diff --git a/notebooks_en/1_Properties.ipynb b/notebooks_en/1_Properties.ipynb index 69be08f..4e4a71e 100644 --- a/notebooks_en/1_Properties.ipynb +++ b/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, diff --git a/notebooks_en/2_Ideal_Gases.ipynb b/notebooks_en/2_Ideal_Gases.ipynb index 886947d..9eb869d 100644 --- a/notebooks_en/2_Ideal_Gases.ipynb +++ b/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, diff --git a/notebooks_en/3_Heat_Transfer.ipynb b/notebooks_en/3_Heat_Transfer.ipynb index 2f114ef..2bb6f1f 100644 --- a/notebooks_en/3_Heat_Transfer.ipynb +++ b/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, diff --git a/notebooks_en/4_Work.ipynb b/notebooks_en/4_Work.ipynb index 6cb1327..c8d2f73 100644 --- a/notebooks_en/4_Work.ipynb +++ b/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", "\n", "\n", @@ -519,7 +519,7 @@ "\n", "\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", "\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, diff --git a/notebooks_en/5_Energy_Balance_Closed_Systems.ipynb b/notebooks_en/5_Energy_Balance_Closed_Systems.ipynb index 5a4dd04..89b9206 100644 --- a/notebooks_en/5_Energy_Balance_Closed_Systems.ipynb +++ b/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", "\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,