Minor corrections after reading and running the notebooks

notebooks_en/1_Properties.ipynb

@@ -182,7 +182,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Water boils at $100 ^\\circ C$ under standard atmospheric pressure.  As it transitions into the gas phase, its specific volume increases dramatically from what it was as a solid.  Let's verify this as we look at temperatures slightly below and above the boiling point."
+    "Water boils at $100 ^\\circ C$ under standard atmospheric pressure.  As it transitions into the gas phase, its specific volume increases dramatically from what it was as a liquid.  Let's verify this as we look at temperatures slightly below and above the boiling point."
    ]
   },
   {
@@ -935,7 +935,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.6"
   }
  },
  "nbformat": 4,

notebooks_en/2_Ideal_Gases.ipynb

@@ -22,7 +22,7 @@
     "\n",
     "In many situations, we want to avoid a phase change because of design constraints.  For example, most pumps and turbines are designed for either a pure liquid or a pure vapor.  A mixture of phases causes wear and tear on these components, leading to early failure.\n",
     "\n",
-    "In this lesson, we will look at two very common approximations to single-phase substances: incompressible liquids and ideal gases.  Using Cantera, which provides exact property values (to within experimental error), we can calculate the accuracy of these approximations."
+    "In this lesson, we will look at two very common approximations to single-phase substances: incompressible liquids and ideal gases.  Using Cantera, which uses the most accurate equations of state, we can estimate the accuracy of these approximations."
    ]
   },
   {
@@ -141,7 +141,7 @@
    "outputs": [],
    "source": [
     "rel_diff_T = np.mean((v_array[:,1]-v_array[:,0])/v_array[:,0]*100.0)\n",
-    "print('Relative difference across pressure range =',rel_diff_T,'%')"
+    "print('Relative difference across temperature range =',rel_diff_T,'%')"
    ]
   },
   {
@@ -611,7 +611,11 @@
    "source": [
     "Let's look at the same situation for carbon dioxide, which we've already seen behaves like an ideal gas under reasonable atmospheric conditions.  But what do we mean by \"reasonable\"?  Is there a quick way we can determine if the ideal gas law is accurate enough to use in design?\n",
     "\n",
-    "Examinging the previous figure, we can see that $Z \\to 1$ as we move up and to the right of the critical point (the red star).  Near this point, the distinction between liquids and gases is blurred -- definitely not the behavior of an ideal gas!\n",
+    "Examining the previous figure, we can see that \n",
+    "\n",
+    "1. Under the vapor dome, the law is just wrong. This is due to the presence of the liquid phase.\n",
+    "\n",
+    "2. $Z \\to 1$ as we move up and to the right of the critical point (the red star).  Near this point, the distinction between liquids and gases is blurred -- definitely not the behavior of an ideal gas!\n",
     "\n",
     "Let $T_c$ and $P_c$ be the temperature and pressure of the critical point, respectively.  Then we can make the following observations:\n",
     "\n",
@@ -624,7 +628,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Let's compare the cricial points of carbon dioxide and water:"
+    "Let's compare the critical points of carbon dioxide and water:"
    ]
   },
   {
@@ -726,6 +730,13 @@
     "css_file = '../style/custom.css'\n",
     "HTML(open(css_file, \"r\").read())"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -744,7 +755,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,

notebooks_en/3_Heat_Transfer.ipynb

@@ -301,6 +301,13 @@
     "import scipy.integrate as integrate"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Next we write c$_v$ as a function of T using cantera:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -315,6 +322,13 @@
     "    return state.cv         # return cv(T)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "And we can now solve the integral approximately using numerical quadrature:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -560,6 +574,15 @@
     "css_file = '../style/custom.css'\n",
     "HTML(open(css_file, \"r\").read())"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "  "
+   ]
   }
  ],
  "metadata": {
@@ -578,7 +601,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,

notebooks_en/4_Work.ipynb

@@ -109,7 +109,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Computing the work done during a process almost always involves evaluating an integral, except in the simplest cases.  In this example, we can evaulate the integral using a formula to get an exact answer, so it provides an opportunity to test a numerical method for doing the same.  The following figure shows the integral we need to compute $\\int\\limits_{x_1}^{x_2} kxdx$, and a numerical approximation of it:\n",
+    "Computing the work done during a process almost always involves evaluating an integral, except in the simplest cases.  In this example, we can evaluate the integral using a formula to get an exact answer, so it provides an opportunity to test a numerical method for doing the same.  The following figure shows the integral we need to compute $\\int\\limits_{x_1}^{x_2} kxdx$, and a numerical approximation of it:\n",
     "\n",
     "<img src=\"../images/spring force integration.png\" width=\"300\" />\n",
     "\n",
@@ -519,7 +519,7 @@
     "\n",
     "<img src=\"../images/piston cylinder const pressure.png\" width=\"600\" />\n",
     "\n",
-    "We can see quickly that the pressure inside the cylinder must be equal to the pressure outside at all times by considering a free body diagram of the piston:\n",
+    "We can see quickly that, assuming negligible piston mass,  the pressure inside the cylinder must be equal to the pressure outside at all times by considering a free body diagram of the piston:\n",
     "\n",
     "<img src=\"../images/piston fbd.png\" width=\"150\" />\n",
     "\n",
@@ -535,7 +535,7 @@
     "\n",
     "where, as usual, we define $Q > 0$ to be heat transferred *to* the system and $W > 0$ to be work done *by* the system (on the surroundings -- in this case, on the piston).\n",
     "\n",
-    "For heat conduction, we make the usual assumption that he rate at which heat transfered can be well approximated by [Fourier's law](https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law):\n",
+    "For heat conduction, we make the usual assumption that the rate at which heat is transfered can be well approximated by [Fourier's law](https://en.wikipedia.org/wiki/Thermal_conduction#Fourier's_law):\n",
     "\n",
     "$\\dfrac{dQ}{dt} = k(T_{room}-T_{sys})$\n",
     "\n",
@@ -547,7 +547,7 @@
     "\n",
     "where \\\\(m\\\\) is the mass of the air, and \\\\(c_v\\\\) is its specific heat at constant volume.\n",
     "\n",
-    "If we assume air is an ideal gas, then mathematically it can be shown that $c_v(T,P) \\approx c_v(T)$, just like incompressible liquids and solids.  Thus, we can convert the partial derivative to an ordinary derivative:\n",
+    "If we assume air is an ideal gas, then mathematically it can be shown that $c_v(T,P) = c_v(T)$, just like incompressible liquids and solids.  Thus, we can convert the partial derivative to an ordinary derivative:\n",
     "\n",
     "$\\dfrac{dU_{sys}}{dT_{sys}} = m c_v$\n",
     "\n",
@@ -774,7 +774,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,

notebooks_en/5_Energy_Balance_Closed_Systems.ipynb

@@ -597,7 +597,7 @@
     "\n",
     "$\\Delta E_{sys} = \\Delta U = m \\Delta u = m(u_2-u_1)$\n",
     "\n",
-    "To determine the work the gas does on the piston, let's look at the free body diagram of the piston:\n",
+    "To determine the work the gas does on the piston, let's look at the free body diagram of the piston. Neglecting piston mass:\n",
     "\n",
     "<img src=\"../images/spring piston fbd.png\" width=\"250\" />\n",
     "\n",
@@ -841,6 +841,13 @@
     "css_file = '../style/custom.css'\n",
     "HTML(open(css_file, \"r\").read())"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -859,7 +866,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.5"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,