354 lines
192 KiB
Text
354 lines
192 KiB
Text
{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "f225380f",
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"metadata": {},
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"source": [
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"# Maxwell-Boltzmann distribution\n",
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"\n",
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"Plot the Maxwell-Boltzmann distribution\n",
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"\n",
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"$$ f(v_x) = \\left ( \\frac{m}{2 \\pi kT} \\right )^{1/2} e^{-mv_x^2/2kT} $$\n",
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"\n",
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"Eric Furst \n",
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"September 2023\n",
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"\n",
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"Updated:\\\n",
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"October 2024 to include velocity averages and comparision to kT"
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]
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},
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{
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"cell_type": "markdown",
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"id": "28594ad2",
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"metadata": {},
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"source": [
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"As ususal, we import the *numpy* and *matplotlib* libraries. We'll also use the *SciPy* constants library."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "8ba8e9f4",
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy import constants"
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]
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},
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{
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"cell_type": "markdown",
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"id": "9cacacf5",
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"metadata": {},
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"source": [
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"We'll plot the distribution over a range of velocities. By equiparition, the average (mean-squared) velocity is \n",
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"$$ \\langle v_x^2 \\rangle = \\frac{kT}{m} $$\n",
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"\n",
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"When the exponential term is on the order of \n",
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"$$ \\frac{m v_x^2}{2kT} \\sim \\mathcal{O}(5) $$\n",
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"then the exponential function will be close to zero. So, we should choose a range of velocities \n",
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"$$ 0 \\le v_x \\le \\left ( \\frac{10kT}{m} \\right )^{1/2}$$\n",
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"or so."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "f3d2f917",
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"metadata": {},
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"outputs": [],
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"source": [
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"# Specify mass (in kg) and temperature (in K)\n",
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"# This is the mass for nitrogen\n",
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"\n",
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"m = 14.007/1000/constants.N_A\n",
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"T = 298\n",
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"kT = constants.k*T\n",
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"\n",
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"# Make a range of velocities\n",
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"vx = np.linspace(0,np.sqrt(10*kT/m),100)\n",
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"\n",
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"# Calculate the distribution\n",
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"fvx = np.sqrt(m/2/np.pi/kT)*np.exp(-m*vx**2/2/kT)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4133d8cd",
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"metadata": {},
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"source": [
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"Now we can plot the function."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "7579e5f6",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"Text(0.5, 1.0, 'Maxwell-Boltzmann Distribution')"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"data": {
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"image/png": 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",
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
]
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"source": [
|
|
"# Plot the data\n",
|
|
"\n",
|
|
"fig, ax = plt.subplots()\n",
|
|
"ax.plot(vx, fvx)\n",
|
|
"plt.xlabel('vx (m/s)')\n",
|
|
"plt.ylabel('f(vx)')\n",
|
|
"plt.title('Maxwell-Boltzmann Distribution')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "db1cf3ea",
|
|
"metadata": {},
|
|
"source": [
|
|
"We should plot this at a few different temperatures!"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 12,
|
|
"id": "0843f5d1",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"Text(0.5, 1.0, 'Maxwell-Boltzmann Distribution')"
|
|
]
|
|
},
|
|
"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": [
|
|
"fig, ax = plt.subplots()\n",
|
|
"\n",
|
|
"for T in range(50, 350, 50) :\n",
|
|
" kT = constants.k*T\n",
|
|
" vx = np.linspace(0,1200,100)\n",
|
|
" fvx = np.sqrt(m/2/np.pi/kT)*np.exp(-m*vx**2/2/kT)\n",
|
|
" ax.plot(vx, fvx,label='{} K'.format(T))\n",
|
|
"\n",
|
|
"plt.legend(frameon=False)\n",
|
|
"plt.xlabel('vx (m/s)')\n",
|
|
"plt.ylabel('f(vx)')\n",
|
|
"plt.title('Maxwell-Boltzmann Distribution')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "f1be1e27",
|
|
"metadata": {},
|
|
"source": [
|
|
"## Maxwell Distribution of Speed\n",
|
|
"\n",
|
|
"We can do a similar calcuation for the total velocity, or *speed*. The distribution function is\n",
|
|
"\n",
|
|
"$$ f(v_x,v_y,v_z) = \\left ( \\frac{m}{2 \\pi kT} \\right )^{3/2} e^{-mv^2/2kT} $$\n",
|
|
"\n",
|
|
"The probability of observing a velocity $v$ is within\n",
|
|
"\n",
|
|
"$$ f(v)dv = f(v_x, v_y, v_z)dv_xdv_ydv_z $$\n",
|
|
"\n",
|
|
"which is a volume integral represented by a spherical shell (since $v^2 = v_x^2 + v_y^2 +v_z^2$).\n",
|
|
"\n",
|
|
"Thus,\n",
|
|
"\n",
|
|
"$$ f(v)dv = \\int_0^{2\\pi} \\int_0^\\pi \\left ( \\frac{m}{2 \\pi kT} \\right )^{3/2} e^{-mv^2/2kT} v^2 \\sin \\theta d\\phi d\\theta dv $$\n",
|
|
"\n",
|
|
"$$ f(v) = 4\\pi \\left ( \\frac{m}{2 \\pi kT} \\right )^{3/2} v^2 e^{-mv^2/2kT} $$"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 13,
|
|
"id": "bbce3bda",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"Text(0.5, 1.0, 'Maxwell Distribution of Speeds')"
|
|
]
|
|
},
|
|
"execution_count": 13,
|
|
"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",
|
|
"\n",
|
|
"for T in range(20, 300, 40) :\n",
|
|
" kT = constants.k*T\n",
|
|
" v = np.linspace(0,1200,100)\n",
|
|
"\n",
|
|
" fvxsq = 4 * np.pi * (np.sqrt(m / (2 * np.pi * kT)))**3 \\\n",
|
|
" * v**2 * np.exp(-m * v**2 / (2 * kT))\n",
|
|
"\n",
|
|
" ax.plot(v, fvxsq, label='{} K'.format(T))\n",
|
|
"\n",
|
|
"plt.legend(frameon=False)\n",
|
|
"plt.xlabel('v (m/s)')\n",
|
|
"plt.ylabel('f(v)')\n",
|
|
"plt.title('Maxwell Distribution of Speeds')"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "6619255d-41ec-4cd4-9da0-321d5fa0ae17",
|
|
"metadata": {},
|
|
"source": [
|
|
"## What is the average velocity and kinetic energy? \n",
|
|
"\n",
|
|
"How does the K.E. compare with kT?"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": 14,
|
|
"id": "ecd7dfd3-2dcc-4634-a98a-60c33c3a1a7a",
|
|
"metadata": {},
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"At T = 200 K:\n",
|
|
"\n",
|
|
"The average value of v is 550 m/s\n",
|
|
"m<v>^2/kT = 0.849 m/s\n",
|
|
"\n",
|
|
"The average rms v is: 597 m/s\n",
|
|
"m<v^2>/3kT = 1.000\n"
|
|
]
|
|
}
|
|
],
|
|
"source": [
|
|
"from scipy.integrate import quad\n",
|
|
"\n",
|
|
"# Define the function fn_fvxsq\n",
|
|
"# The Maxwell-Boltzmann ditribution\n",
|
|
"def fn_fvxsq(v, m, kT):\n",
|
|
" factor = 4 * np.pi * (np.sqrt(m / (2 * np.pi * kT)))**3\n",
|
|
" return factor * v**2 * np.exp(-m * v**2 / (2 * kT))\n",
|
|
"\n",
|
|
"# Average value function <v>\n",
|
|
"def average_value_of_fvx(m, kT):\n",
|
|
" # Define the limits for integration (0 to infinity)\n",
|
|
" lower_limit = 0\n",
|
|
" upper_limit = np.inf\n",
|
|
"\n",
|
|
" # Numerator: Integral of fvx(v) * v\n",
|
|
" numerator_v, _ = quad(lambda v: fn_fvxsq(v, m, kT) * v, lower_limit, upper_limit)\n",
|
|
"\n",
|
|
" # Numerator: Integral of fvx(v) * v * v\n",
|
|
" numerator_vv, _ = quad(lambda v: fn_fvxsq(v, m, kT) * v * v, lower_limit, upper_limit)\n",
|
|
"\n",
|
|
" # Denominator: Integral of fvx(v)\n",
|
|
" denominator, _ = quad(lambda v: fn_fvxsq(v, m, kT), lower_limit, upper_limit)\n",
|
|
"\n",
|
|
" # Calculate the average value\n",
|
|
" average_v = numerator_v / denominator\n",
|
|
" average_vv = numerator_vv / denominator\n",
|
|
"\n",
|
|
" return average_v, average_vv\n",
|
|
"\n",
|
|
"m = 14.007/1000/constants.N_A\n",
|
|
"T = 200\n",
|
|
"kT = constants.k*T\n",
|
|
"\n",
|
|
"avg_v, avg_vv = average_value_of_fvx(m, kT)\n",
|
|
"\n",
|
|
"print(f\"At T = {T} K:\")\n",
|
|
"print()\n",
|
|
"print(f\"The average value of v is {avg_v:.0f} m/s\")\n",
|
|
"print(f\"m<v>^2/kT = {m*avg_v**2/3/kT:.3f} m/s\")\n",
|
|
"print()\n",
|
|
"print(f\"The average rms v is: {np.sqrt(avg_vv):.0f} m/s\")\n",
|
|
"print(f\"m<v^2>/3kT = {m*avg_vv/3/kT:.3f}\")\n"
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "markdown",
|
|
"id": "270cf425-244a-435c-8df8-1f2f0e457249",
|
|
"metadata": {},
|
|
"source": [
|
|
"Notice that we have to use the mean-squared velocity, not the average velocity, in our calculation. The root mean-squared velocity is about 10% higher than the average velocity."
|
|
]
|
|
},
|
|
{
|
|
"cell_type": "code",
|
|
"execution_count": null,
|
|
"id": "8b06bd12-f93c-4cb0-91f8-0072c96733fa",
|
|
"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,
|
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"nbformat_minor": 5
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}
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