added interactive features

examples/ideal_gas_law/first_principles.ipynb

@@ -1,5 +1,15 @@
 {
  "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -15,9 +25,39 @@
     "where, $V$ is the volume of the system and $\\Lambda$ is the de Broglie thermal wavelength, \n",
     "\n",
     "$$\n",
-    "\\Lambda = \\bigg(\\frac{\\beta h^2}{2\\pi m}\\bigg)^{1/2}.\n",
-    "$$\n",
+    "\\Lambda = \\bigg(\\frac{\\beta h^2}{2\\pi m}\\bigg)^{1/2} = \\bigg(\\frac{h^2}{2 k_B T \\pi m}\\bigg)^{1/2}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The De Broglie wavelength for an electron can be calculated using electron mass:\n",
+    "\n",
+    "$$m_e = 9.11*10^{-31}$$ \n",
+    "\n",
+    "Write a function that calculates the De Broglie wavelength for an electron at room temp (293k)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m_e = 9.11e-31\n",
+    "h = 6.626e-34\n",
+    "k_b = 1.38e-23\n",
     "\n",
+    "def db_wavelength(T)\n",
+    "    return ◽◽◽"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "The most useful way to work with the partition function is in its logarithmic form, \n",
     "\n",
     "$$\n",
@@ -49,12 +89,44 @@
     "$$"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "In the cell below, write a function that calculates the pressure using the ideal gas law"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
-   "source": []
+   "source": [
+    "def ideal_pressure(◽◽◽,◽◽◽,◽◽◽)\n",
+    "    return ◽◽◽"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "See how this changes for a range of temperatures"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "T = ◽◽◽\n",
+    "p = ideal_pressure(◽◽◽,◽◽◽,◽◽◽)\n",
+    "\n",
+    "plt.plot(T, p)\n",
+    "plt.xlabel('Temperature')\n",
+    "plt.ylabel('Ideal Pressure')\n",
+    "plt.show()"
+   ]
   }
  ],
  "metadata": {