Fast Slow Timescale Analysis.1
•
1 like•1,107 views
The document discusses using timescale separation to simplify dynamic models with fast and slow processes. It provides two examples: (1) a calcium ion channel model that has fast activation and slower inactivation rates, allowing separation into fast and slow timescales; (2) a reactor wall heat transfer model where the wall thermal mass is small compared to the reactor, allowing separation based on the fast temperature response of the wall and slower temperature change in the reactor. Both examples non-dimensionalize variables, identify a small parameter epsilon as the ratio of timescales, then take the fast timescale limit of epsilon to zero to obtain simplified equations representing each timescale.
Report
Share
Report
Share
![Dynamic Modeling II Outline ,[object Object],[object Object],[object Object],[object Object],[object Object]](https://image.slidesharecdn.com/fastslowtimescaleanalysis-1-090311152217-phpapp02/85/Fast-Slow-Timescale-Analysis-1-1-320.jpg)
![Calcium Ion Channel in Cells Consider a Model of a Calcium Ion Channel in a cell membrane Channel has three States ,[object Object],[object Object],[object Object],Inactive Open Closed k + 1 K + 2 K - 2 K - 1 x i = fraction of channels in a given state i Ca 2+ Ca 2+ =Ca 2+ d Ca 2+ Low High](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
Recommended
Modeling of constant holdup cstr
This document presents a mathematical model for a system of three continuously stirred tank reactors (CSTRs) in series where reactant A is converted to product B through a first-order reaction. It describes the assumptions made, including constant temperature, volume, and density in each reactor. Component continuity equations are developed for reactant A in each reactor to model how the concentration of A changes over time based on the inlet and outlet flows and the rate of the reaction. The specific reaction rates are defined using the Arrheusius equation. The model results in a set of three non-linear first-order ordinary differential equations that describe the dynamics of the system.
prosess model for series of isothermal constant holdup CSTR.
This document describes a process model for a series of continuous stirred tank reactors (CSTRs) with variable holdup. It involves three CSTRs with a first-order irreversible reaction occurring in each tank. Mass balances are written for each reactor to determine the changes in concentrations of component A over time. The parameters that need to be specified are the rate constants k1, k2, k3, and the disturbances to the inlet flow rate and concentration. Mass balances coupled with equations relating the rate constants to temperature are solved to obtain expressions relating the outlet concentrations to the inlet conditions and other parameters.
Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at ...
Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at ...UK Carbon Capture and Storage Research Centre
Presentation given by Dr David Vega-Maza from University of Aberdeen on "Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at Temperatures Between (218 and 303) K and at Pressures up to 15 MPa" in the Effects of Impurities Technical Session at the UKCCSRC Biannual Meeting - CCS in the Bigger Picture - held in Cambridge on 2-3 April 2014Thermodynamics lecture 6
The document discusses the ideal gas model and deviations from ideality in real gases. It introduces compressibility factor Z, which equals 1 for ideal gases and varies from 1 for real gases. Z < 1 indicates attractive intermolecular forces dominate, while Z > 1 indicates repulsive forces dominate. The document presents various equations of state that model real gas behavior better than the ideal gas model. It also shows compressibility charts that collapse data for different gases onto corresponding states based on reduced temperature and pressure.
Rayegan thermo i-cengel-chapter 4-p2
This document discusses energy analysis of closed systems, including specific heats at constant volume and pressure, internal energy, enthalpy, and specific heats of ideal gases and incompressible substances like solids and liquids. It provides equations relating these concepts and explains how to calculate changes in internal energy and enthalpy using data tables, functional forms of specific heats, or average specific heat values. Examples are also included.
Chapter 1thermodynamics
Thermodynamics is the study of energy transfer through heat and work. It has applications in many engineering fields involving energy transfer, like engines and power plants. There are two approaches to thermodynamics - classical and statistical. Classical thermodynamics takes a macroscopic view while statistical views systems at the molecular level. A thermodynamic system exchanges heat and work with its surroundings, and its state is defined by intensive properties like pressure and temperature. A system in equilibrium has no imbalances and its properties remain constant. Processes occur as a system moves between equilibrium states, and cycles occur when the final state matches the initial one.
Real Gases and the Virial Equation
The document discusses real gases and how they deviate from ideal gas behavior. It introduces the virial equation as a way to model real gases over a wider range of pressures and temperatures compared to the ideal gas law. The virial equation treats the deviation of real gases from ideality as a power series in terms of the molar volume. It also discusses how the second virial coefficient, which accounts for intermolecular forces, varies with temperature and exhibits a minimum value at the Boyle temperature for some gases like hydrogen and helium. Finally, it introduces the van der Waals equation as a simplified model compared to the virial equation that treats real gas behavior using just two constants related to molecular size and attraction.
Clausius-clapeyron Equation
The document discusses the Clausius-Clapeyron equation, which relates the rate of change of vapor pressure or melting point with temperature to the latent heat of vaporization, fusion, or sublimation. It presents the derivation of the equation based on an infinitely small Carnot cycle involving a two-phase system. The document then applies the Clausius-Clapeyron equation to analyze the relationships between pressure, temperature, and phase transitions for vaporization, melting, and sublimation.
Recommended
Modeling of constant holdup cstr
This document presents a mathematical model for a system of three continuously stirred tank reactors (CSTRs) in series where reactant A is converted to product B through a first-order reaction. It describes the assumptions made, including constant temperature, volume, and density in each reactor. Component continuity equations are developed for reactant A in each reactor to model how the concentration of A changes over time based on the inlet and outlet flows and the rate of the reaction. The specific reaction rates are defined using the Arrheusius equation. The model results in a set of three non-linear first-order ordinary differential equations that describe the dynamics of the system.
prosess model for series of isothermal constant holdup CSTR.
This document describes a process model for a series of continuous stirred tank reactors (CSTRs) with variable holdup. It involves three CSTRs with a first-order irreversible reaction occurring in each tank. Mass balances are written for each reactor to determine the changes in concentrations of component A over time. The parameters that need to be specified are the rate constants k1, k2, k3, and the disturbances to the inlet flow rate and concentration. Mass balances coupled with equations relating the rate constants to temperature are solved to obtain expressions relating the outlet concentrations to the inlet conditions and other parameters.
Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at ...
Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at ...UK Carbon Capture and Storage Research Centre
Presentation given by Dr David Vega-Maza from University of Aberdeen on "Vapour-Liquid and Solid-Vapour-Liquid Equilibria of the System (CO2 + H2) at Temperatures Between (218 and 303) K and at Pressures up to 15 MPa" in the Effects of Impurities Technical Session at the UKCCSRC Biannual Meeting - CCS in the Bigger Picture - held in Cambridge on 2-3 April 2014Thermodynamics lecture 6
The document discusses the ideal gas model and deviations from ideality in real gases. It introduces compressibility factor Z, which equals 1 for ideal gases and varies from 1 for real gases. Z < 1 indicates attractive intermolecular forces dominate, while Z > 1 indicates repulsive forces dominate. The document presents various equations of state that model real gas behavior better than the ideal gas model. It also shows compressibility charts that collapse data for different gases onto corresponding states based on reduced temperature and pressure.
Rayegan thermo i-cengel-chapter 4-p2
This document discusses energy analysis of closed systems, including specific heats at constant volume and pressure, internal energy, enthalpy, and specific heats of ideal gases and incompressible substances like solids and liquids. It provides equations relating these concepts and explains how to calculate changes in internal energy and enthalpy using data tables, functional forms of specific heats, or average specific heat values. Examples are also included.
Chapter 1thermodynamics
Thermodynamics is the study of energy transfer through heat and work. It has applications in many engineering fields involving energy transfer, like engines and power plants. There are two approaches to thermodynamics - classical and statistical. Classical thermodynamics takes a macroscopic view while statistical views systems at the molecular level. A thermodynamic system exchanges heat and work with its surroundings, and its state is defined by intensive properties like pressure and temperature. A system in equilibrium has no imbalances and its properties remain constant. Processes occur as a system moves between equilibrium states, and cycles occur when the final state matches the initial one.
Real Gases and the Virial Equation
The document discusses real gases and how they deviate from ideal gas behavior. It introduces the virial equation as a way to model real gases over a wider range of pressures and temperatures compared to the ideal gas law. The virial equation treats the deviation of real gases from ideality as a power series in terms of the molar volume. It also discusses how the second virial coefficient, which accounts for intermolecular forces, varies with temperature and exhibits a minimum value at the Boyle temperature for some gases like hydrogen and helium. Finally, it introduces the van der Waals equation as a simplified model compared to the virial equation that treats real gas behavior using just two constants related to molecular size and attraction.
Clausius-clapeyron Equation
The document discusses the Clausius-Clapeyron equation, which relates the rate of change of vapor pressure or melting point with temperature to the latent heat of vaporization, fusion, or sublimation. It presents the derivation of the equation based on an infinitely small Carnot cycle involving a two-phase system. The document then applies the Clausius-Clapeyron equation to analyze the relationships between pressure, temperature, and phase transitions for vaporization, melting, and sublimation.
Lect 6
This document discusses several key concepts in thermodynamics:
1) Two reversible adiabatic processes cannot intersect each other, as this would violate the second law of thermodynamics.
2) Any reversible path between two end states can be substituted by a reversible zig-zag path consisting of a reversible adiabatic, reversible isotherm, and another reversible adiabatic.
3) The Clausius theorem states that entropy is a property that is independent of path, and the change in entropy for any reversible cyclic process is zero.
Rayegan thermo i-cengel-chapter 4-p1
Thermodynamics I discusses energy analysis of closed systems. It examines moving boundary work from processes like in engines and compressors. The first law of thermodynamics states the principle of conservation of energy for closed systems. The general energy balance applied to closed systems relates the change in internal energy to heat and work. Specific heats at constant volume and pressure are defined and used to calculate changes in internal energy and enthalpy for ideal gases and incompressible substances.
Lab4_HeatExchange
The document summarizes a lab experiment that tested the efficiency of parallel and counter-flow heat exchangers. Equations were developed to calculate efficiency based on inlet and outlet temperatures and flow rates. The results showed that parallel flow had higher efficiency values than counter-flow, with efficiencies ranging from 22-56% for parallel flow and 4-13% for counter-flow. The higher efficiency of parallel flow was due to its larger temperature differences and faster mass flow rates.
Clausius - Clapeyron Equation
The Clausius-Clapeyron equation relates the rate of change of vapor pressure with temperature to the latent heat of vaporization. It is derived by considering a system where a liquid and its vapor are in equilibrium and the piston containing them is moved in or out at constant temperature. This causes vaporization or condensation while keeping the Gibbs free energy constant. Taking into account the relationships between internal energy, entropy, and volume changes leads to the final form of the Clausius-Clapeyron equation.
The new gas law
The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, and volume, by considering their molecular composition
Thermodynamics of phase transitions akkamma
This document discusses thermodynamics of phase transitions. It defines key terms like phase, phase transition, and phase diagram. It explains that phases with the lowest free energy will exist under given temperature and pressure conditions. It describes first order phase transitions as discontinuous changes in Gibbs free energy and latent heat. Second order transitions involve continuous Gibbs free energy but discontinuous susceptibilities. Common phase transition lines are the sublimation line where solid and gas coexist, the melting line where solid and liquid coexist, and the condensation line where gas and liquid coexist from the triple point to critical point.
Leverrule
The document describes the lever rule, which is used to determine both the compositions of phases present at a given temperature in a multi-phase alloy system, as well as the relative amounts of each phase. It explains that a tie line is drawn through the given composition point on a phase diagram. The intercepts of the tie line with phase boundaries indicate the compositions of the phases. The relative amounts of each phase are inversely proportional to the distances from the composition point to the intercepts with each phase boundary.
Deviation of real gas from ideal behaviour
Real gases deviate from ideal gas behavior at high pressures and low temperatures due to the assumptions of negligible molecular volume and no intermolecular forces being incorrect in those conditions. Van der Waals proposed an equation to account for these deviations that includes pressure and volume correction terms related to intermolecular attractive forces and molecular size. The compressibility factor Z, which is the ratio of PV to nRT, can quantify this deviation from ideal behavior for real gases as it equals 1 for ideal gases but varies from 1 for real gases.
Deriving the ideal gas law
This document summarizes key points from Chapter 11 of Holt Modern Chemistry regarding Avogadro's law and relating the volume and number of moles of gases. It provides an example problem of calculating the number of moles of gas in 46.5 liters at 28°C and 2.75 atm by converting to STP conditions. The document notes how the combined gas law can be used to convert volumes to moles using the definition that 1 mole of any gas at STP occupies 22.414 liters. It also suggests developing a conversion factor or "multiplier" to more directly calculate moles without intermediate steps. Finally, it directs the reader to practice problems #40-52 at the end of chapter 11.
Midterm test sem thermodynamics 1
This document contains a 9-page midterm test for a Thermodynamics I course. It consists of 4 questions worth a total of 60 marks. Question 1 has 5 parts related to defining the state postulate and analyzing a piston-cylinder device containing liquid and vapor water. Question 2 involves analyzing a constant pressure process for a refrigerant, while Question 3 covers the energy equation for an insulated air diffuser. Question 4 asks about relating mass and volume flow rates and analyzing an air conditioning mixing process.
Evaluating Properties For mechanical and Industrial Engineering
The document discusses properties of substances such as water. It defines key concepts like state principle, phase diagrams, and phase changes. It provides examples of using property tables to determine specific volumes and enthalpies at given temperatures and pressures. The document also covers the ideal gas model and its applications, such as using the gas equation of state and determining work in polytropic processes.
Phase transition:A brief introduction
This document provides a brief introduction to phase transitions, including:
1) It defines a phase as a region of uniform physical properties and discusses the main states of matter.
2) It explains that a phase transition occurs when a system transforms between phases via heat transfer, changing its thermodynamic parameters and often its symmetry.
3) It outlines the main types of phase transitions - first order, second order, and lambda - based on properties like latent heat and discontinuities in heat capacity or thermodynamic free energy derivatives.
Thermodynamics lecture 2
The document discusses key concepts in thermodynamics including:
1) Thermal equilibrium occurs when two systems in contact across a thermal conductor reach the same temperature.
2) A pure substance's phase behavior is characterized by its temperature-volume diagram, with liquid-vapor coexistence occurring along the saturation curve.
3) A substance's vapor pressure increases uniquely with temperature and defines its boiling point at given pressures, terminating at the critical point where liquid and vapor can no longer be distinguished.
Bab 3 Thermodynamic of Engineering Approach
This document discusses properties of pure substances and phase changes. It introduces concepts like saturated liquid, saturated vapor, and phase diagrams. Properties are presented in tables that show how quantities like enthalpy and temperature vary with pressure and phase for substances like water. The ideal gas law is presented as a simple equation of state to model gas behavior.
Week 7 entrophy
1. A cylinder separated by an adiabatic piston initially contains nitrogen on one side and helium on the other at 20°C and 95 kPa.
2. Heat is added to the nitrogen side from a 500°C reservoir until the helium pressure reaches 120 kPa.
3. The final temperature of helium is calculated to be 321.7K, the final volume of nitrogen is 0.2838 m3, and the heat transferred to the nitrogen is 46.6287 kJ. The entropy generation is determined to be 0.057 kJ/K.
Rayegan thermo i-cengel-chapter 3-p2
1) The document discusses properties of pure substances and how they are presented in tables. It focuses on water properties and steam tables.
2) It explains different phases like saturated liquid, saturated vapor, superheated vapor, and compressed liquid. It also discusses quality and using tables to find properties through interpolation.
3) The ideal gas equation of state is presented along with when it can be applied to water vapor. The compressibility factor is introduced as a measure of how gases deviate from ideal behavior.
Thermodynamics lecture 5
The document discusses phase behavior and properties of pure substances. It covers three key points:
1) It introduces the Gibbs phase rule, which relates the number of degrees of freedom in a system to the number of components and phases present.
2) It discusses vapor-liquid equilibrium, including properties like quality along the saturation line and the dependence of temperature and pressure in two-phase regions.
3) It introduces the ideal gas law and compressibility factor, noting that the ideal gas model breaks down at higher pressures and densities due to intermolecular forces.
Jm menendez poster - EHPRG 49
Inthisworkweinvestigatetheequationsofstate(EOS)ofPbinthethreecrystalstructuresbymeansoftheDFTformalismwithaplane-wavepseudopotentialapproach.Both,scalarrelativisticandfullyrelativisticpseudopotentialshavebeenused.OuraimistoprovidereliableEOSisothermsforPbcoveringwiderangesofpressureandtemperatureconditions.Thermaleffectsonthestaticenergy-volumecurvesoffcc,hcpandbccstructureshavebeenevaluatedbyusinganon-empiricalDebyemodel.Inaddition,anempiricalenergycorrectionisintroducedtocheckthequalityofthecalculatedisotherms,andtoextendpressureandtemperatureintervals
Rayegan thermo i-cengel-chapter 3-p1
This document discusses thermodynamic properties of pure substances. It introduces pure substances and their phases of solid, liquid, and gas. Phase change processes are described, including saturated liquid, vapor, and superheated regions. T-V, P-V, and P-T diagrams are presented to illustrate the relationships between these properties. Key concepts covered include saturation temperature/pressure, latent heats of fusion and vaporization, the p-v-T surface, and how substances' behaviors differ when expanding or contracting during phase changes. Objectives are listed for understanding pure substance thermodynamics and properties.
Chapter 2 thermodynamics 1
This chapter discusses work and heat transfer in thermodynamic systems. It defines work as force times distance for simple mechanical systems, and as the potential to lift a mass for thermodynamic systems. Positive work is done by a system when it could potentially lift a mass. Heat is defined as energy transfer due solely to temperature differences. The chapter also covers various forms of work including displacement work, units of work and power, and the sign conventions for work and heat. It discusses different thermodynamic processes like isothermal, isovolumetric and polytropic processes. The path dependence and additivity of work are also covered.
RD Lab - Exp-05 - G-A1.pdf
The document describes a laboratory experiment to determine the reaction order and rate constant of the reaction between sodium hydroxide (NaOH) and ethyl acetate (CH3COOC2H5). The group prepared 0.1 M solutions of each reactant and mixed them in a batch reactor at room temperature while measuring conductivity over time. Calculations using the conductivity readings showed the reaction was second order. The rate constant was determined to be 1.291651 × 10-3 at 21°C based on the nonlinear ln(CA/CAo) vs time graph.
Math cad effective radiation heat transfer coefficient.xmcd
The document discusses the effective radiation heat transfer coefficient (hr) and provides an example calculation. It defines hr as the "radiation heat transfer coefficient" and gives the equation for calculating hr based on the emissivities and absolute temperatures of two surfaces. The example calculates hr for a heated cylindrical rod in a vacuum furnace, finding the heat flux and total heat transfer rate based on the surface area and temperature difference. A plot is provided showing how hr varies with the sink temperature.
More Related Content
What's hot
Lect 6
This document discusses several key concepts in thermodynamics:
1) Two reversible adiabatic processes cannot intersect each other, as this would violate the second law of thermodynamics.
2) Any reversible path between two end states can be substituted by a reversible zig-zag path consisting of a reversible adiabatic, reversible isotherm, and another reversible adiabatic.
3) The Clausius theorem states that entropy is a property that is independent of path, and the change in entropy for any reversible cyclic process is zero.
Rayegan thermo i-cengel-chapter 4-p1
Thermodynamics I discusses energy analysis of closed systems. It examines moving boundary work from processes like in engines and compressors. The first law of thermodynamics states the principle of conservation of energy for closed systems. The general energy balance applied to closed systems relates the change in internal energy to heat and work. Specific heats at constant volume and pressure are defined and used to calculate changes in internal energy and enthalpy for ideal gases and incompressible substances.
Lab4_HeatExchange
The document summarizes a lab experiment that tested the efficiency of parallel and counter-flow heat exchangers. Equations were developed to calculate efficiency based on inlet and outlet temperatures and flow rates. The results showed that parallel flow had higher efficiency values than counter-flow, with efficiencies ranging from 22-56% for parallel flow and 4-13% for counter-flow. The higher efficiency of parallel flow was due to its larger temperature differences and faster mass flow rates.
Clausius - Clapeyron Equation
The Clausius-Clapeyron equation relates the rate of change of vapor pressure with temperature to the latent heat of vaporization. It is derived by considering a system where a liquid and its vapor are in equilibrium and the piston containing them is moved in or out at constant temperature. This causes vaporization or condensation while keeping the Gibbs free energy constant. Taking into account the relationships between internal energy, entropy, and volume changes leads to the final form of the Clausius-Clapeyron equation.
The new gas law
The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container. Kinetic theory explains macroscopic properties of gases, such as pressure, temperature, and volume, by considering their molecular composition
Thermodynamics of phase transitions akkamma
This document discusses thermodynamics of phase transitions. It defines key terms like phase, phase transition, and phase diagram. It explains that phases with the lowest free energy will exist under given temperature and pressure conditions. It describes first order phase transitions as discontinuous changes in Gibbs free energy and latent heat. Second order transitions involve continuous Gibbs free energy but discontinuous susceptibilities. Common phase transition lines are the sublimation line where solid and gas coexist, the melting line where solid and liquid coexist, and the condensation line where gas and liquid coexist from the triple point to critical point.
Leverrule
The document describes the lever rule, which is used to determine both the compositions of phases present at a given temperature in a multi-phase alloy system, as well as the relative amounts of each phase. It explains that a tie line is drawn through the given composition point on a phase diagram. The intercepts of the tie line with phase boundaries indicate the compositions of the phases. The relative amounts of each phase are inversely proportional to the distances from the composition point to the intercepts with each phase boundary.
Deviation of real gas from ideal behaviour
Real gases deviate from ideal gas behavior at high pressures and low temperatures due to the assumptions of negligible molecular volume and no intermolecular forces being incorrect in those conditions. Van der Waals proposed an equation to account for these deviations that includes pressure and volume correction terms related to intermolecular attractive forces and molecular size. The compressibility factor Z, which is the ratio of PV to nRT, can quantify this deviation from ideal behavior for real gases as it equals 1 for ideal gases but varies from 1 for real gases.
Deriving the ideal gas law
This document summarizes key points from Chapter 11 of Holt Modern Chemistry regarding Avogadro's law and relating the volume and number of moles of gases. It provides an example problem of calculating the number of moles of gas in 46.5 liters at 28°C and 2.75 atm by converting to STP conditions. The document notes how the combined gas law can be used to convert volumes to moles using the definition that 1 mole of any gas at STP occupies 22.414 liters. It also suggests developing a conversion factor or "multiplier" to more directly calculate moles without intermediate steps. Finally, it directs the reader to practice problems #40-52 at the end of chapter 11.
Midterm test sem thermodynamics 1
This document contains a 9-page midterm test for a Thermodynamics I course. It consists of 4 questions worth a total of 60 marks. Question 1 has 5 parts related to defining the state postulate and analyzing a piston-cylinder device containing liquid and vapor water. Question 2 involves analyzing a constant pressure process for a refrigerant, while Question 3 covers the energy equation for an insulated air diffuser. Question 4 asks about relating mass and volume flow rates and analyzing an air conditioning mixing process.
Evaluating Properties For mechanical and Industrial Engineering
The document discusses properties of substances such as water. It defines key concepts like state principle, phase diagrams, and phase changes. It provides examples of using property tables to determine specific volumes and enthalpies at given temperatures and pressures. The document also covers the ideal gas model and its applications, such as using the gas equation of state and determining work in polytropic processes.
Phase transition:A brief introduction
This document provides a brief introduction to phase transitions, including:
1) It defines a phase as a region of uniform physical properties and discusses the main states of matter.
2) It explains that a phase transition occurs when a system transforms between phases via heat transfer, changing its thermodynamic parameters and often its symmetry.
3) It outlines the main types of phase transitions - first order, second order, and lambda - based on properties like latent heat and discontinuities in heat capacity or thermodynamic free energy derivatives.
Thermodynamics lecture 2
The document discusses key concepts in thermodynamics including:
1) Thermal equilibrium occurs when two systems in contact across a thermal conductor reach the same temperature.
2) A pure substance's phase behavior is characterized by its temperature-volume diagram, with liquid-vapor coexistence occurring along the saturation curve.
3) A substance's vapor pressure increases uniquely with temperature and defines its boiling point at given pressures, terminating at the critical point where liquid and vapor can no longer be distinguished.
Bab 3 Thermodynamic of Engineering Approach
This document discusses properties of pure substances and phase changes. It introduces concepts like saturated liquid, saturated vapor, and phase diagrams. Properties are presented in tables that show how quantities like enthalpy and temperature vary with pressure and phase for substances like water. The ideal gas law is presented as a simple equation of state to model gas behavior.
Week 7 entrophy
1. A cylinder separated by an adiabatic piston initially contains nitrogen on one side and helium on the other at 20°C and 95 kPa.
2. Heat is added to the nitrogen side from a 500°C reservoir until the helium pressure reaches 120 kPa.
3. The final temperature of helium is calculated to be 321.7K, the final volume of nitrogen is 0.2838 m3, and the heat transferred to the nitrogen is 46.6287 kJ. The entropy generation is determined to be 0.057 kJ/K.
Rayegan thermo i-cengel-chapter 3-p2
1) The document discusses properties of pure substances and how they are presented in tables. It focuses on water properties and steam tables.
2) It explains different phases like saturated liquid, saturated vapor, superheated vapor, and compressed liquid. It also discusses quality and using tables to find properties through interpolation.
3) The ideal gas equation of state is presented along with when it can be applied to water vapor. The compressibility factor is introduced as a measure of how gases deviate from ideal behavior.
Thermodynamics lecture 5
The document discusses phase behavior and properties of pure substances. It covers three key points:
1) It introduces the Gibbs phase rule, which relates the number of degrees of freedom in a system to the number of components and phases present.
2) It discusses vapor-liquid equilibrium, including properties like quality along the saturation line and the dependence of temperature and pressure in two-phase regions.
3) It introduces the ideal gas law and compressibility factor, noting that the ideal gas model breaks down at higher pressures and densities due to intermolecular forces.
Jm menendez poster - EHPRG 49
Inthisworkweinvestigatetheequationsofstate(EOS)ofPbinthethreecrystalstructuresbymeansoftheDFTformalismwithaplane-wavepseudopotentialapproach.Both,scalarrelativisticandfullyrelativisticpseudopotentialshavebeenused.OuraimistoprovidereliableEOSisothermsforPbcoveringwiderangesofpressureandtemperatureconditions.Thermaleffectsonthestaticenergy-volumecurvesoffcc,hcpandbccstructureshavebeenevaluatedbyusinganon-empiricalDebyemodel.Inaddition,anempiricalenergycorrectionisintroducedtocheckthequalityofthecalculatedisotherms,andtoextendpressureandtemperatureintervals
Rayegan thermo i-cengel-chapter 3-p1
This document discusses thermodynamic properties of pure substances. It introduces pure substances and their phases of solid, liquid, and gas. Phase change processes are described, including saturated liquid, vapor, and superheated regions. T-V, P-V, and P-T diagrams are presented to illustrate the relationships between these properties. Key concepts covered include saturation temperature/pressure, latent heats of fusion and vaporization, the p-v-T surface, and how substances' behaviors differ when expanding or contracting during phase changes. Objectives are listed for understanding pure substance thermodynamics and properties.
Chapter 2 thermodynamics 1
This chapter discusses work and heat transfer in thermodynamic systems. It defines work as force times distance for simple mechanical systems, and as the potential to lift a mass for thermodynamic systems. Positive work is done by a system when it could potentially lift a mass. Heat is defined as energy transfer due solely to temperature differences. The chapter also covers various forms of work including displacement work, units of work and power, and the sign conventions for work and heat. It discusses different thermodynamic processes like isothermal, isovolumetric and polytropic processes. The path dependence and additivity of work are also covered.
What's hot (20)
Evaluating Properties For mechanical and Industrial Engineering
Evaluating Properties For mechanical and Industrial Engineering
Similar to Fast Slow Timescale Analysis.1
RD Lab - Exp-05 - G-A1.pdf
The document describes a laboratory experiment to determine the reaction order and rate constant of the reaction between sodium hydroxide (NaOH) and ethyl acetate (CH3COOC2H5). The group prepared 0.1 M solutions of each reactant and mixed them in a batch reactor at room temperature while measuring conductivity over time. Calculations using the conductivity readings showed the reaction was second order. The rate constant was determined to be 1.291651 × 10-3 at 21°C based on the nonlinear ln(CA/CAo) vs time graph.
Math cad effective radiation heat transfer coefficient.xmcd
The document discusses the effective radiation heat transfer coefficient (hr) and provides an example calculation. It defines hr as the "radiation heat transfer coefficient" and gives the equation for calculating hr based on the emissivities and absolute temperatures of two surfaces. The example calculates hr for a heated cylindrical rod in a vacuum furnace, finding the heat flux and total heat transfer rate based on the surface area and temperature difference. A plot is provided showing how hr varies with the sink temperature.
Chemical Reaction Engineering Lab v3.0
This laboratory report summarizes an experiment analyzing the residence time distribution of a continuously stirred tank reactor (CSTR) using a tracer method. Sodium chloride was injected as an inert tracer and its concentration over time was measured in the reactor effluent. The data was used to calculate residence time distribution and cumulative distribution functions, which provide insight into how real reactors operate compared to ideal models. Mean residence time and a tanks-in-series model were also determined to diagnose any non-ideal reactor behaviors like dead volumes or bypassing.
Principles-of-Thermodynamics
The document discusses principles of thermodynamics and heat transfer. It defines thermodynamics and heat transfer, and explains the first and second laws of thermodynamics. The first law concerns the conservation of energy, while the second law concerns the spontaneous direction of heat transfer from hot to cold and the increase in entropy. Examples are provided to illustrate applications of the first law for heat exchanger duties and cooling of sheets.
Heat flow through concrete floor
To understand the heating mechanism and behaviour of a concrete floor slab with hollow cores, a transient heat flow problem was modeled and solved.
Heat exchanger lecture ppt
This document discusses heat transfer and heat exchangers. It begins by explaining different heat transfer mechanisms including conduction, convection, and natural and forced convection. It then defines heat exchangers and discusses their applications. The document goes on to explain principles of heat transfer like boundary layers, heat transfer coefficients, and equations to calculate the overall heat transfer coefficient using methods like log mean temperature difference. It concludes by describing an experimental apparatus used to test heat exchangers.
Fm 4
The document discusses fluid mechanics concepts relevant to power generation, including:
1. It describes Lagrangian and Eulerian approaches to analyzing velocity fields in fluids, with the Eulerian approach being more useful as it focuses on velocity at fixed points rather than tracking individual particles.
2. Conservation laws for mass, momentum and energy are presented using the control volume approach, with the Reynolds Transport Theorem relating changes in an extensive property within a control volume to flux of that property across its boundaries.
3. Complex flows encountered in power generation equipment are classified, with turbulent internal pipe flows and external flows around bodies requiring both viscous and inviscid analyses highlighted.
RD Lab - Exp-12 - G-A1.pdf
This lab report summarizes an experiment examining the impact of ethyl acetate flow rate on conversion in a plug flow reactor at 21°C. Students measured conductivity at four increasing flow rates and calculated conversion using conductivity readings. Results showed conversion decreased as flow rate increased, because higher flow rates gave reactants less time to fully react before exiting the reactor. The experiment helped students learn how conversion in a plug flow reactor is affected by changing an inlet flow rate.
calculation of currents in nanowires
This paper was published by my former Supervisor and involves partly my calculations and the concepts used during my MSci Thesis at University College London.
RD Lab - Exp-03 - G-A1.pdf
This lab report summarizes an experiment conducted using a continuous stirred tank reactor (CSTR) to test the conversion of a reaction between NaOH and ethyl acetate. The report includes the procedure, tools and apparatus used, recorded data tables of conductivity measurements over time, calculations of concentration and conversion from the data, and graphs plotting these values against time. The discussions from the student group analyze the relationships between conductivity, concentration, and conversion over time for the CSTR, noting proportional and inverse relationships, and compare the continuous reactor performance to their previous batch reactor experiment.
Lecture 8: Phase Diagrams
1. The document discusses phase diagrams and thermodynamics of mixing.
2. It explains how phase diagrams can be used to determine the number and types of phases present, the composition of each phase, and the amount of each phase at a given temperature and composition.
3. Binary eutectic and eutectoid systems allow for a range of microstructures depending on the cooling rate, and alloying generally increases strength but decreases ductility due to solid solution strengthening.
Thermoelectric and magnetic properties of Ca3Co4-xCuxO9+ δ with x = 0.00, 0.0...
This document summarizes research on the thermoelectric and magnetic properties of Ca3Co4–xCuxO9 + d materials with varying amounts of copper substitution (x = 0.00, 0.05, 0.07, 0.10, and 0.15). Key findings include:
1) All samples were single phase according to XRD analysis. Electrical resistivity decreased with increasing copper content due to higher hole carrier concentrations.
2) The thermopower was positive over the entire temperature range, indicating hole carriers. The sample with x = 0.15 had the highest power factor of 2.17 mW/cm-K^2 at 141 K.
3) Magnetization measurements
Hydraulic Engineering Assignment Help
I am Moffat K. I am a Hydraulic Engineering Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Engineering, from Harvard University, USA. I have been helping students with their assignments for the past 8 years. I solve assignments related to Hydraulic Engineering.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com. You can also call on +1 678 648 4277 for any assistance with Hydraulic Engineering Assignments.
Nuclear Engineering Exam Help
I am Dave J. I am a Nuclear Engineering Exam Helper at liveexamhelper.com. I hold a Masters' Degree in Nuclear Physics from, University of Chicago, USA. I have been helping students with their exams for the past 12 years. You can hire me to take your exam in Nuclear Engineering.
Visit liveexamhelper.com or email info@liveexamhelper.com.
You can also call on +1 678 648 4277 for any assistance with the Nuclear Engineering exams.
Chapter 2-Lecture 3.pptx
Energy transfer by heat occurs between systems with a temperature difference, even if no work is done. Heat transfer is driven by decreasing temperature, with a higher rate of transfer for larger temperature differences. Heat transfer between a system and its surroundings is represented by Q, with a positive Q indicating heat transfer to the system. For transient processes, the rate of energy transfer to or from a system can be determined by integrating heat (Q) and work (W) terms over time.
RD Lab - Exp-09 - G-A1.pdf
The students conducted an experiment using a laminar flow reactor to determine conductivity and conversion of reactants at 20°C. They introduced 0.05M solutions of NaOH and CH3COOHC2H5 into the reactor and measured a conductivity of 2.8μS. Using the conductivity readings and known values, they calculated the concentration of reactants and determined the conversion to be 0.99. The students discussed the procedure and goals of the experiment and potential sources of error in their measurements and calculations.
Kirchhoff's rules and rc circuits
1. An RC circuit consists of a resistor and capacitor connected in series or parallel. When a voltage is applied across the circuit, the capacitor will charge up over time through the resistor according to the time constant of the circuit, which is equal to RC.
2. Kirchhoff's laws can be applied to the RC circuit to derive differential equations describing how the current and charge on the capacitor change over time during the charging and discharging processes. The solutions to these equations show that the current and charge decay exponentially with the time constant RC.
3. An oscilloscope can be used to observe the input voltage waveform and voltage across the capacitor to understand the capacitor's charging and discharging behavior in response to
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
In the present work, the point kinetics equations are solved numerically using the stiffness confinement
method (SCM). The solution is applied to the kinetics equations in the presence of different types of
reactivities, and is compared with other methods. This method is, also used to analyze reactivity accidents
in thermal reactor at start-up, and full power conditions for control rods withdrawal. Thermal reactor
(HTR-M) is fuelled by uranium-235. This analysis presents the effect of negative temperature feedback, and
the positive reactivity of control rods withdrawal. Power, temperature pulse, and reactivity following the
reactivity accidents are calculated using programming language (FORTRAN), and (MATLAB) Codes. The
results are compared with previous works and satisfactory agreement is found.
Similar to Fast Slow Timescale Analysis.1 (20)
Math cad effective radiation heat transfer coefficient.xmcd
Math cad effective radiation heat transfer coefficient.xmcd
Thermoelectric and magnetic properties of Ca3Co4-xCuxO9+ δ with x = 0.00, 0.0...
Thermoelectric and magnetic properties of Ca3Co4-xCuxO9+ δ with x = 0.00, 0.0...
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
Analysis of Reactivity Accident for Control Rods Withdrawal at the Thermal Re...
More from ahmad bassiouny
Work Study & Productivity
This document discusses work study techniques used to analyze human work and improve efficiency. It defines work study, method study, and work measurement. Method study examines work processes to develop more effective methods using a six-step approach. Work measurement techniques include time study, activity sampling, and predetermined time systems to establish standard times for tasks. The goals of work study are to optimize the use of resources, increase productivity, reduce costs, and improve working conditions and quality.
Work Study
Work study is a technique used to systematically analyze work processes to improve efficiency. It involves observing work, documenting the current process, analyzing it for improvements, developing a more efficient method, measuring the new method, and implementing it as the standard. The key founders who developed techniques in this area include Frederick Taylor with time motion studies, Frank and Lillian Gilbreth with motion studies, and Henry Gantt with task scheduling. Work study specialists must gain cooperation from supervisors and workers, and consider the human factors, to successfully conduct a study and implement new standards.
Motion And Time Study
Motion and Time Study are methods used to analyze work processes and determine standard times. Frank and Lillian Gilbreth pioneered Motion Study in the 1880s to analyze body motions. Frederick Taylor developed Time Study in the 1880s to measure task completion times. Modern tools like motion cameras, stopwatches, and software are used to study processes in manufacturing, offices, hospitals and more in order to identify inefficiencies and establish performance standards.
Motion Study
The document discusses principles and approaches for improving work efficiency through motion study and work design, including:
1. Four principles of motion economy to reduce unnecessary movement - reduce motions, perform simultaneously, shorten distances, make motions easier.
2. Ergonomic considerations for tool and workstation layout such as positioning parts and tools for sequential use, gravity feeding, and correct working heights.
3. Methods for analyzing and improving operations including eliminating unnecessary steps, simplifying processes, combining tasks, and rearranging sequences.
The Christmas Story
The passage describes the birth of Jesus Christ as foretold by prophets. An angel tells Mary she will conceive and give birth to Jesus, the Son of God. Mary visits her relative Elizabeth, who is also miraculously pregnant. Mary gives birth to Jesus in Bethlehem, where he is visited by shepherds and wise men. The passage establishes Jesus as the promised Messiah through fulfillment of prophecies.
Turkey Photos
The document provides a list of images related to sights and landmarks in Turkey. It includes pictures of mountains, cave houses, mosques, palaces, bridges, museums, universities, and natural areas from various cities across Turkey including Istanbul, Ankara, Konya, Antalya, and Edirne. The images showcase Turkey's rich cultural and architectural heritage as well as natural beauty.
Mission Bo Kv3
The Society of Concurrent Product Development (SOCPD) aims to promote integrated product development practices. Its mission is to disseminate knowledge of concurrent engineering and further develop its body of knowledge. The document outlines SOCPD's history and evolution since the 1980s, including expanding its mission, objectives, and body of knowledge to keep up with emerging techniques and technologies in concurrent product development.
Miramar
The document discusses Miramar Automation's industrial automation and control engineering services. It lists hundreds of successful projects in areas like process control, SCADA, telemetry, water handling, and beverage preparation. It also outlines the company's capabilities such as software development, panel/PLC integration, gas detection systems, engineering documentation, and training.
Mom
The document is a poem about a mother's unconditional love and sacrifice for her child from birth through adulthood. It describes how the mother was always there to support and celebrate her child at each milestone, from standing up and taking first steps to starting school, getting sick, riding a bicycle, and becoming independent. It reminds the reader to show their love and spend time with their mother while they can, as the mother has given her all through the years and now in old age just desires a bit of her child's love and time in return.
Linearization
Linearization involves developing a linear approximation of a nonlinear system around an operating point. This allows tools from linear systems theory to be applied to analyze and design controllers for nonlinear systems. Specifically, Taylor's theorem is used to expand the nonlinear functions as a linear combination of deviations from the operating point. The resulting linearized model is only valid locally but provides an approximate way to analyze system behavior if well-controlled near the operating point. Examples show how to derive linearized models for common nonlinear systems like tanks and chemical reactors.
Kblmt B000 Intro Kaizen Based Lean Manufacturing
The document introduces Kaizen-based Lean Manufacturing (KBLM) as a way for businesses to increase speed, improve quality, and lower costs compared to traditional Material Requirements Planning (MRP) systems. It discusses eight basics of KBLM, including information integrity, motivational measurement, sequential production, point-of-use logistics, cycle time management, production linearity, resource planning, and customer connectivity. Case studies show companies achieving reductions in costs, inventory levels, and product build times by implementing KBLM.
How To Survive
The document provides seven rules for surviving in a new economy: 1) Accept ambiguity and uncertainty; 2) Hold yourself accountable for outcomes; 3) Become a quick change artist and adapt to changes; 4) Add value through your work; 5) Be a problem solver rather than pointing fingers; 6) Practice continuous improvement through lean processes; 7) Continue learning new skills. The introductory quote emphasizes embracing positive change and progress rather than resisting it or becoming part of negative forces that stand in the way.
Dad
A son or daughter's perspective of their father changes dramatically over time, from seeing their father as all-knowing when young, to viewing them as outdated and unreasonable during the teenage years, to later gaining appreciation for all the hardships and sacrifices their father endured to raise them as they become parents themselves.
Ancient Hieroglyphics
Ancient Egyptian hieroglyphics originated as a sacred writing system used since around 3000 BC, combining alphabetic, logographic, and ideographic elements. It was used by priests, scribes, and educated citizens in different scripts until being replaced by Coptic in the 4th century AD. The Rosetta Stone, discovered in 1799, had the key to decrypting hieroglyphics by bearing a decree in three scripts: Greek, Demotic, and hieroglyphic. It was deciphered in 1822, unlocking understanding of ancient Egyptian writings.
DesignPeopleSystem
The document discusses various aspects of job design and work systems, including:
1. Job design involves specifying the content, tasks, responsibilities, and methods associated with a job.
2. Ergonomics and behavioral approaches aim to incorporate human factors and motivate workers through variety, autonomy, and feedback.
3. Traditional efficiency approaches focus on specialization and standardization of tasks from a productivity standpoint.
4. Effective job design balances both human and technical factors to optimize performance and satisfaction.
Organizational Behavior
Organizational behavior (OB) involves studying how individuals and groups function within organizations to accomplish work. Managers play an important role as they interact with others and direct activities to achieve organizational and personal goals. Manager's interpersonal skills are important because views of organizations are changing from seeing them as machines to seeing them as social systems where relationships among individuals are important. OB draws on various behavioral disciplines like psychology, sociology, and anthropology to study individual behavior, group behavior, organizational structure, and their impact on organizational effectiveness and efficiency.
Work Study Workshop
The document summarizes the key aspects of an on-campus work-study program, including eligibility requirements, the roles and responsibilities of various parties, and operational guidelines. It outlines the financial aid application process, how student earnings are subsidized, employment conditions, payroll procedures, and the auditing process to ensure compliance. Departments must submit agreements, post available positions, hire eligible students, and monitor hours worked, while the Work-Study Office reviews placements and provides guidance.
Workstudy
The document discusses various topics related to work study and productivity including:
- Defining work study, productivity, and their importance in analyzing work processes and identifying areas for improvement.
- Key aspects of work study such as method study, work measurement, incentive plans, and examining worker-machine relationships.
- Modeling work processes using tools like flow diagrams and developing standard times.
- The role of work study in broader areas like systems analysis, business process reengineering, and human-computer interface design.
Time And Motion Study
Time and motion studies are methods used to determine the optimal time it takes to complete tasks. They were developed by Frederick Taylor and the Gilbreths to establish fair work standards and eliminate unnecessary motions. While originally used in manufacturing, today time and motion studies can be applied to performance evaluations, planning, problem solving, and cost analysis in various organizations. The objective is to study jobs and determine standard times through observation, task breakdown, and time recording. Allowance factors are added to standard times to account for contingencies. However, studies may not always accurately capture real work conditions due to observer or worker issues.
More from ahmad bassiouny (20)
Recently uploaded
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
Aims and objectives of national policy on information and communication technology(ICT) in school education in india
Creation or Update of a Mandatory Field is Not Set in Odoo 17
In this slide we will discuss Creation or Updation of a mandatory field is not set in Odoo 17.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Accounting for Restricted Grants When and How To Record Properly
In this webinar, member learned how to stay in compliance with generally accepted accounting principles (GAAP) for restricted grants.
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف أحرف الخلاف للقراء العشرةأعد أحرف الخلاف بالتلوين وصلا سمير بسيوني غفر الله له
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
How to Manage Reception Report in Odoo 17
A business may deal with both sales and purchases occasionally. They buy things from vendors and then sell them to their customers. Such dealings can be confusing at times. Because multiple clients may inquire about the same product at the same time, after purchasing those products, customers must be assigned to them. Odoo has a tool called Reception Report that can be used to complete this assignment. By enabling this, a reception report comes automatically after confirming a receipt, from which we can assign products to orders.
How to Fix [Errno 98] address already in use
This slide will represent the cause of the error “[Errno 98] address already in use” and the troubleshooting steps to resolve this error in Odoo.
INTRODUCTION TO HOSPITALS & AND ITS ORGANIZATION
The document discuss about the hospitals and it's organization .
KHUSWANT SINGH.pptx ALL YOU NEED TO KNOW ABOUT KHUSHWANT SINGH
INDIA`S OWN LITERARY GENIUS MR.KHUSHWANT SINGH WAS TRULY A VERY BRAVE SOUL AND WAS AWARDED WITH THE MAGIC OF WORDS BY GOD.
Recently uploaded (20)
220711130097 Tulip Samanta Concept of Information and Communication Technology
220711130097 Tulip Samanta Concept of Information and Communication Technology
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
220711130100 udita Chakraborty Aims and objectives of national policy on inf...
Creation or Update of a Mandatory Field is Not Set in Odoo 17
Creation or Update of a Mandatory Field is Not Set in Odoo 17
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Accounting for Restricted Grants When and How To Record Properly
Accounting for Restricted Grants When and How To Record Properly
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
KHUSWANT SINGH.pptx ALL YOU NEED TO KNOW ABOUT KHUSHWANT SINGH
KHUSWANT SINGH.pptx ALL YOU NEED TO KNOW ABOUT KHUSHWANT SINGH
Fast Slow Timescale Analysis.1
- 3. Fast & Slow Timescales If the time scale of activation is much faster than that of inactivation we can use these two different timescales to simplify the problem. k 1 >>k 2 Scale time by the slow reaction constant: Substitute into equations and look for “small parameter” <<1 ratio of slow to fast timescales
- 4. Slow Timescale Analysis continued The second equation becomes: Now allow 0 From either equation: “ rapid equilibrium” between the open and closed channels quasi-steady state
- 5. Slow timescale continued Rapid equilibrium between open and closed, now we need a differential equation independent of Add the two equations: Let Combined fractions of open and closed channels Have to eliminate x o from this
- 6. Slow Timescale Ion Channel From algebraic equation: y(0)=1 Differential Equation for y:
- 7. Fast Timescale Fast Timescale Differential Equations
- 9. Another Example T o T R T wo T wi m w C pw m R C pR k w Heat Transfer across a reactor wall State Variables, T W and T R , note T W already lumped. Q R
- 10. Heat Transfer Continued Rearrange the Equations for T w and T R [time] -1 Slow time scale Transfer Rate across wall small compared to the thermal mass of reactor
- 11. Heat Transfer Continued The Thermal Mass of Reactor is large compared to the wall, is ratio of wall to reactor thermal mass . The wall temperature is just the average at slow time scale.
- 12. Heat Transfer Continued Eliminate T W by using the relationship from the previous result Now solve the ODE
- 13. Fast Timescale Allow 0 Ratio of rate of heat transfer to thermal mass of the wall is large. Now solve the ODE and substitute into AE Implicitly Q R must also be slow