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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "# Estimation of Absolute Zero by use of the Gas Laws\n", "\n", "##Theory:\n", "\n", "Charles’ law states that for a constant amount of gas, the volume is proportional to the absolute temperature if the pressure remains constant.\n", "V α T for constant P\n", "A plot of volume versus Centigrade temperature intercepts the x-axis at -273 oC which suggests that the gas would occupy no volume at this temperature. This theoretical value is known as absolute zero, and is also known as 0 Kelvin.\n", "\n", "## Apparatus:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "Heat the water using a Bunsen burner and stir regularly. Measure the length of the trapped air every 10 oC up to 80 oC. Plot a graph of the length of trapped air (y-axis) against temperature (x-axis). \n", "\n", "Extrapolating from the gradient should give a value for the x-axis intercept" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The parameters of the line: [[ 0.13452381]\n", " [-0.01035714]]\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Importing the necessary libraries\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "#from prettytable import PrettyTable\n", "\n", "# Preparing the data to be computed and plotted\n", "dt = np.array([\n", " \n", " [1.0, 0.15],\n", " [2.0, 0.29],\n", " [3.0, 0.38],\n", " [4.0, 0.50],\n", " [5.0, 0.60],\n", " [6.0, 0.81],\n", " [7.0, 0.90],\n", " [8.0, 1.13]\n", "])\n", "\n", "# Preparing X and y data from the given data\n", "x = dt[:, 0].reshape(dt.shape[0], 1)\n", "X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)\n", "y = dt[:, 1].reshape(dt.shape[0], 1)\n", "\n", "# Calculating the parameters using the least square method\n", "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n", "\n", "print(f'The parameters of the line: {theta}')\n", "\n", "# Now, calculating the y-axis values against x-values according to\n", "# the parameters theta0 and theta1\n", "y_line = X.dot(theta)\n", "\n", "# Plotting the data points and the best fit line\n", "plt.scatter(x, y)\n", "plt.plot(x, y_line, 'r')\n", "plt.title('Best fit line using regression method')\n", "plt.xlabel('Length in cm')\n", "plt.ylabel('Resistance')\n", "\n", "plt.show()\n", "\n", "\n", "\n", "#def makePrettyTable(table_col1, table_col2):\n", " # table = PrettyTable()\n", " # table.add_column(\"Column-1\", x)\n", " # table.add_column(\"Column-2\", Y)\n", " #return table" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion\n", "In comparison, our calculated resistivity is 0.13 Ohm/m vs a databook value of 0.105 Ohm/m This is well within the expected variance of an A-level practical.\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }