New Application Center Additions
https://www.maplesoft.com/applications
en-us2018 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 23 Apr 2018 13:06:25 GMTMon, 23 Apr 2018 13:06:25 GMTThe latest content added to the Application Centerhttps://www.maplesoft.com/images/Application_center_hp.jpgNew Application Center Additions
https://www.maplesoft.com/applications
Расчет термического КПД парогазовой установки
https://www.maplesoft.com/applications/view.aspx?SID=154437&ref=Feed
Это применение вычисляет тепловую эффективность паровой турбины (на основе цикла Ранкина), в сочетании с газовой турбиной на основе цикла)<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Расчет термического КПД парогазовой установки" style="max-width: 25%;" align="left"/>Это применение вычисляет тепловую эффективность паровой турбины (на основе цикла Ранкина), в сочетании с газовой турбиной на основе цикла)https://www.maplesoft.com/applications/view.aspx?SID=154437&ref=FeedWed, 18 Apr 2018 04:00:00 ZProf. Valery Ochkov, Aung Thu Ya TunProf. Valery Ochkov, Aung Thu Ya TunRecognizing Handwritten Digits with Machine Learning
https://www.maplesoft.com/applications/view.aspx?SID=154434&ref=Feed
Using the DeepLearning package, this application trains a two-layer neural network to recognize the numbers in images of handwritten digits. The trained neural network is then applied to a number of test images.
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The training and testing images are a very small subset of the MNIST database of handwritten digits; these consist of 28 x 28 pixel images of a handwritten digit, ranging from 0 to 9.
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The DeepLearning package is a partial interface to Tensorflow, an open-source machine learning framework.<img src="https://www.maplesoft.com/view.aspx?si=154434/recognizing_digits.png" alt="Recognizing Handwritten Digits with Machine Learning" style="max-width: 25%;" align="left"/>Using the DeepLearning package, this application trains a two-layer neural network to recognize the numbers in images of handwritten digits. The trained neural network is then applied to a number of test images.
<BR><BR>
The training and testing images are a very small subset of the MNIST database of handwritten digits; these consist of 28 x 28 pixel images of a handwritten digit, ranging from 0 to 9.
<BR><BR>
The DeepLearning package is a partial interface to Tensorflow, an open-source machine learning framework.https://www.maplesoft.com/applications/view.aspx?SID=154434&ref=FeedMon, 09 Apr 2018 04:00:00 ZSamir KhanSamir KhanGráficas de funciones y de su primera derivada
https://www.maplesoft.com/applications/view.aspx?SID=154433&ref=Feed
La construcción del gráfico de la primera derivada de una función, a partir del estudio cualitativo de la pendiente de la recta tangente en cada punto de su dominio, proporciona una visión más enriquecedora al estudiante que el simple hecho de calcular la derivada de una función y construir su gráfica utilizando el comando plot de Maple.
Esta hoja utiliza las capacidades de Maple para que el estudiante pueda observar la construcción mencionada anteriormente, de una forma interactiva y visual,la cual le permitirá comprender mejor el proceso y entender el tipo de información que pueden extraer de la gráfica de la derivada de una función.
La hoja también permite al estudiante realizar ejercicios en los que, en un grupo, se pide que construya la gráfica de la primera derivada, a partir del estudio cualitativo de la pendiente de la recta tangente de una función; en otro grupo de ejercicios, se pide al estudiante que construya la gráfica de una función, a partir del estudio cualitativo de la gráfica de su primera derivada.<img src="https://www.maplesoft.com/view.aspx?si=154433/db83795d261dcf0a21a5ee294d2425a6.gif" alt="Gráficas de funciones y de su primera derivada" style="max-width: 25%;" align="left"/>La construcción del gráfico de la primera derivada de una función, a partir del estudio cualitativo de la pendiente de la recta tangente en cada punto de su dominio, proporciona una visión más enriquecedora al estudiante que el simple hecho de calcular la derivada de una función y construir su gráfica utilizando el comando plot de Maple.
Esta hoja utiliza las capacidades de Maple para que el estudiante pueda observar la construcción mencionada anteriormente, de una forma interactiva y visual,la cual le permitirá comprender mejor el proceso y entender el tipo de información que pueden extraer de la gráfica de la derivada de una función.
La hoja también permite al estudiante realizar ejercicios en los que, en un grupo, se pide que construya la gráfica de la primera derivada, a partir del estudio cualitativo de la pendiente de la recta tangente de una función; en otro grupo de ejercicios, se pide al estudiante que construya la gráfica de una función, a partir del estudio cualitativo de la gráfica de su primera derivada.https://www.maplesoft.com/applications/view.aspx?SID=154433&ref=FeedSun, 08 Apr 2018 04:00:00 ZRanferi GutierrezRanferi GutierrezCalculation of thermal efficiency of combined-cycle plant
https://www.maplesoft.com/applications/view.aspx?SID=154432&ref=Feed
This application calculates the thermal efficiency of a steam turbine (based on a Rankine cycle), combined with a gas turbine based on the Brayton Cycle)<img src="https://www.maplesoft.com/view.aspx?si=154432/Calculation_of__thermal__efficiency_of_combined-cycle_plant.png" alt="Calculation of thermal efficiency of combined-cycle plant" style="max-width: 25%;" align="left"/>This application calculates the thermal efficiency of a steam turbine (based on a Rankine cycle), combined with a gas turbine based on the Brayton Cycle)https://www.maplesoft.com/applications/view.aspx?SID=154432&ref=FeedFri, 06 Apr 2018 04:00:00 ZProf. Valery OchkovProf. Valery OchkovSudoku in .mw format
https://www.maplesoft.com/applications/view.aspx?SID=154431&ref=Feed
The worksheet is in .mw format so that the font of character is displayed on sudokus saved in gif format so that we can import them into softwares that scans them.
This worksheet displays a maplet.<img src="https://www.maplesoft.com/view.aspx?si=154431/sudoku-1.gif" alt="Sudoku in .mw format" style="max-width: 25%;" align="left"/>The worksheet is in .mw format so that the font of character is displayed on sudokus saved in gif format so that we can import them into softwares that scans them.
This worksheet displays a maplet.https://www.maplesoft.com/applications/view.aspx?SID=154431&ref=FeedTue, 03 Apr 2018 04:00:00 Zxavier cormierxavier cormierGödel's Universe
https://www.maplesoft.com/applications/view.aspx?SID=154430&ref=Feed
In 1949, Kurt Gödel proposed a solution to Einstein's field equations that exhibited a rotation of matter (with a nonvanishing cosmological constant). This solution allows the existence of closed timelike curves, which implies the possibility of time travel. In this worksheet, we demonstrate the use of DifferentialGeometry and Tensor packages to calculate the Ricci tensor, Ricci scalar, and Einstein tensor. We also apply the calculus of variations to calculate the null geodesics (trajectories of light rays) in Gödel's universe. The notation is based on the presentation in the monograph of Stephen Hawking and George Ellis.<img src="https://www.maplesoft.com/view.aspx?si=154430/godelnullgeodesics.png" alt="Gödel's Universe" style="max-width: 25%;" align="left"/>In 1949, Kurt Gödel proposed a solution to Einstein's field equations that exhibited a rotation of matter (with a nonvanishing cosmological constant). This solution allows the existence of closed timelike curves, which implies the possibility of time travel. In this worksheet, we demonstrate the use of DifferentialGeometry and Tensor packages to calculate the Ricci tensor, Ricci scalar, and Einstein tensor. We also apply the calculus of variations to calculate the null geodesics (trajectories of light rays) in Gödel's universe. The notation is based on the presentation in the monograph of Stephen Hawking and George Ellis.https://www.maplesoft.com/applications/view.aspx?SID=154430&ref=FeedMon, 02 Apr 2018 04:00:00 ZDr. Frank WangDr. Frank WangSolving 2nd Order Differential Equations
https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=Feed
This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.<img src="https://www.maplesoft.com/view.aspx?si=154426/2nd_order_des.PNG" alt="Solving 2nd Order Differential Equations" style="max-width: 25%;" align="left"/>This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonDE Phase Portraits - Animated Trajectories
https://www.maplesoft.com/applications/view.aspx?SID=154427&ref=Feed
This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.<img src="https://www.maplesoft.com/view.aspx?si=154427/phase_portrait.PNG" alt="DE Phase Portraits - Animated Trajectories" style="max-width: 25%;" align="left"/>This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.https://www.maplesoft.com/applications/view.aspx?SID=154427&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonNewton’s Method
https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=Feed
Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.<img src="https://www.maplesoft.com/view.aspx?si=154421/newtons_method.PNG" alt="Newton’s Method" style="max-width: 25%;" align="left"/>Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSolving ODEs using Maple: An Introduction
https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=Feed
In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.<img src="https://www.maplesoft.com/view.aspx?si=154422/ode.PNG" alt="Solving ODEs using Maple: An Introduction" style="max-width: 25%;" align="left"/>In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=FeedFri, 23 Mar 2018 04:00:00 ZDr. Francis PoulinDr. Francis PoulinRiemann Sums
https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=Feed
This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154423/riemann_sums.PNG" alt="Riemann Sums" style="max-width: 25%;" align="left"/>This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonBurgers' Vortex
https://www.maplesoft.com/applications/view.aspx?SID=154424&ref=Feed
The Burgers vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations.<img src="https://www.maplesoft.com/view.aspx?si=154424/burgersvortex.PNG" alt="Burgers' Vortex" style="max-width: 25%;" align="left"/>The Burgers vortex is a well known solution of the Navier Stokes equations that combines vorticity and shear. It allows for the study of a realistic flow in analytical form, thereby offering intuition for more complex flows. However, the cylindrical coordinate system makes certain calculations cumbersome to carry out by hand. This worksheet allows the user to explore aspects of the flow without having to carry out the calculations.https://www.maplesoft.com/applications/view.aspx?SID=154424&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSlow Manifold Analysis
https://www.maplesoft.com/applications/view.aspx?SID=154425&ref=Feed
This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.<img src="https://www.maplesoft.com/view.aspx?si=154425/slow_manifold_analysis.PNG" alt="Slow Manifold Analysis" style="max-width: 25%;" align="left"/>This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.https://www.maplesoft.com/applications/view.aspx?SID=154425&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonAdiabatic Flame Temperature of Butane
https://www.maplesoft.com/applications/view.aspx?SID=154396&ref=Feed
Liquid butane at standard temperature and pressure is burned with 100% theoretical air. The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>4</SUB>H<SUB>10</SUB> (l) + 6.5 O<SUB>2</SUB> (g) + 24.44 N<SUB>2</SUB> (g) → 4 CO<SUB>2</SUB> (g) + 5 H<SUB>2</SUB>O (g) + 24.44 N<SUB>2</SUB> (g)
</CENTER>
<BR><BR>
This application calculates the adiabatic flame temperature of the combustion products.
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The enthalpy of the reactants (which is known) is equated to the enthalpy of the products (which is a function of the unknown flame temperature). The resulting equation is solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
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Units are used throughout the calculation, and the ThermophysicalData:-Chemicals package is used to compute temperature-dependent values of enthalpy.
<BR><BR><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Adiabatic Flame Temperature of Butane" style="max-width: 25%;" align="left"/>Liquid butane at standard temperature and pressure is burned with 100% theoretical air. The combustion reaction is
<BR><BR>
<CENTER>
C<SUB>4</SUB>H<SUB>10</SUB> (l) + 6.5 O<SUB>2</SUB> (g) + 24.44 N<SUB>2</SUB> (g) → 4 CO<SUB>2</SUB> (g) + 5 H<SUB>2</SUB>O (g) + 24.44 N<SUB>2</SUB> (g)
</CENTER>
<BR><BR>
This application calculates the adiabatic flame temperature of the combustion products.
<BR><BR>
The enthalpy of the reactants (which is known) is equated to the enthalpy of the products (which is a function of the unknown flame temperature). The resulting equation is solved numerically using <A HREF="/support/help/maple/view.aspx?path=fsolve">fsolve</A>.
<BR><BR>
Units are used throughout the calculation, and the ThermophysicalData:-Chemicals package is used to compute temperature-dependent values of enthalpy.
<BR><BR>https://www.maplesoft.com/applications/view.aspx?SID=154396&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanC Code to Calculate Adiabatic Flame Temperature of Octane
https://www.maplesoft.com/applications/view.aspx?SID=154397&ref=Feed
This application will generate C code that gives the constant volume adiabatic flame temperature of octane for any initial reactant temperature.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="C Code to Calculate Adiabatic Flame Temperature of Octane" style="max-width: 25%;" align="left"/>This application will generate C code that gives the constant volume adiabatic flame temperature of octane for any initial reactant temperature.https://www.maplesoft.com/applications/view.aspx?SID=154397&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanCarbon Monoxide Combustion
https://www.maplesoft.com/applications/view.aspx?SID=154398&ref=Feed
One mole of carbon monoxide and 0.5 moles of oxygen are ignited at 298.15 K and 1 atm. The reaction is
<BR><BR>
CO + 0.5 O<SUB>2</SUB> → CO<SUB>2</SUB>
<BR><BR>
The combustion products undergo dissociation and contain CO<SUB>2</SUB>, CO, O and O<SUB>2</SUB>.
<UL>
<LI>The equilibrium composition is found by minimizing the Gibbs Energy of the combustion products (formulated as a series of equations constructed via the method of Lagrange multipliers)
<LI>The adiabatic flame temperature is found by balancing the enthalpy of the reactants against the enthalpy of the products
</UL>
The resulting equations are solved numerically to give the adiabatic flame temperature and equilibrium composition of the mixture.<img src="https://www.maplesoft.com/view.aspx?si=154398/image.png" alt="Carbon Monoxide Combustion" style="max-width: 25%;" align="left"/>One mole of carbon monoxide and 0.5 moles of oxygen are ignited at 298.15 K and 1 atm. The reaction is
<BR><BR>
CO + 0.5 O<SUB>2</SUB> → CO<SUB>2</SUB>
<BR><BR>
The combustion products undergo dissociation and contain CO<SUB>2</SUB>, CO, O and O<SUB>2</SUB>.
<UL>
<LI>The equilibrium composition is found by minimizing the Gibbs Energy of the combustion products (formulated as a series of equations constructed via the method of Lagrange multipliers)
<LI>The adiabatic flame temperature is found by balancing the enthalpy of the reactants against the enthalpy of the products
</UL>
The resulting equations are solved numerically to give the adiabatic flame temperature and equilibrium composition of the mixture.https://www.maplesoft.com/applications/view.aspx?SID=154398&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanCatalytic Cracking of Ethane
https://www.maplesoft.com/applications/view.aspx?SID=154399&ref=Feed
Ethylene and hydrogen are generated by a steam cracker using ethane as a feedstock.
<BR><BR>
<CENTER>
C<SUB>2</SUB>H<SUB>6</SUB> (g) ⇌ C<SUB>2</SUB>H<SUB>4</SUB> (g) + H<SUB>2</SUB> (g)
</CENTER>
<BR>
The feed is 4 mol of H<SUB>2</SUB>O to 1 mol of ethane, with the cracker operating at 1.01 bar and 1000 K. The products contain CH<SUB>4</SUB>, C<SUB>2</SUB>H<SUB>4</SUB>, C<SUB>2</SUB>H<SUB>2</SUB>, CO<SUB>2</SUB>, CO, O<SUB>2</SUB>, H<SUB>2</SUB>, H<SUB>2</SUB>O, and C<SUB>2</SUB>H<SUB>6</SUB>.<BR><BR>
This application calculates the composition of the reaction products by
<UL>
<LI>calculating the Gibbs Energy of Formation of the individual species in the products, employing data from the ThermophysicalData:-Chemicals package
<LI>constructing a function that describes Gibbs Energy of the products as a function of product composition
<LI>and minimizing the Gibbs Energy of the products, subject to constraints on the carbon and hydrogen in the system (this employs the Optimization package)
</UL><img src="https://www.maplesoft.com/view.aspx?si=154399/image.png" alt="Catalytic Cracking of Ethane" style="max-width: 25%;" align="left"/>Ethylene and hydrogen are generated by a steam cracker using ethane as a feedstock.
<BR><BR>
<CENTER>
C<SUB>2</SUB>H<SUB>6</SUB> (g) ⇌ C<SUB>2</SUB>H<SUB>4</SUB> (g) + H<SUB>2</SUB> (g)
</CENTER>
<BR>
The feed is 4 mol of H<SUB>2</SUB>O to 1 mol of ethane, with the cracker operating at 1.01 bar and 1000 K. The products contain CH<SUB>4</SUB>, C<SUB>2</SUB>H<SUB>4</SUB>, C<SUB>2</SUB>H<SUB>2</SUB>, CO<SUB>2</SUB>, CO, O<SUB>2</SUB>, H<SUB>2</SUB>, H<SUB>2</SUB>O, and C<SUB>2</SUB>H<SUB>6</SUB>.<BR><BR>
This application calculates the composition of the reaction products by
<UL>
<LI>calculating the Gibbs Energy of Formation of the individual species in the products, employing data from the ThermophysicalData:-Chemicals package
<LI>constructing a function that describes Gibbs Energy of the products as a function of product composition
<LI>and minimizing the Gibbs Energy of the products, subject to constraints on the carbon and hydrogen in the system (this employs the Optimization package)
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154399&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanEquilibrium Concentration of the Catalytic Reforming of Methane with Steam
https://www.maplesoft.com/applications/view.aspx?SID=154400&ref=Feed
This application calculates the equilibrium concentration of the products when methane is reformed with steam at 1000 K and 1.01 bar.
<BR><BR>
Methane reacts with water to generate carbon dioxide and hydrogen.<BR>
<CENTER>
CH<SUB>4</SUB> + 2 H<SUB>2</SUB>O → CO<SUB>2</SUB> + 4 H<SUB>2</SUB>
</CENTER>
<BR>
In parallel, the water-gas shift reaction generates carbon monoxide from carbon dioxide and hydrogen.
<BR>
<CENTER>
CO<SUB>2</SUB> + H<SUB>2</SUB> → CO + H<SUB>2</SUB>O
</CENTER>
<BR>
This application
<UL>
<LI>calculates the Gibbs free energy of formation of the individual species in the products
<LI>constructs a function that gives the total Gibbs free energy of the products, as a function of the number of moles of each species
<LI>and minimizes the total Gibbs free energy
</UL>
This application employs thermodynamic data from the ThermosphysicalData:-Chemicals package
</UL><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Equilibrium Concentration of the Catalytic Reforming of Methane with Steam" style="max-width: 25%;" align="left"/>This application calculates the equilibrium concentration of the products when methane is reformed with steam at 1000 K and 1.01 bar.
<BR><BR>
Methane reacts with water to generate carbon dioxide and hydrogen.<BR>
<CENTER>
CH<SUB>4</SUB> + 2 H<SUB>2</SUB>O → CO<SUB>2</SUB> + 4 H<SUB>2</SUB>
</CENTER>
<BR>
In parallel, the water-gas shift reaction generates carbon monoxide from carbon dioxide and hydrogen.
<BR>
<CENTER>
CO<SUB>2</SUB> + H<SUB>2</SUB> → CO + H<SUB>2</SUB>O
</CENTER>
<BR>
This application
<UL>
<LI>calculates the Gibbs free energy of formation of the individual species in the products
<LI>constructs a function that gives the total Gibbs free energy of the products, as a function of the number of moles of each species
<LI>and minimizes the total Gibbs free energy
</UL>
This application employs thermodynamic data from the ThermosphysicalData:-Chemicals package
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154400&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanCoaxial Cable Transmission Line Design
https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=Feed
An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
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This application will calculate the outer radius of the line.<img src="https://www.maplesoft.com/view.aspx?si=154401/image.png" alt="Coaxial Cable Transmission Line Design" style="max-width: 25%;" align="left"/>An electrical engineer is asked to design a coaxial transmission line with a characteristic impedance of 50 Ω and a phase velocity of at least 1.8 x 108 m s-1
<BR><BR>
This application will calculate the outer radius of the line.https://www.maplesoft.com/applications/view.aspx?SID=154401&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir KhanConcentration of NOx in Clean Air
https://www.maplesoft.com/applications/view.aspx?SID=154402&ref=Feed
The chemical species NO and NO<SUB>2</SUB> are collectively known as NOx. This application will predict the equilibrium concentration of NOx in clean, unpolluted air at 1 atm pressure and 298 K. This establishes a background concentration of NOx; pollution from vehicle emissions and other sources will increase this level.
<BR><BR>
Air is assumed to be 21% O<SUB>2</SUB> and 79% N<SUB>2</SUB> by mole, some of which reacts into NO and NO<SUB>2</SUB>; no other species are considered.
<BR><BR>
Balancing the moles of O<SUB>2</SUB>, N<SUB>2</SUB>, NO and NO<SUB>2</SUB> gives this equation
<BR>
<BR>
<CENTER>
0.21 O<SUB>2</SUB> + 0.79 N<SUB>2</SUB> = n1 O<SUB>2</SUB> + n2 N<SUB>2</SUB> + n3 NO + n4 NO<SUB>2</SUB>
</CENTER>
<BR>
where n1, n2, n3 and n4 are the number of moles of O<SUB>2</SUB>, N<SUB>2</SUB>, NO and NO<SUB>2</SUB>.
<BR><BR>
First, the we will develop a function that describes the total Gibbs Free Energy of the system as a function of the moles of the individual species. Then, we will minimize the Gibbs Free Energy to find the equilibrium composition
<BR><BR>
This will give the values of n1, n2, n3 and n4. The number of moles of NOx in the system is then simply n3 + n4.
<BR><BR>
This application uses the empirical correlations in the ThermophysicalData:-Chemicals package to calculate values of enthalpy and entropy.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Concentration of NOx in Clean Air" style="max-width: 25%;" align="left"/>The chemical species NO and NO<SUB>2</SUB> are collectively known as NOx. This application will predict the equilibrium concentration of NOx in clean, unpolluted air at 1 atm pressure and 298 K. This establishes a background concentration of NOx; pollution from vehicle emissions and other sources will increase this level.
<BR><BR>
Air is assumed to be 21% O<SUB>2</SUB> and 79% N<SUB>2</SUB> by mole, some of which reacts into NO and NO<SUB>2</SUB>; no other species are considered.
<BR><BR>
Balancing the moles of O<SUB>2</SUB>, N<SUB>2</SUB>, NO and NO<SUB>2</SUB> gives this equation
<BR>
<BR>
<CENTER>
0.21 O<SUB>2</SUB> + 0.79 N<SUB>2</SUB> = n1 O<SUB>2</SUB> + n2 N<SUB>2</SUB> + n3 NO + n4 NO<SUB>2</SUB>
</CENTER>
<BR>
where n1, n2, n3 and n4 are the number of moles of O<SUB>2</SUB>, N<SUB>2</SUB>, NO and NO<SUB>2</SUB>.
<BR><BR>
First, the we will develop a function that describes the total Gibbs Free Energy of the system as a function of the moles of the individual species. Then, we will minimize the Gibbs Free Energy to find the equilibrium composition
<BR><BR>
This will give the values of n1, n2, n3 and n4. The number of moles of NOx in the system is then simply n3 + n4.
<BR><BR>
This application uses the empirical correlations in the ThermophysicalData:-Chemicals package to calculate values of enthalpy and entropy.https://www.maplesoft.com/applications/view.aspx?SID=154402&ref=FeedFri, 09 Mar 2018 05:00:00 ZSamir KhanSamir Khan