ex-16-070.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6e963640",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from scipy.constants import R, zero_Celsius\n",
    "from oetils import init_plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "af0eba87",
   "metadata": {},
   "outputs": [],
   "source": [
    "W = init_plotting(latex=True, sans=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e6b73ffd",
   "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>T</th>\n",
       "      <th>v</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>253.15</td>\n",
       "      <td>324.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>273.15</td>\n",
       "      <td>337.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>293.15</td>\n",
       "      <td>349.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>313.15</td>\n",
       "      <td>361.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>333.15</td>\n",
       "      <td>372.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>353.15</td>\n",
       "      <td>383.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        T      v\n",
       "0  253.15  324.0\n",
       "1  273.15  337.0\n",
       "2  293.15  349.0\n",
       "3  313.15  361.0\n",
       "4  333.15  372.0\n",
       "5  353.15  383.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gam = 1.40  # Heat capacity ratio of gas\n",
    "data = pd.DataFrame({\n",
    "    'T': [-20.0, 0.0, 20.0, 40.0, 60.0, 80.0],  # Gas temperature [°C]\n",
    "    'v': [324., 337., 349., 361., 372., 383.],  # Speed of sound [m / s]\n",
    "})\n",
    "\n",
    "# Convert to SI\n",
    "data['T'] += zero_Celsius\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "53cc05be",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x2086.34 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Least squares fit\n",
    "x = data['T'].values[:, None]\n",
    "y = data.v**2\n",
    "w = np.linalg.lstsq(x, y, rcond=None)[0][0]\n",
    "\n",
    "# Plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel(r\"$T\\quad/\\quad\\mathrm{K}$\")\n",
    "ax.set_ylabel(r\"$v^2\\quad/\\quad\\mathrm{m^2 s^{-2}}$\")\n",
    "ax.plot(data['T'], y, 'r.', label=\"Data\")\n",
    "x = np.linspace(data['T'].min(), data['T'].max())\n",
    "ax.plot(x, w * x, label=\"Fit\")\n",
    "ax.ticklabel_format(axis='y', style='sci', scilimits=(0, 0))\n",
    "ax.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6306995b-c581-47fe-8282-9aef99e73f7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The molar mass of the gas is M = 28.0 g / mol.\n"
     ]
    }
   ],
   "source": [
    "M = gam * R / w * 1000\n",
    "print(f\"The molar mass of the gas is M = {M:.1f} g / mol.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a230309e-0270-4f07-87b6-780da2b6ef0b",
   "metadata": {},
   "source": [
    "The most likely diatomic gas with this molar mass is N2 (nitrogen)."
   ]
  }
 ],
 "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}