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   "source": [
    "# Introduction to Thermodynamics and Statistical Physics"
   ]
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    "In this lecture, we are going to discuss the 1st law of thermodynamics. In particular, we'll cover:\n",
    "\n",
    "* The First Law.\n",
    "* Heat Capacity.\n",
    "    - Of an Ideal Gas.\n",
    "* Reversibility.\n",
    "* Isothermal/Adiabatic Expansions.\n"
   ]
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   "source": [
    "## The First Law of Thermodynamics"
   ]
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    "At the end of the last lecture, we stated the first law. In mathematical form, this is:\n",
    "$$ \n",
    "    {\\rm d U} = {\\rm d}Q + {\\rm d}W.\n",
    "$$\n",
    "Our first task is to see if there's an easy form for expressing how the ${\\rm d}W$ term behaves. To do this, consider the below setup.\n",
    "\n",
    "![Sealed_Container](Figures/Sealed_Container.png)\n",
    "\n",
    "The force used on the piston to compress the gas is $F=P A$, where $A$ is the area of the piston. By compressing the gas such that it's change in volume is $-{\\rm d}V$, we also get that $A{\\rm d}x=-{\\rm d}V$. Thus, the work done in compressing the gas is given by\n",
    "$$\n",
    "    {\\rm d}W = F {\\rm d} x = -P {\\rm d} V\n",
    "$$\n",
    "This assumes that the process is reversible, but we'll come back to that later on. So, the first law can also be written as\n",
    "$$ \n",
    "    {\\rm d U} = {\\rm d}Q -P {\\rm d} V\n",
    "$$\n",
    "for reversible processes."
   ]
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   "source": [
    "## Revisiting Heat Capacity"
   ]
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    "Ok, let's return to our definition of heat capacity from lecture 1, which stated that\n",
    "$$\n",
    "    {\\rm d}Q = C {\\rm d T}  \\Rightarrow C = \\frac{{\\rm d}Q}{{\\rm d}T}\n",
    "$$\n",
    "We now want to use this expression in combination with the first law to see how adding heat changes the internal energy of a gas.\n",
    "\n",
    "To do this, let's start with the internal energy of gas, and say that this is only a function of temperature and volume such that $U=U(T,V)$. A small change in the internal energy can thus be written as\n",
    "$$\n",
    "    {\\rm d} U = \\left(\\frac{\\partial U}{\\partial T}\\right)_V {\\rm d} T + \\left(\\frac{\\partial U}{\\partial V}\\right)_T {\\rm d} V\n",
    "$$\n",
    "which is a mathematical operation we can do as $U$ is a function of state (i.e. ${\\rm d} U$ is an exact differential). Rearranging the first law such that it's in relation to ${\\rm d} Q$ gives\n",
    "$$\n",
    "    {\\rm d} Q = {\\rm d}U +P {\\rm d} V = \\left(\\frac{\\partial U}{\\partial T}\\right)_V {\\rm d} T + \\left[ \\left(\\frac{\\partial U}{\\partial V}\\right)_T +P \\right] {\\rm d} V.\n",
    "$$\n",
    "Now, taking the derivative of this with respect to ${\\rm d} T$ gives\n",
    "$$\n",
    "    \\frac{{\\rm d} Q}{{\\rm d} T} = \\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[ \\left(\\frac{\\partial U}{\\partial V}\\right)_T +P \\right] \\frac{{\\rm d} V}{{\\rm d}T}\n",
    "$$\n",
    "So the heat capacity at constant volume then becomes\n",
    "$$\n",
    "    C_V = \\left(\\frac{{\\rm d} Q}{{\\rm d} T}\\right)_V = \\left(\\frac{\\partial U}{\\partial T}\\right)_V.\n",
    "$$\n",
    "The heat capacity at constant pressure is then\n",
    "$$\n",
    "    C_P = \\left(\\frac{{\\rm d} Q}{{\\rm d} T}\\right)_P = \\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[ \\left(\\frac{\\partial U}{\\partial V}\\right)_T +P \\right] \\left( \\frac{{\\rm d} V}{{\\rm d}T}\\right)_P\n",
    "$$\n",
    "which then gives\n",
    "$$\n",
    "    C_P-C_V = \\left[ \\left(\\frac{\\partial U}{\\partial V}\\right)_T +P \\right] \\left( \\frac{{\\rm d} V}{{\\rm d}T}\\right)_P.\n",
    "$$\n",
    "Finally, the ratio of these two heat capacities is called the Adiabatic Index, and is given by\n",
    "$$\n",
    "    \\gamma = \\frac{C_P}{C_V}\n",
    "$$"
   ]
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   "source": [
    "## The Heat Capacity of an Ideal Gas"
   ]
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    "Given that the internal energy of an ideal gas is given by $U=\\frac{3}{2} N k_{\\rm B} T$, let's derive expressions for $C_P$ and $C_V$.\n",
    "First, note that the internal energy is independant of volume. As such \n",
    "$$\n",
    "    \\frac{\\partial U}{\\partial V}=0.\n",
    "$$\n",
    "For one mole of ideal gas, we know that $P V = N k_{\\rm B} T$, so\n",
    "$$\n",
    "    V = \\frac{N k_{\\rm B} T}{P}\n",
    "$$\n",
    "which gives\n",
    "$$\n",
    "    \\left(\\frac{\\partial V}{\\partial T}\\right)_P = \\frac{N k_{\\rm B}}{P}\n",
    "$$\n",
    "So then the heat capacities are\n",
    "\\begin{align}\n",
    "    C_V &= \\left(\\frac{\\partial U}{\\partial T}\\right)_V = \\frac{3}{2}N k_{\\rm B}\\\\\n",
    "    C_P-C_V &= \\left[ \\left(\\frac{\\partial U}{\\partial V}\\right)_T +P \\right] \\left( \\frac{{\\partial} V}{{\\partial}T}\\right)_P = N k_{\\rm B}\\\\\n",
    "    C_P &= \\frac{5}{2}N k_{\\rm B}\n",
    "\\end{align}"
   ]
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   "cell_type": "markdown",
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   "source": [
    "## Reversibility, Isothermal Expansions, and Adiabatic expansions"
   ]
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    "In most scenarios, a physical process involves heat being dissipated away into the surrounding environment. This means that such a process is very difficult to naturally reverse as it is very unlikely that the lost energy will flow back into the system. A nice example of this is to consider an egg falling off a table. It will hit the floor and shatter, losing some energy into the ground in the process. \n",
    "\n",
    "A more formal way of thinking about this is that, for large numbers, the statistical behaviour of them make more outcomes more likely than order (remember how graph of the statistical weight looked). As such, this suggests that when dealing with large numbers, physical changes appear to be driven in an irreverisble direction.\n",
    "\n",
    "Our challenge now is to come up with a way of carrying out a process reversibly (and was the challenge faced by physicists when attempting to construct the most efficient engine possible).\n",
    "\n",
    "So, how do we do things reverisbly? Consider expanding or compressing a gas. If we do it very, very slowly, then the gas will remain in equilibrium throughout the process. Such a process is referred to as **quasistatic**.\n",
    "\n",
    "There are two such processes which we consider below."
   ]
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   "source": [
    "## Isothermal expansion of an Ideal Gas"
   ]
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    "Consider a reversible, isothermal expansion of an ideal gas. Isothermal here means \"at constant temperature\", such that ${\\rm \\Delta}T=0$. We want to know what the heat change of such a gas is. As a starting point, let's consider the internal energy of the gas:\n",
    "$$\n",
    "    {\\rm d} U = C {\\rm dT} = 0.\n",
    "$$\n",
    "This means that, from the first law,\n",
    "$$\n",
    "    {\\rm d} Q = -{\\rm d}W\n",
    "$$\n",
    "So, the work done by the gas as it expands is equal to the heat it absorbs from its surroundings. Recalling from earlier that ${\\rm d}W=-P {\\rm d}V$ for a reversible process, we can then obtain the total heat absorbed by the gas:\n",
    "\\begin{align}\n",
    "    {\\rm \\Delta} Q &= \\int {\\rm d} Q\\\\\n",
    "     &= -\\int {\\rm d} W\\\\\n",
    "     &= \\int^{V_2}_{V_1} P{\\rm d} V\\\\\n",
    "     &= \\int^{V_2}_{V_1} \\frac{N k_{\\rm B} T}{V}{\\rm d} V\\\\\n",
    "     &= N k_{\\rm B} T \\ln \\frac{V_2}{V_1}\\\\\n",
    "     &= R T \\ln \\frac{V_2}{V_1}\n",
    "\\end{align}\n",
    "where that last expression is for one mole of ideal gas.\n",
    "\n",
    "So, for an expansion $V_2>V_1$, so ${\\rm \\Delta} Q > 0$"
   ]
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   "source": [
    "## Adiabatic expansion of an Ideal Gas"
   ]
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    "Consider a reversible, adiathermal expansion of an ideal gas. Adiathermal here means \"without flow of heat\". A process which is both adiathermal and reversible is **adiabatic**. For this process\n",
    "$$\n",
    "    {\\rm d} Q = 0.\n",
    "$$\n",
    "This means that, from the first law,\n",
    "$$\n",
    "    {\\rm d} U = {\\rm d}W\n",
    "$$\n",
    "For an ideal gas, we have that ${\\rm d} U = C_V {\\rm d T}$, and because the process is reversible we again have that ${\\rm d}W=-P {\\rm d}V$. As such, we have that\n",
    "\\begin{align}\n",
    "    C_V {\\rm d T} &= -P {\\rm d}V = - \\frac{Nk_{\\rm B}}{V} {\\rm d}V\\\\\n",
    "\\end{align}\n",
    "Let's work with one mole of ideal gas for the moment ($N_{\\rm A} k_{\\rm B}=R$). As such, we get\n",
    "\\begin{align}\n",
    "    \\ln \\frac{T_2}{T_1} &= -\\frac{R}{C_V} \\ln \\frac{V_2}{V_1}.\n",
    "\\end{align}\n",
    "Recalling that $C_P=C_V+R$ we find that\n",
    "$$\n",
    "    \\gamma = \\frac{C_P}{C_V}=1+\\frac{R}{C_V}\n",
    "$$\n",
    "which gives\n",
    "$$\n",
    "    -\\frac{R}{C_V} = 1-\\gamma.\n",
    "$$\n",
    "This let's us simplify the above expression to get\n",
    "$$\n",
    "    \\ln \\frac{T_2}{T_1} = (1-\\gamma) \\ln \\frac{V_2}{V_1} = \\ln \\left(\\frac{V_2}{V_1}\\right)^{1-\\gamma}\n",
    "$$\n",
    "Finally, we get that\n",
    "$$\n",
    "    TV^{\\gamma-1} = const\n",
    "$$\n",
    "Using the ideal gas law ($P V \\propto T$) let's us rewrites this as both\n",
    "\\begin{align}\n",
    "    P^{1-\\gamma} T^{\\gamma} &= const\\\\\n",
    "    P V^{\\gamma} &= const\n",
    "\\end{align}"
   ]
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   "source": [
    "## Isotherms & Adiabats"
   ]
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   "source": [
    "So now we have two scenarios for working an ideal gas. It can undergo an adiabatic process, in which case $P V^\\gamma = const$, or it can undergo an isothermal expansion, in which case $PV=const$. We'll cover what these processes can be used for later, but the below can be treated as a prelude, as it plots pressure versus volume for both processes for two different initial conditions."
   ]
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\n",
      "text/plain": [
       "<Figure size 600x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import astropy.units as u\n",
    "import astropy.constants as c\n",
    "\n",
    "def adiabatic(V_i,P_i,V):\n",
    "    gamma = 5/3\n",
    "    return (P_i*V_i**gamma)/(V**gamma)\n",
    "\n",
    "def isothermal(V_i,P_i,V):\n",
    "    T = P_i*V_i/c.R\n",
    "    return (c.R*T/V)\n",
    "\n",
    "P_is = np.arange(3,5,1)*u.Pa\n",
    "V = np.arange(0.5,2.02,0.01)\n",
    "\n",
    "plt.figure(figsize=[4,3],dpi=150)\n",
    "for P_i in P_is:\n",
    "    V_i = 1*u.m**3\n",
    "    P_a = adiabatic(V_i,P_i,V)\n",
    "    P_isot = isothermal(V_i,P_i,V)\n",
    "    if P_i == 3.0*u.Pa:\n",
    "        plt.plot(V,P_a,'C0-',label='Adiabat, $PV^\\gamma=const$')\n",
    "        plt.plot(V,P_isot,'C1--',label='Isotherm, $PV=const$')\n",
    "    else:\n",
    "        plt.plot(V,P_a,'C0-',label='')\n",
    "        plt.plot(V,P_isot,'C1--',label='')\n",
    "frame1 = plt.gca()\n",
    "frame1.axes.get_xaxis().set_ticks([])\n",
    "frame1.axes.get_yaxis().set_ticks([])\n",
    "plt.xlim(0.5,2)\n",
    "plt.ylim(0.0,13)\n",
    "plt.ylabel(\"Pressure\")\n",
    "plt.xlabel(\"Volume\")\n",
    "plt.title(\"Adiabats and Isotherms for\\n different initial conditions.\")\n",
    "plt.legend()\n",
    "plt.savefig(\"Figures/Adiabats_vs_isotherms.jpg\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}