Improved text and corrected typos

book/content/modelling/04_thermodynamics/01_fundamentals.ipynb

@@ -32,7 +32,9 @@
    "source": [
     "# Fundamentals\n",
     "\n",
-    "Thermodynamics is the branch of physics that focuses on describing the macroscopic changes in energy and work of a system. In classical thermodynamics, the behavior of macroscopic systems is governed by a set of laws, which were derived from empirical observations. At first, the laws of thermodynamics were built on the basis of properties that could be measured (e.g. temperature, volume, pressure), and no connection with theories concerning the molecular nature of the matter existed. Later, however, the approach based on statistical mechanics provided linkages between molecular interactions and their manifestations in the macroscopic observable properties of a system.      \n",
+    "Thermodynamics is the branch of physics that focuses on describing the macroscopic changes in energy and work of a system. In classical thermodynamics, the behaviour of macroscopic systems is governed by a set of laws, which were derived from empirical observations. At first, the laws of thermodynamics were built on the basis of properties of the system that could be measured (e.g. temperature, volume, pressure), and no connection with theories concerning the molecular nature of the matter existed. \n",
+    "\n",
+    "Later, however, the approach based on statistical mechanics provided linkages between molecular interactions and their manifestations in the macroscopic observable properties of a system. This lead to what is referred to as statistical thermodynamics. By means of the statistical approach, it is possible to derive all the laws of thermodynamics as well as all thermodynamic properties based on the description of the microscopic states of a system on a molecular level.\n",
     "\n",
     "\n",
     "<!---\n",
@@ -47,24 +49,31 @@
    "source": [
     "## Systems\n",
     "\n",
-    "In a thermodynamic analysis it is essential to define the investigated system and its interaction with the ambient environment. \n",
-    "\n",
-    "<!---\n",
-    "A system is a volume containing a (fixed) number of particles.\n",
-    "-->\n",
+    "In a thermodynamic analysis it is essential to define the investigated system and its interactions with the surroundings. A system can be any region that is clearly defined in terms of spatial coordinates which can be fixed or moving. The surface delimiting this region is referred to as the boundary. The boundary of a system may be an actual wall or an imaginary surface. The external region to the system boundary is called the environment or surroundings. \n",
     "\n",
-    "The interaction of systems can be described with the following three process quantities:\n",
+    "A system can interact with the surroundings through the following three process quantities:\n",
     "\n",
-    "* **work**, $\\mf W$, e.g. mechanical or electrical work, like the compression of a volume due to a moving pistion, \n",
+    "* **work**, $\\mf W$, e.g. mechanical or electrical work, like the compression or expansion of a volume due to a moving piston, \n",
     "* **heat**, $\\mf Q$, e.g. energy transfer due to a temperature difference, and\n",
     "* **mass flow**, e.g. addition of mass into a system.\n",
     "\n",
-    "There are four definitions of system boundaries / interactions of systems (including the ambient environment):\n",
     "\n",
-    "* **isolated**: no mass flow, no heat flow ($\\mf \\Delta Q=0$) and no work done ($\\mf \\Delta W=0$),\n",
-    "* **closed**: no mass flow, possibility for heat flow ($\\mf \\Delta Q\\neq 0$) and / or work to be done ($\\mf \\Delta W\\neq 0$)\n",
+    "The interactions between a system and the environment is determined by the nature of the system boundary. There are four definitions of system boundaries / interactions between systems and surroundings:\n",
+    "\n",
+    "* **isolated**: no mass flow, no heat flow ($\\mf \\Delta Q=0$) and no work done ($\\mf \\Delta W=0$);\n",
+    "* **closed**: no mass flow, possibility for heat flow ($\\mf \\Delta Q\\neq 0$) and / or work to be done ($\\mf \\Delta W\\neq 0$);\n",
     "* **adiabatic**: no mass and no heat flow ($\\mf \\Delta Q=0$), yet work can to be done ($\\mf \\Delta W\\neq 0$), and\n",
-    "* **open**: possibility for mass and heat flow, as well as for work to be done."
+    "* **open**: possibility for mass and heat flow, as well as for work to be done.\n",
+    "\n",
+    "\n",
+    "\n",
+    "<!---\n",
+    "A system is a volume containing a (fixed) number of particles.\n",
+    "\n",
+    "\n",
+    "\n",
+    "\n",
+    "-->"
    ]
   },
   {
@@ -74,13 +83,13 @@
    "source": [
     "## State Quantities\n",
     "\n",
-    "The state of a thermodynamic system can be expressed with these measurable quantities like\n",
+    "The state of a thermodynamic system can be expressed with the following primitive properties like\n",
     "\n",
     "* **pressure**, $\\mf p$,\n",
     "* **volume**, $\\mf V$, and\n",
     "* **temperature**, $\\mf T$,\n",
     "\n",
-    "and the deduced quantites like\n",
+    "and the derived properties like\n",
     "\n",
     "* **internal energy**, $\\mf U$,\n",
     "* **enthalpy**, $\\mf H$, and\n",
@@ -90,7 +99,7 @@
     "\n",
     "In contrast to that, the process quantites (heat and work) do depend on the way the system changes.\n",
     "\n",
-    "Some of the quantities depend on the system size, e.g. the system's mass, and are called extensive quantities. Examples are the inner energy or enthalpy.\n",
+    "Some of the quantities depend on the system size, e.g. the system's mass, and are called extensive quantities. Examples are the internal energy or enthalpy.\n",
     "\n",
     "Intensive quantities, like pressure or temperature, do not depend on the system's size.\n",
     "\n",
@@ -114,7 +123,7 @@
     "\n",
     "The SI-unit of temperature is Kelvin, where $\\mf 0~K$ is the absolute lowest temperature and $\\mf 0~^\\circ C$ corresponds to $\\mf 273.15~K$. Temperature differences have the same values in Kelvin as in Celsius. \n",
     "\n",
-    "At finite temperatre, the particles in a gas have not a single velocity, but a distributed over a broad range. This is an important aspect, as many chemical reactions require the involved particles to overcome the activation energy. Thus, there is always a probability that a particle has the needed kinetic energy. This velocitiy distribution, the Maxwell distribution, depends only on the temperature and the gas properties:\n",
+    "At finite temperature, the particles in a gas have not a single velocity, but a distributed over a broad range. This is an important aspect, as many chemical reactions require the involved particles to overcome the activation energy. Thus, there is always a probability that a particle has the needed kinetic energy. This velocitiy distribution, the Maxwell-Boltzmann distribution, depends only on the temperature and the gas properties:\n",
     "\n",
     "$$\n",
     "\\mf f(v) = 4\\pi v^2 \\left(\\frac{m_M}{2\\pi k_B T}\\right)^{\\frac{3}{2}} \\cdot e^{\\left(-\\frac{m_M v^2}{2 k_B T}\\right)}\\quad ,\n",