLyMjA0qVL0alTJ7i7u2PevHl45ZVXcPHiRRw+fLg8YiSictaitj3+HtEKPk5WSL2fjX4LD2HlkQSpwyIiolIw+LKsmZkZbG1t0adPH7z11lto0qRJecVWJcj5tC5VPQ+y8zB27SlsOfv48Xx9gtzw3571YaoyljgyIiJ5kXP/bXByt337dnTs2BFGRpzdvizIuXFQ1aTRCMyLvILvtl+ARgAvuVhj/oBAuNuZSx0aEZFsyLn/5iTGEpNz46Cqbf+lVIxcFY07D3JgY6bCD30bo51PDanDIiKSBTn33zz9RkRFalXXHps+bIVG7tWQ/igX7/x2FLMjLiJfw38PEhHJGZM7IiqWSzUzrBnaHAObe0AI4Kedl/D2sqO4+4ATlxMRyRWTOyIqkYnSGNN71cfsPo1gqjLC3ou30f3n/YhOuCt1aEREVASDkrvc3Fy0a9cOFy9eLK94iEimege4Yf37LeFZ3Rw37j3CG/Oj8OveOD62jIhIZgxK7lQqFc6ePQuFQlFe8RCRjPk6W+PvD1uhWwNn5GkEvtwci/d+O8bLtEREMmLwZdlBgwZh8eLF5RELEVUA1qYq/PKmP77oVR9qpRF2nk9B15/24ehVPtWCiEgOlIaukJOTg0WLFiEiIgJBQUGwsLDQ+Xz27NllFhwRyZNCocCA5h4IqGmLEX+eQFzqA/RbeAgfd/LG8JDaMDLi2X0iIqkYPM9du3btit+YQoFdu3Y9d1BViZznySHSx/3sPHy2/gw2nLwJAGhd1x6z+zSGg5WJxJEREZUfOfffnMRYYnJuHET6EkJg7fHr+HzjWWTlamBvqcY3bzRCu3qc9JiIKic599+cCoWInptCoUCfIHf8PaIVvB0tkXo/B28vPYqpf59DVm6+1OEREVUppTpzd/ToUaxduxYJCQnIydEdJbdu3boyC64qkHPmT1QaWbn5mLnlPJYdvAoAqOdohR/7N4aPE9s3EVUecu6/DT5zt2rVKrRs2RIxMTFYv349cnNzERMTg127dsHGxqY8YiSiCsRUZYypPV7C0rebwN7SBBduZaLHLwewZH88NHx0GRFRuTM4ufvqq6/w/fffY9OmTVCr1fjxxx8RGxuLPn36oGbNmuURIxFVQO3q1cDWUa3RwacGcvI0+O+mGAxedhQpGVlSh0ZEVKkZnNxduXIF3bp1AwCYmJjgwYMHUCgUGD16NBYuXFjmARJRxWVvaYJFYUGY3qs+TJSPH13W5cd92Ho2SerQiIgqLYOTOzs7O2RmZgIAXF1dcfbsWQDAvXv38PDhw7KNjogqPIVCgYHNPbDpw1bwdbbGnQc5GPbHCYxaFY30h7lSh0dEVOkYnNy1bt0aERERAIA+ffrgo48+wpAhQ9C/f3906NChzAMkosqhrqMVNnzQAh+0qw0jBbDh5E2E/hCJ3RdSpA6NiKhSMXi07J07d5CVlQUXFxdoNBp8++232L9/P+rUqYPJkyfD1ta2vGKtlOQ82oaovEQn3MWYNacQl/oAANCviTsmdfOFlalK4siIiPQj5/6bkxhLTM6Ng6g8PcrJxzfbLmDpwXgIAbhWM8M3bzREi9r2UodGRPRMcu6/9UruMjIy9N6g3A5Q7uTcOIhehENxafjkr1NIvPMIADC4hSfGdfGBmdpY4siIiIon5/5br+TOyMgICkXJDwIXQkChUCA/n7PRG0LOjYPoRbmfnYevNsfiz8MJAAAvewvMeq0hmnrZSRwZEVHR5Nx/65XcRUZG6r3BkJCQ5wqoqpFz4yB60SIv3sa4v04j+X9z4Q1s7oFPu9TjvXhEJDty7r95z53E5Nw4iKSQ/igXMzbHYtXRRACAs40pvny1Ptr7OEocGRHR/5Nz/12q5O7evXtYvHgxYmNjoVAo4Ofnh3feeYePHysFOTcOIikduJyKCevOIOHO4/kzezRywZRX/FDd0kTiyIiI5N1/G5zcHTt2DJ07d4aZmRmaNm0KIQSOHTuGR48eYfv27QgICCivWCslOTcOIqk9ysnH7IgLWLw/HhoB2JqrMOWVl9Czscsz7wMmIipPcu6/DU7uWrdujTp16uDXX3+FUqkEAOTl5eG9995DXFwc9u7dWy6BVlZybhxEcnEq8R7GhZ/G+eTHT8dpV88BX7zaAK7VzCSOjIiqKjn33wYnd2ZmZoiOjoaPj4/O8piYGAQFBfERZAaSc+MgkpOcPA0WRF7Bz7suIydfAwu1McaE1sOgYA8ojQ1+2A4R0XORc/9t8C+itbU1EhISCi1PTEyElZVVmQRFRPQ0tdIIH3aoi80ftUKghy0e5OTjv5ti0HPOAZxMvCd1eEREsmFwcte3b1+8++67WL16NRITE3H9+nWsWrUK7733Hvr3718eMRIRadWpYYW1Q4Px5av1YW2qxLmbGXh17gF8tuEM0h/lSh0eEZHkDL4sm5OTg08++QTz589HXl4eAEClUmH48OGYOXMmTEw4ks0Qcj6tSyR3tzOz8dXmWKyPvgEAsLc0wWfdfDnggojKnZz771LPc/fw4UNcuXIFQgjUqVMH5ubmZR1blSDnxkFUURy8korPNpxF3O0HAIAWtatjeq/6qO1gKXFkRFRZybn/5iTGEpNz4yCqSLLz8vHr3jj8vOsysvM0UBsbYVhILbzfrg5MVXxOLRGVLTn333ond++8845eG1yyZMlzBVTVyLlxEFVECWkP8fnfZ7Hnwm0AgJutGT7r5ofOLznyUi0RlRk59996J3dGRkbw8PCAv78/Slpl/fr1ZRZcVSDnxkFUUQkhsOVsMqZvikFS+uPn1LaqY48pr/ihriNH9RPR85Nz/613cvf+++9j1apVqFmzJt555x0MGDAAdnZ25R1fpSfnxkFU0T3MycO8PVewYG8ccvI0MDZSICzYE6M61YW1qUrq8IioApNz/23QPXfZ2dlYt24dlixZgoMHD6Jbt2549913ERoayssdpSTnxkFUWSSkPcT0f2MQEXMLAGBvqcannX3weqAbjIz420VEhpNz/13qARXXrl3DsmXLsHz5cuTm5iImJgaWlhyZZig5Nw6iyiby4m1M++ecdlRtIzcbTO3xEvxr2kocGRFVNHLuv0v9zB6FQgGFQgEhBDQaTVnGRERULkK8HbD1ozaY1NUXliZKnLqejlfnHsTHq0/i5r1HUodHRFQmDErusrOzsXLlSnTq1An16tXDmTNn8MsvvyAhIYFn7YioQlArjTCkTS3sGhuC1wPdAADrom+g3bd78N32C7ifnSdxhEREz6dUAyrefvttDBgwANWrVy/v+Co9OZ/WJaoKTiXew5f/xuLI1TsAHj/lYkyoN/oEucOY9+MRUTHk3H8bNBVKzZo14e/vX+LgiXXr1pVZcFWBnBsHUVUhhMC2c8mYseU8rqU9BAD4OFlhYldftPF2kDg6IpIjOfffSn0LDho0iCNiiahSUigU6FLfGe19HPH7oWv4ccdFnE/OxKAlR9C2ngMmdfXl/HhEVGHw8WMSk3PmT1RV3X2Qg592XcLvUdeQpxEwUgB9m7jjow7ecLIxlTo8IpIBOfffTO4kJufGQVTVxd2+j5lbzmP7/+bHM1Ea4e2WXhgeUhs25pwEmagqk3P/zeROYnJuHET02NGrdzBry3kcu3YXAGBtqsTwtnUwuIUnzNTGEkdHRFKQc//N5E5icm4cRPT/hBDYGZuCr7edx8Vb9wEAjtYmGNXRG28EukFpXOppQ4moApJz/83kTmJybhxEVFi+RmBD9A3MjriIG/+b+LiWvQXGdq6Hl+s7ceAZURUh5/6byZ3E5Nw4iKh42Xn5+ONQAubsvow7D3IAPH6c2bguPmhRx17i6IiovMm5/2ZyJzE5Nw4ierbMrFz8ui8ei/bF4WFOPgCgeS07fNypHpp62UkcHRGVFzn330zuJCbnxkFE+ku9n41fdl3Gn4cTkJP/+HnbrerYY3QnbwR62EocHRGVNTn330zuJCbnxkFEhrt57xHm7L6MNccSkZv/+Oc1xNsBozt5o7F7NWmDI6IyI+f+m8mdxOTcOIio9BLvPMSc3Zex9vh15Gse/8x28KmB0Z28Ud/VRuLoiOh5ybn/ZnInMTk3DiJ6ftfSHuDnXZex7sR1/C/HQ6ifI0Z19IafC//miSoqOfffTO4kJufGQURlJ+72ffy86zI2nLyBgl/dzi85YkS7umjgxjN5RBWNnPtvJncSk3PjIKKydzklEz/uvIxNp29qk7y29Rwwol0dBHlydC1RRSHn/lvyKdXnzp0LLy8vmJqaIjAwEPv27SuxfGRkJAIDA2FqaopatWph/vz5hcqEh4fDz88PJiYm8PPzw/r16w3e77p169C5c2fY29tDoVDg5MmThbaRnZ2NDz/8EPb29rCwsECPHj1w/fp1wyqAiKqUOjWs8HN/f2wf1Qav+rvCSAHsuXAbr8+PQr+FUThwORX8NzcRPQ9Jk7vVq1dj1KhRmDRpEqKjo9G6dWu8/PLLSEhIKLJ8fHw8unbtitatWyM6OhoTJ07EyJEjER4eri0TFRWFvn37YuDAgTh16hQGDhyIPn364PDhwwbt98GDB2jZsiVmzpxZbPyjRo3C+vXrsWrVKuzfvx/3799H9+7dkZ+fXwa1Q0SVWV1HK3zftzF2jWmLfk3coTJW4FDcHby16DBenXsQO2NvMckjolKR9LJss2bNEBAQgHnz5mmX+fr6olevXpgxY0ah8uPGjcPff/+N2NhY7bJhw4bh1KlTiIqKAgD07dsXGRkZ2LJli7ZMly5dYGtri5UrVxq836tXr8LLywvR0dFo3Lixdnl6ejocHBzw+++/o2/fvgCAmzdvwt3dHZs3b0bnzp31qgM5n9Ylohfn5r1HWLg3DiuPJCA77/E8eb7O1hjRrg661HeCsREfa0YkJ3LuvyU7c5eTk4Pjx48jNDRUZ3loaCgOHjxY5DpRUVGFynfu3BnHjh1Dbm5uiWUKtlma/Rbl+PHjyM3N1dmOi4sL6tevX+J2srOzkZGRofMiInKpZoapPV7C/nHtMTSkFszVxohNysAHf55A6PeRWHM0Edl5vCpARM8mWXKXmpqK/Px8ODo66ix3dHREcnJykeskJycXWT4vLw+pqakllinYZmn2W1wsarUatra6M88/azszZsyAjY2N9uXu7q73Pomo8nOwMsGEl31xYFx7jOxQF9amSly5/QCfhp9G61m7MT/yCjKycqUOk4hkTPIBFQqF7qUGIUShZc8q//RyfbZp6H719aztTJgwAenp6dpXYmLic++TiCofWws1Pu7kjQPj22NiVx84WpsgJTMbM7ecR4sZuzBjcyyS07OkDpOIZEiy5M7e3h7GxsaFznKlpKQUOqtWwMnJqcjySqUS1atXL7FMwTZLs9/iYsnJycHdu3cN2o6JiQmsra11XkRExbEyVeE/bWpj36ft8c3rDVG3hiXuZ+dhwd44tP56Fz5ZewqXbmVKHSYRyYhkyZ1arUZgYCAiIiJ0lkdERKBFixZFrhMcHFyo/Pbt2xEUFASVSlVimYJtlma/RQkMDIRKpdLZTlJSEs6ePWvQdoiI9KFWGuGNIHdsG9UGi8OC0NTLDrn5AmuPX0en7/fivd+O4ujVOxxhS0RQSrnzjz/+GAMHDkRQUBCCg4OxcOFCJCQkYNiwYQAeX8K8ceMGli9fDuDxyNhffvkFH3/8MYYMGYKoqCgsXrxYOwoWAD766CO0adMGs2bNQs+ePbFx40bs2LED+/fv13u/AHDnzh0kJCTg5s2bAIALFy4AeHzGzsnJCTY2Nnj33XcxZswYVK9eHXZ2dhg7diwaNGiAjh07lnvdEVHVZGSkQAdfR3TwdcSJhLtYGBmHbTHJ2BGbgh2xKWjkXg3vtvLCy/WdoDKW/M4bIpKCkNicOXOEh4eHUKvVIiAgQERGRmo/CwsLEyEhITrl9+zZI/z9/YVarRaenp5i3rx5hba5du1aUa9ePaFSqYSPj48IDw83aL9CCLF06VIBoNBrypQp2jKPHj0SI0aMEHZ2dsLMzEx0795dJCQkGHT86enpAoBIT083aD0iogJXUjLF+PDTou6kzcJj3CbhMW6TaP7VDjF392Vx90G21OERVUpy7r/5+DGJyXmeHCKqWFLvZ2PFoQT8fugqUu/nAADMVMZ4LdAVb7f0Qm0HS4kjJKo85Nx/M7mTmJwbBxFVTNl5+fjnVBIW749HbNL/z6XZrp4D3mnlhVZ17MtkdgCiqkzO/TeTO4nJuXEQUcUmhMChuDtYvD8eO8/fQsGvvbejJd5p6YWejV1hpjaWNkiiCkrO/TeTO4nJuXEQUeVxNfUBlh28irXHEvEg5/GTLmzMVOgT5IYBzT3gUd1C4giJKhY5999M7iQm58ZBRJVP+qNcrDmaiOWHriLxziMAgEIBhHg7YFCwB0K8a/A5tkR6kHP/zeROYnJuHERUeeVrBCIvpmB51DXsuXBbu9zdzgwDmnmgT5A7bC3UEkZIJG9y7r+Z3ElMzo2DiKqGq6kP8Meha1hzLBEZWXkAABOlEV5p5IJBwR5o6FZN2gCJZEjO/TeTO4nJuXEQUdXyKCcff5+6geVR13Du5v+Psm3kXg2DmnugW0NnmKo4AIMIkHf/zeROYnJuHERUNQkhcCLhHn6Puop/zyQhN/9xN2FjpkLvAFf0b1oT3o5WEkdJJC05999M7iQm58ZBRHQ7MxurjyZg5ZFE3Lj3SLs8yMMW/ZvWRNcGzpxOhaokOfffTO4kJufGQURUIF8jsPfSbaw8nICd51OQr3ncdViZKtHb3xX9m9WEjxN/w6jqkHP/zeROYnJuHERERUnJyMLa49ex8kgCrt/9/7N5/jWroX/Tmuje0BnmaqWEERKVPzn330zuJCbnxkFEVBKNRmD/5VSsPJKAiJhbyCs4m2eiRE9/F/QNqon6rtZ81BlVSnLuv5ncSUzOjYOISF+3M7Px1/HrWHU0AdfSHmqX+zhZ4fVAN/Tyd4W9pYmEERKVLTn330zuJCbnxkFEZCiNRiAqLg2rjiZi27lk5ORpAABKIwXa+dTAG4FuaOdTAypjI4kjJXo+cu6/mdxJTM6Ng4joeaQ/zMXfp2/ir+PXcSrxnna5vaUavRq74o0gd9Rz4pQqVDHJuf9mcicxOTcOIqKycvFWJv46fh3rTtxA6v1s7fIGrjZ4I8gNPRq5oJo5H3dGFYec+28mdxKTc+MgIiprufkaRF64jb+OX8fO87e0EySrjY3QwbcGevm7om09B5goOXceyZuc+28mdxKTc+MgIipPafezsfHkTaw9fh2xSf//uDMbMxW6NXRGb39XBHrYcrQtyZKc+28mdxKTc+MgInpRzt1Mx8aTN7Hx5A3cyvj/y7ZutmZ41d8VPRu7ok4NSwkjJNIl5/6byZ3E5Nw4iIhetHyNwKG4NKyPvoGtZ5NxPztP+1lDNxv0auyKVxq5wMGK06qQtOTcfzO5k5icGwcRkZQe5eRjR+wtbIi+gciLt7WTJBspgFZ1HfCqvwtC/ZxgYcKnYdCLJ+f+m8mdxOTcOIiI5CLtfjb+PZOE9dE3EJ1wT7vcTGWM9r418EpDF7St5wBTFQdi0Ish5/6byZ3E5Nw4iIjk6GrqA2w4eQMbom/g6hNPw7A0UaKTnyO6N3RG67oOUCs5UTKVHzn330zuJCbnxkFEJGdCCJy5kY5Np5Ow6dRN3EzP0n5mY6ZC55cc0b2hC1rUrg4ln4hBZUzO/TeTO4nJuXEQEVUUGo1AdOJd/HMqCf+eScLtzP8fcVvdQo0u9Z3QvaELmnrZwdiIU6vQ85Nz/83kTmJybhxERBVRvkbgSPwdbDp9E1vOJuPOgxztZzWsTNC1gTO6NXRGYE1bGDHRo1KSc//N5E5icm4cREQVXV6+BgevpOGfUzex7VwyMrL+f2oVBysTdH7JES/Xd0YzLzteuiWDyLn/ZnInMTk3DiKiyiQnT4N9l25j0+kk7Ii9hcwnEj1bcxU6+TmiS30ntKxjz8ef0TPJuf9mcicxOTcOIqLKKidPgwNXUrH1TDK2xyTj7sNc7WdWJkp08K2BLvWdEeLtADM1Ez0qTM79N5M7icm5cRARVQV5+RocuXoHW88mY+vZZKQ8MRjDTGWMdj4O6FLfGe3qOcDKVCVhpCQncu6/mdxJTM6Ng4ioqikYdbvlTDK2nE3GjXuPtJ+pjY0QXLs6Ovk5opOfIxytTSWMlKQm5/6byZ3E5Nw4iIiqMiEEzt3MwJazSdhyNhlxtx/ofN7IzQYdfR3R6SVH1HO0gkLBkbdViZz7byZ3EpNz4yAioseEELhy+z4iYlIQEZOM6MR7eLL3dLcze5zo+TmiiacdVBx5W+nJuf9mcicxOTcOIiIq2u3MbOyMvYUdsbew71IqsvM02s9szFRoV88Bnfyc0MbbnvfpVVJy7r+Z3ElMzo2DiIie7WFOHvZdSsWOmFvYeT5FZ9JktbERmv/vPr32PjXgWs1MwkipLMm5/2ZyJzE5Nw4iIjJMvkbgRMJd7Ii5hYiYW4hL1b1Pz9vREu18aqBdvRoI9LDl5dsKTM79N5M7icm5cRAR0fO5nHIfETG3sDP2Fk4k3IXmiR7XylSJNt4OaFevBtrWc4C9pYl0gZLB5Nx/M7mTmJwbBxERlZ17D3Ow91Iqdp9PwZ4LKToTJysUQENXG+1ZvQauNnzurczJuf9mcicxOTcOIiIqH/kagVPX72H3+RTsvpCCszcydD63t1QjxLsG2vvUQKu69rAx46AMuZFz/83kTmJybhxERPRi3MrIQuSF29h1PgX7L6fifvb/P/fW2EiBgJrV0LquA9p4O6CBqw2MeVZPcnLuv5ncSUzOjYOIiF68nDwNjl29g90XUrDrfAquPDV5cjVzFVrVsUebug5o7W0PZxuOwJWCnPtvJncSk3PjICIi6SXeeYi9l25j78XbOHg5DZlPnNUDHo/ALTir18zLDqYqY4kirVrk3H8zuZOYnBsHERHJS16+BicT72HvpVTsvXgbp6/f0xmBq1YaoZmXHdr8L9nzdrTkY9HKiZz7byZ3EpNz4yAiInm79zAHBy6nYe/F29h76TaS0rN0Pne0NkHL2vZoUcceLetU5yXcMiTn/pvJncTk3DiIiKjiEELgcsp97Vm9w/FpyMrV6JSpZW+BFnWqo1UdezSvVR3VzNUSRVvxybn/ZnInMTk3DiIiqriycvNx/NpdHLicigNX0nDmqUu4CgVQ38UGLepUR8va9mjiaQczNe/X05ec+28mdxKTc+MgIqLKI/1RLg7FpeHg/5K9yyn3dT5XGxvBv2Y1tPzfJdyGbtX4eLQSyLn/ZnInMTk3DiIiqrxuZWTh4JVUHLj8OOG7+dT9ehZqYzSrVR0taldH81rV4etszfn1niDn/pvJncTk3DiIiKhqEELgatpDHLicioNXUhF1JU3n8WjA42fhNvW0Q7Nadmheqzr8nK2hrMJn9uTcfzO5k5icGwcREVVNGo1ATFIGDl5JxaG4Ozgaf6fQ/HqWJko08bRFs1qPz+zVd6layZ6c+28mdxKTc+MgIiICHs+vF5OUgcNxd3A4Pg2H4+8gM0s32bNQGyPof2f2mnlVR0M3m0p9z56c+28mdxKTc+MgIiIqSr5GIDYpA4fiHid6R+LvIP2R7mVcc7UxAj1s0bxWdTTxtENDN5tK9fQMOfffTO4kJufGQUREpA+NRuB8cub/kr3HCd+9p+7ZUxsboaGbDYI87dDE0xaBHrYVep49OfffTO4kJufGQUREVBoajcDFlEwcuvI40Tt69S5S72cXKuftaKlN9oI87OBma1ZhHpcm5/6byZ3E5Nw4iIiIyoIQAtfSHuLo1Ts4dvUujl67g7jbDwqVc7I2RZCnLZp42iHI0xY+TvKdfkXO/TeTO4nJuXEQERGVl9T72Th+7S6OXX18Zu/sjXTkaXRTEisTJfw9bNHEwxZNvOzQyK2abJ6iIef+m8mdxOTcOIiIiF6URzn5OJl473Gyd+0uTly7i/tPTb+iNFLA19kaATWrIcDDFgE1bSW7lCvn/pvJncTk3DiIiIikkq8ROJ+c8fgy7tU7OHr1Dm5lFL5vz8HK5HGyV9MWAR62aOD6Ykblyrn/ZnInMTk3DiIiIrkQQuBmehZOXLuL49fuIjrhLs7dzCh0KVdlrICfi41OwudiY1rmZ/fk3H8zuZOYnBsHERGRnGXl5uPMjXScuHYXJxLu4kTCPdzOLHx2b2yoN0a0r1um+5Zz/62UOgAiIiKi0jBVGaOJpx2aeNoBeHx27/rdR48TvWuPk72YpAz4Ossr+SpvTO6IiIioUlAoFHC3M4e7nTl6NnYF8HighlHlfQpakZjcERERUaUll6lTXiTJc9m5c+fCy8sLpqamCAwMxL59+0osHxkZicDAQJiamqJWrVqYP39+oTLh4eHw8/ODiYkJ/Pz8sH79eoP3K4TA1KlT4eLiAjMzM7Rt2xbnzp3TKdO2bVsoFAqdV79+/UpRC0RERERlQ9LkbvXq1Rg1ahQmTZqE6OhotG7dGi+//DISEhKKLB8fH4+uXbuidevWiI6OxsSJEzFy5EiEh4dry0RFRaFv374YOHAgTp06hYEDB6JPnz44fPiwQfv9+uuvMXv2bPzyyy84evQonJyc0KlTJ2RmZurENGTIECQlJWlfCxYsKONaIiIiItKfpKNlmzVrhoCAAMybN0+7zNfXF7169cKMGTMKlR83bhz+/vtvxMbGapcNGzYMp06dQlRUFACgb9++yMjIwJYtW7RlunTpAltbW6xcuVKv/Qoh4OLiglGjRmHcuHEAgOzsbDg6OmLWrFkYOnQogMdn7ho3bowffvih1HUg59E2REREVDQ599+SnbnLycnB8ePHERoaqrM8NDQUBw8eLHKdqKioQuU7d+6MY8eOITc3t8QyBdvUZ7/x8fFITk7WKWNiYoKQkJBCsa1YsQL29vZ46aWXMHbs2EJn9oiIiIheJMkGVKSmpiI/Px+Ojo46yx0dHZGcnFzkOsnJyUWWz8vLQ2pqKpydnYstU7BNffZb8N+iyly7dk37/q233oKXlxecnJxw9uxZTJgwAadOnUJERESxx52dnY3s7P+fgycjI6PYskRERESGkny07NMzRgshSpxFuqjyTy/XZ5tlUWbIkCHa/69fvz7q1q2LoKAgnDhxAgEBAUXGP2PGDEybNq3Iz4iIiIiel2SXZe3t7WFsbFzoLF1KSkqhM2YFnJyciiyvVCpRvXr1EssUbFOf/To5OQGAQbEBQEBAAFQqFS5dulRsmQkTJiA9PV37SkxMLLYsERERkaEkS+7UajUCAwMLXcKMiIhAixYtilwnODi4UPnt27cjKCgIKpWqxDIF29RnvwWXWp8sk5OTg8jIyGJjA4Bz584hNzcXzs7OxZYxMTGBtbW1zouIiIiozAgJrVq1SqhUKrF48WIRExMjRo0aJSwsLMTVq1eFEEKMHz9eDBw4UFs+Li5OmJubi9GjR4uYmBixePFioVKpxF9//aUtc+DAAWFsbCxmzpwpYmNjxcyZM4VSqRSHDh3Se79CCDFz5kxhY2Mj1q1bJ86cOSP69+8vnJ2dRUZGhhBCiMuXL4tp06aJo0ePivj4ePHvv/8KHx8f4e/vL/Ly8vSug/T0dAFApKenl7oeiYiI6MWSc/8taXInhBBz5swRHh4eQq1Wi4CAABEZGan9LCwsTISEhOiU37Nnj/D39xdqtVp4enqKefPmFdrm2rVrRb169YRKpRI+Pj4iPDzcoP0KIYRGoxFTpkwRTk5OwsTERLRp00acOXNG+3lCQoJo06aNsLOzE2q1WtSuXVuMHDlSpKWlGXT8cm4cREREVDQ599+SznNH8p4nh4iIiIom5/5b8sePEREREVHZYXJHREREVIlIPs9dVVdwVZyTGRMREVUcBf22HO9uY3InsYLHlbm7u0scCRERERkqMzMTNjY2UoehgwMqJKbRaHDz5k1YWVmV+GQOQ2VkZMDd3R2JiYmyu9FTjlhf+mNdGYb1pT/Wlf5YV4Ypj/oSQiAzMxMuLi4wMpLXXW48cycxIyMjuLm5ldv2OVGyYVhf+mNdGYb1pT/Wlf5YV4Yp6/qS2xm7AvJKNYmIiIjouTC5IyIiIqpEmNxVUiYmJpgyZQpMTEykDqVCYH3pj3VlGNaX/lhX+mNdGaaq1RcHVBARERFVIjxzR0RERFSJMLkjIiIiqkSY3BERERFVIkzuiIiIiCoRJncVzN69e/HKK6/AxcUFCoUCGzZs0Pl88ODBUCgUOq/mzZvrlMnOzsaHH34Ie3t7WFhYoEePHrh+/foLPIoXY8aMGWjSpAmsrKxQo0YN9OrVCxcuXNApI4TA1KlT4eLiAjMzM7Rt2xbnzp3TKVMV6kufumLbemzevHlo2LChdjLU4OBgbNmyRfs525SuZ9UX21XxZsyYAYVCgVGjRmmXsX0Vrai6qspti8ldBfPgwQM0atQIv/zyS7FlunTpgqSkJO1r8+bNOp+PGjUK69evx6pVq7B//37cv38f3bt3R35+fnmH/0JFRkbigw8+wKFDhxAREYG8vDyEhobiwYMH2jJff/01Zs+ejV9++QVHjx6Fk5MTOnXqpH3mL1A16kufugLYtgDAzc0NM2fOxLFjx3Ds2DG0b98ePXv21HawbFO6nlVfANtVUY4ePYqFCxeiYcOGOsvZvgorrq6AKty2BFVYAMT69et1loWFhYmePXsWu869e/eESqUSq1at0i67ceOGMDIyElu3bi2nSOUhJSVFABCRkZFCCCE0Go1wcnISM2fO1JbJysoSNjY2Yv78+UKIqltfT9eVEGxbJbG1tRWLFi1im9JTQX0JwXZVlMzMTFG3bl0REREhQkJCxEcffSSE4G9WUYqrKyGqdtvimbtKaM+ePahRowa8vb0xZMgQpKSkaD87fvw4cnNzERoaql3m4uKC+vXr4+DBg1KE+8Kkp6cDAOzs7AAA8fHxSE5O1qkLExMThISEaOuiqtbX03VVgG1LV35+PlatWoUHDx4gODiYbeoZnq6vAmxXuj744AN069YNHTt21FnO9lVYcXVVoKq2LaXUAVDZevnll/HGG2/Aw8MD8fHxmDx5Mtq3b4/jx4/DxMQEycnJUKvVsLW11VnP0dERycnJEkVd/oQQ+Pjjj9GqVSvUr18fALTH6+joqFPW0dER165d05apavVVVF0BbFtPOnPmDIKDg5GVlQVLS0usX78efn5+2g6BbUpXcfUFsF09bdWqVThx4gSOHj1a6DP+Zukqqa6Aqt22mNxVMn379tX+f/369REUFAQPDw/8+++/6N27d7HrCSGgUCheRIiSGDFiBE6fPo39+/cX+uzp49anLipzfRVXV2xb/69evXo4efIk7t27h/DwcISFhSEyMlL7OduUruLqy8/Pj+3qCYmJifjoo4+wfft2mJqaFluO7Uu/uqrKbYuXZSs5Z2dneHh44NKlSwAAJycn5OTk4O7duzrlUlJSCv1rsLL48MMP8ffff2P37t1wc3PTLndycgKAQv9Ce7Iuqlp9FVdXRanKbUutVqNOnToICgrCjBkz0KhRI/z4449sU8Uorr6KUpXb1fHjx5GSkoLAwEAolUoolUpERkbip59+glKp1B4v29ez66qoARFVqW0xuavk0tLSkJiYCGdnZwBAYGAgVCoVIiIitGWSkpJw9uxZtGjRQqowy4UQAiNGjMC6deuwa9cueHl56Xzu5eUFJycnnbrIyclBZGSkti6qSn09q66KUpXb1tOEEMjOzmab0lNBfRWlKrerDh064MyZMzh58qT2FRQUhLfeegsnT55ErVq12L7+51l1ZWxsXGidKtW2XvwYDnoemZmZIjo6WkRHRwsAYvbs2SI6Olpcu3ZNZGZmijFjxoiDBw+K+Ph4sXv3bhEcHCxcXV1FRkaGdhvDhg0Tbm5uYseOHeLEiROiffv2olGjRiIvL0/CIyt7w4cPFzY2NmLPnj0iKSlJ+3r48KG2zMyZM4WNjY1Yt26dOHPmjOjfv79wdnaucvX1rLpi2/p/EyZMEHv37hXx8fHi9OnTYuLEicLIyEhs375dCME29bSS6ovt6tmeHgHK9lW8J+uqqrctJncVzO7duwWAQq+wsDDx8OFDERoaKhwcHIRKpRI1a9YUYWFhIiEhQWcbjx49EiNGjBB2dnbCzMxMdO/evVCZyqCoegIgli5dqi2j0WjElClThJOTkzAxMRFt2rQRZ86c0dlOVaivZ9UV29b/e+edd4SHh4dQq9XCwcFBdOjQQZvYCcE29bSS6ovt6tmeTu7Yvor3ZF1V9balEEKIF322kIiIiIjKB++5IyIiIqpEmNwRERERVSJM7oiIiIgqESZ3RERERJUIkzsiIiKiSoTJHREREVElwuSOiIiIqBJhckdERERUiTC5IyLZUCgUJb4GDx4sdYhlrm3bthg1apTUYegYPHgwevXqpbPsr7/+gqmpKb7++mtpgiIivSmlDoCIqEBSUpL2/1evXo3PP/8cFy5c0C4zMzOTIqxSyc3NhUqlqhT7W7RoET744APMmTMH7733Xrnsg4jKDs/cEZFsODk5aV82NjZQKBQ6y/bu3YvAwECYmpqiVq1amDZtGvLy8rTrKxQKLFiwAN27d4e5uTl8fX0RFRWFy5cvo23btrCwsEBwcDCuXLmiXWfq1Klo3LgxFixYAHd3d5ibm+ONN97AvXv3dGJbunQpfH19YWpqCh8fH8ydO1f72dWrV6FQKLBmzRq0bdsWpqam+OOPP5CWlob+/fvDzc0N5ubmaNCgAVauXKldb/DgwYiMjMSPP/6oPTt59epVLFu2DNWqVdPZ/4YNG6BQKArFvWTJEtSqVQsmJiYQQiA9PR3/+c9/UKNGDVhbW6N9+/Y4depUqb+Tr7/+GiNGjMCff/7JxI6ogmByR0QVwrZt2zBgwACMHDkSMTExWLBgAZYtW4Yvv/xSp9z06dMxaNAgnDx5Ej4+PnjzzTcxdOhQTJgwAceOHQMAjBgxQmedy5cvY82aNfjnn3+wdetWnDx5Eh988IH2819//RWTJk3Cl19+idjYWHz11VeYPHkyfvvtN53tjBs3DiNHjkRsbCw6d+6MrKwsBAYGYtOmTTh79iz+85//YODAgTh8+DAA4Mcff0RwcDCGDBmCpKQkJCUlwd3dXe86KYg7PDwcJ0+eBAB069YNycnJ2Lx5M44fP46AgAB06NABd+7c0Xu7BcaPH4/p06dj06ZNeO211wxen4gkIoiIZGjp0qXCxsZG+75169biq6++0inz+++/C2dnZ+17AOKzzz7Tvo+KihIAxOLFi7XLVq5cKUxNTbXvp0yZIoyNjUViYqJ22ZYtW4SRkZFISkoSQgjh7u4u/vzzT519T58+XQQHBwshhIiPjxcAxA8//PDM4+ratasYM2aM9n1ISIj46KOPSjx2IYRYv369ePIne8qUKUKlUomUlBTtsp07dwpra2uRlZWls27t2rXFggULnhlbgbCwMKFWqwUAsXPnTr3XIyJ54D13RFQhHD9+HEePHtU5U5efn4+srCw8fPgQ5ubmAICGDRtqP3d0dAQANGjQQGdZVlYWMjIyYG1tDQCoWbMm3NzctGWCg4Oh0Whw4cIFGBsbIzExEe+++y6GDBmiLZOXlwcbGxudGIOCgnTe5+fnY+bMmVi9ejVu3LiB7OxsZGdnw8LC4nmrAwDg4eEBBwcH7fvjx4/j/v37qF69uk65R48e6VyK1kfDhg2RmpqKzz//HE2aNIGVlVWZxExE5Y/JHRFVCBqNBtOmTUPv3r0LfWZqaqr9/ycHFRTco1bUMo1GU+y+CsooFAptuV9//RXNmjXTKWdsbKzz/umk7bvvvsP333+PH374AQ0aNICFhQVGjRqFnJyc4g8UgJGREYQQOstyc3MLlXt6fxqNBs7OztizZ0+hsk/fw/csrq6uCA8PR7t27dClSxds3bqVCR5RBcHkjogqhICAAFy4cAF16tQp820nJCTg5s2bcHFxAQBERUXByMgI3t7ecHR0hKurK+Li4vDWW28ZtN19+/ahZ8+eGDBgAIDHydelS5fg6+urLaNWq5Gfn6+znoODAzIzM/HgwQNtAldwT11JAgICkJycDKVSCU9PT4NiLUrNmjURGRmJdu3aITQ0FNu2bdOe7SQi+eKACiKqED7//HMsX74cU6dOxblz5xAbG4vVq1fjs88+e+5tm5qaIiwsDKdOncK+ffswcuRI9OnTB05OTgAej0ydMWMGfvzxR1y8eBFnzpzB0qVLMXv27BK3W6dOHURERODgwYOIjY3F0KFDkZycrFPG09MThw8fxtWrV5GamgqNRoNmzZrB3NwcEydOxOXLl/Hnn39i2bJlzzyOjh07Ijg4GL169cK2bdtw9epVHDx4EJ999pl2MImh3NzcsGfPHqSlpSE0NBTp6eml2g4RvThM7oioQujcuTM2bdqEiIgINGnSBM2bN8fs2bPh4eHx3NuuU6cOevfuja5duyI0NBT169fXmerkvffew6JFi7Bs2TI0aNAAISEhWLZsGby8vErc7uTJkxEQEIDOnTujbdu2cHJyKjQ58NixY2FsbAw/Pz84ODggISEBdnZ2+OOPP7B582bt9ClTp0595nEoFAps3rwZbdq0wTvvvANvb2/069cPV69e1d5/WDBtS1GXbovj6uqKyMhI3Lt3D506dSo0TQwRyYtCPH1jBxFRFTJ16lRs2LBBr8uelcGePXvw6quvIi4uDra2tlKHQ0TlgGfuiIiqkK1bt2LixIlM7IgqMQ6oICKqQmbOnCl1CERUznhZloiIiKgS4WVZIiIiokqEyR0RERFRJcLkjoiIiKgSYXJHREREVIkwuSMiIiKqRJjcEREREVUiTO6IiIiIKhEmd0RERESVCJM7IiIiokrk/wBZEButNu0CnwAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"plt.title('Difference between real and ideal molar volume calculations, CO2')\n",
"ax.plot(T,V_ideal-V_vdw)\n",
"ax.set(xlabel='Temperature, K',ylabel='Molar volume, m^3/mol')\n",
"#ax.legend(loc='best')\n",
"#plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1676e828-98e8-48a1-ade0-ef7942eb6080",
"metadata": {},
"source": [
"The molar volume of the van der Waals EOS is lower than the ideal gas volume. As a percentage,"
]
},
{
"cell_type": "code",
"execution_count": 89,
"id": "61136f86-ea20-4f04-a2ff-8efae9d49f9a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0.5, 0, 'Temperature, K'), Text(0, 0.5, 'Molar volume, m^3/mol')]"
]
},
"execution_count": 89,
"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": [
"fig, ax = plt.subplots()\n",
"plt.title('Fraction difference between real and ideal molar volume calculations, CO2')\n",
"ax.plot(T,(V_ideal-V_vdw)/V_vdw)\n",
"ax.set(xlabel='Temperature, K',ylabel='Molar volume, m^3/mol')\n",
"#ax.legend(loc='best')\n",
"#plt.show()"
]
},
{
"cell_type": "markdown",
"id": "cb3f0057-b222-43ef-997e-2837b352e8f8",
"metadata": {},
"source": [
"As the temperature increases from 150K to 450K, the difference between the real and ideal properties changes from over 10% to less than 1%. The fluid becomes more ideal as the temeprature increases (at this pressure)."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8ec9c46e-5cf0-40f6-9146-21caf531c46c",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.4"
}
},
"nbformat": 4,
"nbformat_minor": 5
}