4. Introduction to Heat & Mass Transfer


 Jocelin Norton
 2 years ago
 Views:
Transcription
1 4. Introduction to Heat & Mass Transfer This section will cover the following concepts: A rudimentary introduction to mass transfer. Mass transfer from a molecular point of view. Fundamental similarity of heat and mass transfer. Application of mass transfer concepts:  Evaporation of a liquid layer  Evaporation of a liquid droplet 4. Heat & Mass Transfer 1 AER 1304 ÖLG
2 MassTransfer Rate Laws: Mass Transfer: Fick s Law of Diffusion: Describes, in its basic form, the rate at which two gas species diffuse through each other. For onedimensional binary diffusion: ṁ A mass flow of A per unit area = Y A (ṁ A +ṁ B) mass flow of A associated with bulk flow per unit area dy A ρd AB dx mass flow of A associated with molecular diffusion (4.1) 4. Heat & Mass Transfer 2 AER 1304 ÖLG
3 A is transported by two means: (a) bulk motion of the fluid, and (b) molecular diffusion. Mass flux is defined as the mass flowrate of species A per unit area perpendicular to the flow: ṁ A = ṁ A /A (4.2) ṁ A has the units kg/(s m2 ). The binary diffusivity, orthemolecular diffusion coefficient, D AB is a property of the mixture and has units of m 2 /s. 4. Heat & Mass Transfer 3 AER 1304 ÖLG
4 In the absence of diffusion: ṁ A = Y A (ṁ A +ṁ B)=Y A ṁ Bulk flux of species A (4.3a) where ṁ is the mixture mass flux. The diffusional flux adds an additional component to the flux of A: ρd AB dy A dx Diffusional flux of A, ṁ A,diff (4.3b) 4. Heat & Mass Transfer 4 AER 1304 ÖLG
5 Note that the negative sign causes the flux to be postive in the xdirection when the concentration gradient is negative. Analogy between the diffusion of heat (conduction) and molecular diffusion.  Fourier s law of heat conduction: Q x = k dt (4.4) dx Both expressions indicate a flux (ṁ A,diff or Q x) being proportional to the gradient of a scalar quantity [(dy A /dx) or(dt/dx)]. 4. Heat & Mass Transfer 5 AER 1304 ÖLG
6 A more general form of Eqn 4.1: ṁ A = Y A ( ṁ A + ṁ B) ρd AB Y A (4.5) symbols with over arrows represent vector quantities. Molar form of Eqn 4.5 Ṅ A = χ A ( Ṅ A + Ṅ B) cd AB χ A (4.6) where Ṅ A,(kmol/(sm2 ), is the molar flux of species A; χ A is mole fraction, and c is the molar concentration, kmol/m Heat & Mass Transfer 6 AER 1304 ÖLG
7 Meanings of bulk flow and diffusional flux can be better explained if we consider that: ṁ mixture mass flux = ṁ A species A mass flux + ṁ B species B mass flux (4.7) If we substitute for individual species fluxes from Eqn 4.1 into 4.7: ṁ = Y A ṁ dy A ρd AB dx + Y Bṁ dy B ρd BA dx (4.8a) 4. Heat & Mass Transfer 7 AER 1304 ÖLG
8 Or: ṁ =(Y A + Y B )ṁ dy A ρd AB dx ρd dy B BA dx (4.8b) For a binary mixture, Y A + Y B =1; then: ρd AB dy A dx diffusional flux of species A ρd BA dy B dx diffusional flux of species B =0 (4.9) In general ṁ i =0 4. Heat & Mass Transfer 8 AER 1304 ÖLG
9 Some cautionary remarks:  We are assuming a binary gas and the diffusion is a result of concentration gradients only (ordinary diffusion).  Gradients of temperature and pressure can produce species diffusion.  Soret effect: species diffusion as a result of temperature gradient.  In most combustion systems, these effects are small and can be neglected. 4. Heat & Mass Transfer 9 AER 1304 ÖLG
10 Molecular Basis of Diffusion: We apply some concepts from the kinetic theory of gases.  Consider a stationary (no bulk flow) plane layer of a binary gas mixture consisting of rigid, nonattracting molecules.  Molecular masses of A and B are identical.  A concentration (massfraction) gradient exists in xdirection, and is sufficiently small that over smaller distances the gradient can be assumed to be linear. 4. Heat & Mass Transfer 10 AER 1304 ÖLG
11 4. Heat & Mass Transfer 11 AER 1304 ÖLG
12 Average molecular properties from kinetic theory of gases: v Z A Mean speed of species A = molecules Wall collision frequency of A 8kB T 1/2 πm A molecules per unit area = 1 4 λ Mean free path = na v V 1 2π(ntot /V )σ 2 (4.10a) (4.10b) (4.10c) a Average perpendicular distance from plane of last collision to plane where next collision occurs = 2 3 λ (4.10d) 4. Heat & Mass Transfer 12 AER 1304 ÖLG
13 where  k B : Boltzmann s constant.  m A : mass of a single A molecule.  (n A /V ): number of A molecules per unit volume.  (n tot /V ): total number of molecules per unit volume.  σ: diameter of both A and B molecules. Net flux of A molecules at the xplane: ṁ A = ṁ A,(+)x dir ṁ A,( )x dir (4.11) 4. Heat & Mass Transfer 13 AER 1304 ÖLG
14 In terms of collision frequency, Eqn 4.11 becomes ṁ A Net mass flux of species A = (ZA) x a Number of A crossing plane x originating from plane at (x a) m A (ZA) x+a Number of A crossing plane x originating from plane at (x+a) m A (4.12) Since ρ m tot /V tot, then we can relate Z A to mass fraction, Y A (from Eqn 4.10b) Z Am A = 1 4 n A m A m tot ρ v = 1 4 Y Aρ v (4.13) 4. Heat & Mass Transfer 14 AER 1304 ÖLG
15 Substituting Eqn 4.13 into 4.12 ṁ A = 1 4 ρ v(y A,x a Y A,x+a ) (4.14) With linear concentration assumption dy dx = Y A,x a Y A,x+a 2a = Y A,x a Y A,x+a 4λ/3 (4.15) 4. Heat & Mass Transfer 15 AER 1304 ÖLG
16 From the last two equations, we get ṁ A = ρ vλ 3 dy A dx Comparing Eqn with Eqn. 3.3b, D AB is (4.16) D AB = vλ/3 (4.17) Substituting for v and λ, along with idealgas equation of state, PV = nk B T D AB = 2 k 3 B T 1/2 T 3 π 3 m A σ 2 (4.18a) P 4. Heat & Mass Transfer 16 AER 1304 ÖLG
17 or D AB T 3/2 P 1 (4.18b) Diffusivity strongly depends on temperature and is inversely proportional to pressure. Mass flux of species A, however, depends on ρd AB, which then gives: ρd AB T 1/2 P 0 = T 1/2 (4.18c) In some practical/simple combustion calculations, the weak temperature dependence is neglected and ρd is treated as a constant. 4. Heat & Mass Transfer 17 AER 1304 ÖLG
18 Comparison with Heat Conduction: We apply the same kinetic theory concepts to the transport of energy. Same assumptions as in the molecular diffusion case. v and λ have the same definitions. Molecular collision frequency is now based on the total number density of molecules, n tot /V, Z = Average wall collision frequency per unit area = 1 4 ntot V v (4.19) 4. Heat & Mass Transfer 18 AER 1304 ÖLG
19 4. Heat & Mass Transfer 19 AER 1304 ÖLG
20 In the nointeractionatadistance hardsphere model of the gas, the only energy storage mode is molecular translational (kinetic) energy. Energy balance at the xplane; Net energy flow in x direction = kinetic energy flux with molecules from x a to x kinetic energy flux with molecules from x+a to x ke is given by Q x = Z (ke) x a Z (ke) x+a (4.20) ke = 1 2 m v2 = 3 2 k BT (4.21) 4. Heat & Mass Transfer 20 AER 1304 ÖLG
21 heat flux can be related to temperature as Q x = 3 2 k BZ (T x a T x+a ) (4.22) The temperature gradient dt dx = T x+a T x a 2a (4.23) Eqn into 3.22, and definitions of Z and a Q x = 1 n 2 k B vλ dt (4.24) V dx 4. Heat & Mass Transfer 21 AER 1304 ÖLG
22 Comparing to Eqn. 4.4, k is k = 1 n 2 k B V vλ (4.25) In terms of T and molecular size, k = k 3 B π 3 mσ 4 1/2 T 1/2 Dependence of k on T (similar to ρd) (4.26) k T 1/2 (4.27)  Note: For real gases T dependency is larger. 4. Heat & Mass Transfer 22 AER 1304 ÖLG
23 4. Heat & Mass Transfer 23 AER 1304 ÖLG
24 Species Conservation: Onedimensional control volume Species A flows into and out of the control volume as a result of the combined action of bulk flow and diffusion. Within the control volume, species A may be created or destroyed as a result of chemical reaction. The net rate of increase in the mass of A within the control volume relates to the mass fluxes and reaction rate as follows: 4. Heat & Mass Transfer 24 AER 1304 ÖLG
25 dm A,cv dt Rate of increase of mass A within CV where =[ṁ AA] x Mass flow of A into CV [ṁ AA] x+ x Mass flow of A out of the CV + ṁ A V Mass prod. rate of A by reaction (4.28)  ṁ A is the mass production rate of species A per unit volume.  ṁ A is defined by Eqn Heat & Mass Transfer 25 AER 1304 ÖLG
26 Within the control volume m A,cv = Y A m cv = Y A ρv cv, and the volume V cv = A x; Eqn A x (ρy A) = A Y A ṁ Y A ρd AB t x x A Y A ṁ Y A ρd AB x x+ x +ṁ A A x (4.29) Dividing by A x and taking limit as x 0, (ρy A ) = Y A ṁ Y A ρd AB +ṁ A t x x (4.30) 4. Heat & Mass Transfer 26 AER 1304 ÖLG
27 For the steadyflow, ṁ A d dx Y A ṁ ρd AB dy A dx =0 (4.31) Eqn is the steadyflow, onedimensional form of species conservation for a binary gas mixture. For a multidimensional case, Eqn can be generalized as ṁ A Net rate of species A production by chemical reaction ṁ A Net flow of species A out of control volume =0 (4.32) 4. Heat & Mass Transfer 27 AER 1304 ÖLG
28 Some Applications of Mass Transfer: The Stefan Problem: 4. Heat & Mass Transfer 28 AER 1304 ÖLG
29 Assumptions:  Liquid A in the cylinder maintained at a fixed height.  Steadystate  [A]intheflowinggasislessthan[A]atthe liquidvapour interface.  B is insoluble in liquid A Overall conservation of mass: ṁ (x) =constant=ṁ A +ṁ B (4.33) 4. Heat & Mass Transfer 29 AER 1304 ÖLG
30 Since ṁ B =0,then ṁ A = ṁ (x) =constant (4.34) Then, Eqn.4.1 now becomes ṁ A = Y A ṁ A ρd AB dy A dx (4.35) Rearranging and separating variables ṁ A ρd AB dx = dy A 1 Y A (4.36) 4. Heat & Mass Transfer 30 AER 1304 ÖLG
31 Assuming ρd AB to be constant, integrate Eqn ṁ A ρd AB x = ln[1 Y A ]+C (4.37) With the boundary condition Y A (x =0)=Y A,i (4.38) We can eliminate C; then Y A (x) =1 (1 Y A,i )exp ṁ A x ρd AB (4.39) 4. Heat & Mass Transfer 31 AER 1304 ÖLG
32 The mass flux of A, ṁ A, can be found by letting Y A (x = L) =Y A, Then, Eqn reads ṁ A = ρd AB L 1 ln YA, 1 Y A,i (4.40) Mass flux is proportional to ρd, andinversely proportional to L. 4. Heat & Mass Transfer 32 AER 1304 ÖLG
33 LiquidVapour Interface: Saturation pressure P A,i = P sat (T liq,i ) (4.41) Partial pressure can be related to mole fraction and mass fraction Y A,i = P sat(t liq,i ) P MW A MW mix,i (4.42) TofindY A,i we need to know the interface temperature. 4. Heat & Mass Transfer 33 AER 1304 ÖLG
34 In crossing the liquidvapour boundary, we maintain continuity of temperature T liq,i (x =0 )=T vap,i (x =0 + )=T (0) (4.43) and energy is conserved at the interface. Heat is transferred from gas to liquid, Q g i.someofthis heats the liquid, Q i l, while the remainder causes phase change. Q g i Q i l = ṁ(h vap h liq )=ṁh fg (4.44) or Q net = ṁh fg (4.45) 4. Heat & Mass Transfer 34 AER 1304 ÖLG
35 Droplet Evaporation: 4. Heat & Mass Transfer 35 AER 1304 ÖLG
36 Assumptions:  The evaporation process is quasisteady.  The droplet temperature is uniform, and the temperature is assumed to be some fixed value below the boiling point of the liquid.  The mass fraction of vapour at the droplet surface is determined by liquidvapour equilibrium at the droplet temperature.  We assume constant physical properties, e.g., ρd. 4. Heat & Mass Transfer 36 AER 1304 ÖLG
37 Evaporation Rate: Same approach as the Stefan problem; except change in coordinate sysytem. Overall mass conservation: ṁ(r) =constant=4πr 2 ṁ (4.46) Species conservation for the droplet vapour: ṁ A = Y A ṁ A ρd AB dy A dr (4.47) 4. Heat & Mass Transfer 37 AER 1304 ÖLG
38 Substitute Eqn into 4.47 and solve for ṁ, ṁ = 4πr 2 ρd AB dy A 1 Y A dr (4.48) Integrating and applying the boundary condition yields Y A (r = r s )=Y A,s (4.49) Y A (r) =1 (1 Y A,s)exp[ ṁ/(4πρd AB r) exp [ ṁ/(4πρd AB r s )] (4.50) 4. Heat & Mass Transfer 38 AER 1304 ÖLG
39 Evaporation rate can be determined from Eqn by letting Y A = Y A, for r : ṁ =4πr s ρd AB ln (1 YA, ) (1 Y A,s ) (4.51) In Eqn. 4.51, we can define the dimensionless transfer number, B Y, 1+B Y 1 Y A, 1 Y A,s (4.52a) 4. Heat & Mass Transfer 39 AER 1304 ÖLG
40 or Then the evaporation rate is B Y = Y A,s Y A, 1 Y A,s (4.52b) ṁ =4πr s ρd AB ln (1 + B Y ) (4.53) Droplet Mass Conservation: dm d = ṁ (4.54) dt where m d is given by m d = ρ l V = ρ l πd 3 /6 (4.55) 4. Heat & Mass Transfer 40 AER 1304 ÖLG
41 where D = 2r s,andv is the volume of the droplet. Substituting Eqns 4.55 and 4.53 into 4.54 and differentiating dd dt = 4ρD AB ρ l D ln (1 + B Y ) (4.56) Eqn 4.56 is more commonly expressed in term of D 2 rather than D, dd 2 dt = 8ρD AB ρ l ln (1 + B Y ) (4.57) 4. Heat & Mass Transfer 41 AER 1304 ÖLG
42 Equation 4.57 tells us that time derivative of the square of the droplet diameter is constant. D 2 varies with t with a slope equal to RHS of Eqn This slope is defined as evaporation constant K: K = 8ρD AB ρ l ln (1 + B Y ) (4.58) Droplet evaporation time can be calculated from: 0 D 2 o dd 2 = t d 0 Kdt (4.59) 4. Heat & Mass Transfer 42 AER 1304 ÖLG
43 which yields t d = D 2 o/k (4.60) We can change the limits to get a more general relationship to provide a general expression for the variation of D with time: D 2 (t) =D 2 o Kt (4.61) Eq is referred to as the D 2 law for droplet evaporation. 4. Heat & Mass Transfer 43 AER 1304 ÖLG
44 D 2 law for droplet evaporation: 4. Heat & Mass Transfer 44 AER 1304 ÖLG
Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows
Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3. 1 Basics: equations of continuum mechanics  balance equations for mass and momentum  balance equations for the energy and the chemical
More informationMass Transfer in Laminar & Turbulent Flow. Mass Transfer Coefficients
Mass Transfer in Laminar & Turbulent Flow Mass Transfer Coefficients 25 MassTransfer.key  January 3, 204 Convective Heat & Mass Transfer T T w T in bulk and T w near wall, with a complicated T profile
More informationEnergy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)
Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact
More informationN 2 C balance: 3a = = 9.2 a = H CO = CO H 2. theo. AF ratio =
15.26 Liquid propane is burned with dry air. A volumetric analysis of the products of combustion yields the following volume percent composition on a dry basis: 8.6% CO 2, 0.6% CO, 7.2% O 2 and 83.6% N
More informationMass Transfer Operations I Prof. Bishnupada Mandal Department of Chemical Engineering Indian Institute of Technology, Guwahati
Mass Transfer Operations I Prof. Bishnupada Mandal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module  1 Diffusion Mass Transfer Lecture  6 Diffusion coefficient: Measurement
More informationChapter 6 Energy Equation for a Control Volume
Chapter 6 Energy Equation for a Control Volume Conservation of Mass and the Control Volume Closed systems: The mass of the system remain constant during a process. Control volumes: Mass can cross the boundaries,
More informationKinetic Theory of Gases. Chapter 33. Kinetic Theory of Gases
Kinetic Theory of Gases Kinetic Theory of Gases Chapter 33 Kinetic theory of gases envisions gases as a collection of atoms or molecules. Atoms or molecules are considered as particles. This is based on
More informationPhysics Notes Class 11 CHAPTER 13 KINETIC THEORY
1 P a g e Physics Notes Class 11 CHAPTER 13 KINETIC THEORY Assumptions of Kinetic Theory of Gases 1. Every gas consists of extremely small particles known as molecules. The molecules of a given gas are
More informationTransition state theory
Transition state theory. The equilibrium constant Equilibrium constants can be calculated for any chemical system from the partition functions for the species involved. In terms of the partition function
More informationKinetic Theory of Gases
Kinetic Theory of Gases Important Points:. Assumptions: a) Every gas consists of extremely small particles called molecules. b) The molecules of a gas are identical, spherical, rigid and perfectly elastic
More informationKINETIC THEORY OF GASES. Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure.
KINETIC THEORY OF GASES Boyle s Law: At constant temperature volume of given mass of gas is inversely proportional to its pressure. Charle s Law: At constant pressure volume of a given mass of gas is directly
More informationStatistical Mechanics, Kinetic Theory Ideal Gas. 8.01t Nov 22, 2004
Statistical Mechanics, Kinetic Theory Ideal Gas 8.01t Nov 22, 2004 Statistical Mechanics and Thermodynamics Thermodynamics Old & Fundamental Understanding of Heat (I.e. Steam) Engines Part of Physics Einstein
More informationThe First Law of Thermodynamics: Closed Systems. Heat Transfer
The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy gained
More informationVacuum Technology. Kinetic Theory of Gas. Dr. Philip D. Rack
Kinetic Theory of Gas Assistant Professor Department of Materials Science and Engineering University of Tennessee 603 Dougherty Engineering Building Knoxville, TN 379300 Phone: (865) 9745344 Fax (865)
More informationIntroduction To Materials Science FOR ENGINEERS, Ch. 5. Diffusion. MSE 201 Callister Chapter 5
Diffusion MSE 21 Callister Chapter 5 1 Goals: Diffusion  how do atoms move through solids? Fundamental concepts and language Diffusion mechanisms Vacancy diffusion Interstitial diffusion Impurities Diffusion
More informationHeat Transfer and Energy
What is Heat? Heat Transfer and Energy Heat is Energy in Transit. Recall the First law from Thermodynamics. U = Q  W What did we mean by all the terms? What is U? What is Q? What is W? What is Heat Transfer?
More informationThe Kinetic Theory of Gases Sections Covered in the Text: Chapter 18
The Kinetic Theory of Gases Sections Covered in the Text: Chapter 18 In Note 15 we reviewed macroscopic properties of matter, in particular, temperature and pressure. Here we see how the temperature and
More informationDIFFUSION IN SOLIDS. Materials often heat treated to improve properties. Atomic diffusion occurs during heat treatment
DIFFUSION IN SOLIDS WHY STUDY DIFFUSION? Materials often heat treated to improve properties Atomic diffusion occurs during heat treatment Depending on situation higher or lower diffusion rates desired
More informationBoltzmann Distribution Law
Boltzmann Distribution Law The motion of molecules is extremely chaotic Any individual molecule is colliding with others at an enormous rate Typically at a rate of a billion times per second We introduce
More information1 The basic equations of fluid dynamics
1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which
More informationSaturation Vapour Pressure above a Solution Droplet
Appendix C Saturation Vapour Pressure above a Solution Droplet In this appendix, the Köhler equation is derived. As in Appendix B, the theory summarised here can be found in Pruppacher & Klett (1980) and
More informationmomentum change per impact The average rate of change of momentum = Time interval between successive impacts 2m x 2l / x m x m x 2 / l P = l 2 P = l 3
Kinetic Molecular Theory This explains the Ideal Gas Pressure olume and Temperature behavior It s based on following ideas:. Any ordinary sized or macroscopic sample of gas contains large number of molecules.
More informationGases. Gas: fluid, occupies all available volume Liquid: fluid, fixed volume Solid: fixed volume, fixed shape Others?
CHAPTER 5: Gases Chemistry of Gases Pressure and Boyle s Law Temperature and Charles Law The Ideal Gas Law Chemical Calculations of Gases Mixtures of Gases Kinetic Theory of Gases Real Gases Gases The
More informationChapter 3 Properties of A Pure Substance
Chapter 3 Properties of A Pure Substance Pure substance: A pure substance is one that has a homogeneous and invariable chemical composition. Air is a mixture of several gases, but it is considered to be
More informationHEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases
UNIT HEAT. KINETIC THEORY OF GASES.. Introduction Molecules have a diameter of the order of Å and the distance between them in a gas is 0 Å while the interaction distance in solids is very small. R. Clausius
More informationKINETIC THEORY. 1.Name any one scientist who explained the behavior of gases considering it to be made up of tiny particles.
KINETIC THEORY ONE MARK OUESTION: 1.Name any one scientist who explained the behavior of gases considering it to be made up of tiny particles. 2.Based on which idea kinetic theory of gases explain the
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationThermodynamics and Kinetics. Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University
Thermodynamics and Kinetics Lecture 14 Properties of Mixtures Raoult s Law Henry s Law Activity NC State University Measures of concentration There are three measures of concentration: molar concentration
More informationThe Equipartition Theorem
The Equipartition Theorem Degrees of freedom are associated with the kinetic energy of translations, rotation, vibration and the potential energy of vibrations. A result from classical statistical mechanics
More informationChapter 15 Chemical Equilibrium
Chapter 15 Chemical Equilibrium Chemical reactions can reach a state of dynamic equilibrium. Similar to the equilibrium states reached in evaporation of a liquid in a closed container or the dissolution
More informationME19b. SOLUTIONS. Feb. 11, 2010. Due Feb. 18
ME19b. SOLTIONS. Feb. 11, 21. Due Feb. 18 PROBLEM B14 Consider the long thin racing boats used in competitive rowing events. Assume that the major component of resistance to motion is the skin friction
More informationChapter 13 Gases. An Introduction to Chemistry by Mark Bishop
Chapter 13 Gases An Introduction to Chemistry by Mark Bishop Chapter Map Gas Gas Model Gases are composed of tiny, widelyspaced particles. For a typical gas, the average distance between particles is
More informationThermodynamics: Lecture 8, Kinetic Theory
Thermodynamics: Lecture 8, Kinetic Theory Chris Glosser April 15, 1 1 OUTLINE I. Assumptions of Kinetic Theory (A) Molecular Flux (B) Pressure and the Ideal Gas Law II. The MaxwellBoltzmann Distributuion
More informationBasic Equations, Boundary Conditions and Dimensionless Parameters
Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were
More informationLaboratory exercise No. 4 Water vapor and liquid moisture transport
Laboratory exercise No. 4 Water vapor and liquid moisture transport Water vapor transport in porous materials Due to the thermal conductivity of water and other unfavourable properties and effects in porous
More informationWed Sep 12, 2007 THE GASEOUS STATE
Chapter 5: Gases Gas Stoichiometry Partial Pressure Kinetic Theory Effusion and Diffusion Wed Sep 12, 2007 Exam #1  Friday, Sep 14 Attendance is mandatory! Practice exam today in recitation Week 3 CHEM
More informationCLASSICAL CONCEPT REVIEW 8
CLASSICAL CONCEPT REVIEW 8 Kinetic Theory Information concerning the initial motions of each of the atoms of macroscopic systems is not accessible, nor do we have the computational capability even with
More informationCHAPTER 12. Gases and the KineticMolecular Theory
CHAPTER 12 Gases and the KineticMolecular Theory 1 Gases vs. Liquids & Solids Gases Weak interactions between molecules Molecules move rapidly Fast diffusion rates Low densities Easy to compress Liquids
More informationHeterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi
Heterogeneous Catalysis and Catalytic Processes Prof. K. K. Pant Department of Chemical Engineering Indian Institute of Technology, Delhi Module  03 Lecture 10 Good morning. In my last lecture, I was
More informationCONSERVATION LAWS. See Figures 2 and 1.
CONSERVATION LAWS 1. Multivariable calculus 1.1. Divergence theorem (of Gauss). This states that the volume integral in of the divergence of the vectorvalued function F is equal to the total flux of F
More informationENSC 283 Introduction and Properties of Fluids
ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force
More informationChemistry 13: States of Matter
Chemistry 13: States of Matter Name: Period: Date: Chemistry Content Standard: Gases and Their Properties The kinetic molecular theory describes the motion of atoms and molecules and explains the properties
More informationCHEMICAL ENGINEERING AND CHEMICAL PROCESS TECHNOLOGY  Vol. I  Interphase Mass Transfer  A. Burghardt
INTERPHASE MASS TRANSFER A. Burghardt Institute of Chemical Engineering, Polish Academy of Sciences, Poland Keywords: Turbulent flow, turbulent mass flux, eddy viscosity, eddy diffusivity, Prandtl mixing
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationSimple Mixtures. Atkins 7th: Sections ; Atkins 8th: The Properties of Solutions. Liquid Mixtures
The Properties of Solutions Simple Mixtures Atkins 7th: Sections 7.47.5; Atkins 8th: 5.45.5 Liquid Mixtures Colligative Properties Boiling point elevation Freezing point depression Solubility Osmosis
More informationPROPERTIES OF PURE SUBSTANCES
Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGrawHill, 2011 Chapter 3 PROPERTIES OF PURE SUBSTANCES Mehmet Kanoglu University of Gaziantep Copyright
More informationFundamentals of Heat and Mass Transfer
2008 AGIInformation Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA
More information15. The Kinetic Theory of Gases
5. The Kinetic Theory of Gases Introduction and Summary Previously the ideal gas law was discussed from an experimental point of view. The relationship between pressure, density, and temperature was later
More informationSolving Equilibrium Problems. AP Chemistry Ms. Grobsky
Solving Equilibrium Problems AP Chemistry Ms. Grobsky Types of Equilibrium Problems A typical equilibrium problem involves finding the equilibrium concentrations (or pressures) of reactants and products
More informationUnits and Dimensions in Physical Chemistry
Units and Dimensions in Physical Chemistry Units and dimensions tend to cause untold amounts of grief to many chemists throughout the course of their degree. My hope is that by having a dedicated tutorial
More informationFluids and Solids: Fundamentals
Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.
More informationChapter 3 Temperature and Heat
Chapter 3 Temperature and Heat In Chapter, temperature was described as an intensive property of a system. In common parlance, we understand temperature as a property which is related to the degree of
More informationVaporLiquid Equilibria
31 Introduction to Chemical Engineering Calculations Lecture 7. VaporLiquid Equilibria Vapor and Gas Vapor A substance that is below its critical temperature. Gas A substance that is above its critical
More informationFLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions
FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or
More informationPhysics of the Atmosphere I
Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uniheidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:
More informationGas  a substance that is characterized by widely separated molecules in rapid motion.
Chapter 10  Gases Gas  a substance that is characterized by widely separated molecules in rapid motion. Mixtures of gases are uniform. Gases will expand to fill containers (compare with solids and liquids
More informationHEAT AND MASS TRANSFER
MEL242 HEAT AND MASS TRANSFER Prabal Talukdar Associate Professor Department of Mechanical Engineering g IIT Delhi prabal@mech.iitd.ac.in MECH/IITD Course Coordinator: Dr. Prabal Talukdar Room No: III,
More informationStability of Evaporating Polymer Films. For: Dr. Roger Bonnecaze Surface Phenomena (ChE 385M)
Stability of Evaporating Polymer Films For: Dr. Roger Bonnecaze Surface Phenomena (ChE 385M) Submitted by: Ted Moore 4 May 2000 Motivation This problem was selected because the writer observed a dependence
More informationChapter 14. CHEMICAL EQUILIBRIUM
Chapter 14. CHEMICAL EQUILIBRIUM 14.1 THE CONCEPT OF EQUILIBRIUM AND THE EQUILIBRIUM CONSTANT Many chemical reactions do not go to completion but instead attain a state of chemical equilibrium. Chemical
More informationBoundary Conditions in Fluid Mechanics
Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial
More informationThermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am  10:00am & Monday 8:00am  9:00am MEP 261 Class ZA
Thermodynamics I Spring 1432/1433H (2011/2012H) Saturday, Wednesday 8:00am  10:00am & Monday 8:00am  9:00am MEP 261 Class ZA Dr. Walid A. Aissa Associate Professor, Mech. Engg. Dept. Faculty of Engineering
More informationChapter 28 Fluid Dynamics
Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example
More informationME 239: Rocket Propulsion. Nozzle Thermodynamics and Isentropic Flow Relations. J. M. Meyers, PhD
ME 39: Rocket Propulsion Nozzle Thermodynamics and Isentropic Flow Relations J. M. Meyers, PhD 1 Assumptions for this Analysis 1. Steady, onedimensional flow No motor start/stopping issues to be concerned
More informationCh 3. Rate Laws and Stoichiometry
Ch 3. Rate Laws and Stoichiometry How do we obtain r A = f(x)? We do this in two steps 1. Rate Law Find the rate as a function of concentration, r A = k fn (C A, C B ). Stoichiometry Find the concentration
More informationGases. Macroscopic Properties. Petrucci, Harwood and Herring: Chapter 6
Gases Petrucci, Harwood and Herring: Chapter 6 CHEM 1000A 3.0 Gases 1 We will be looking at Macroscopic and Microscopic properties: Macroscopic Properties of bulk gases Observable Pressure, volume, mass,
More informationKinetic Molecular Theory
Kinetic Molecular Theory Particle volume  The volume of an individual gas particle is small compaired to that of its container. Therefore, gas particles are considered to have mass, but no volume. There
More informationThe Boltzmann distribution law and statistical thermodynamics
1 The Boltzmann distribution law and statistical thermodynamics 1.1 Nature and aims of statistical mechanics Statistical mechanics is the theoretical apparatus with which one studies the properties of
More informationGas Laws. The kinetic theory of matter states that particles which make up all types of matter are in constant motion.
Name Period Gas Laws Kinetic energy is the energy of motion of molecules. Gas state of matter made up of tiny particles (atoms or molecules). Each atom or molecule is very far from other atoms or molecules.
More informationCopper, Zinc and Brass (an alloy of Cu and Zn) have very similar specific heat capacities. Why should this be so?
Thermal Properties 1. Specific Heat Capacity The heat capacity or thermal capacity of a body is a measure of how much thermal energy is required to raise its temperature by 1K (1 C). This will depend on
More informationChemistry 223: Collisions, Reactions, and Transport David Ronis McGill University
Chemistry 223: Collisions, Reactions, and Transport David Ronis McGill University. Effusion, Surface Collisions and Reactions In the previous section, we found the parameter b by computing the average
More informationMajor chemistry laws. Mole and Avogadro s number. Calculating concentrations.
Major chemistry laws. Mole and Avogadro s number. Calculating concentrations. Major chemistry laws Avogadro's Law Equal volumes of gases under identical temperature and pressure conditions will contain
More informationChapter 5: Diffusion. 5.1 SteadyState Diffusion
: Diffusion Diffusion: the movement of particles in a solid from an area of high concentration to an area of low concentration, resulting in the uniform distribution of the substance Diffusion is process
More information1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids
1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids  both liquids and gases.
More informationTransient Mass Transfer
Lecture T1 Transient Mass Transfer Up to now, we have considered either processes applied to closed systems or processes involving steadystate flows. In this lecture we turn our attention to transient
More informationChapter 18 The Micro/Macro Connection
Chapter 18 The Micro/Macro Connection Chapter Goal: To understand a macroscopic system in terms of the microscopic behavior of its molecules. Slide 182 Announcements Chapter 18 Preview Slide 183 Chapter
More information(1) The size of a gas particle is negligible as compared to the volume of the container in which the gas is placed.
Gas Laws and Kinetic Molecular Theory The Gas Laws are based on experiments, and they describe how a gas behaves under certain conditions. However, Gas Laws do not attempt to explain the behavior of gases.
More information= 1.038 atm. 760 mm Hg. = 0.989 atm. d. 767 torr = 767 mm Hg. = 1.01 atm
Chapter 13 Gases 1. Solids and liquids have essentially fixed volumes and are not able to be compressed easily. Gases have volumes that depend on their conditions, and can be compressed or expanded by
More informationAbsorption of Heat. Internal energy is the appropriate energy variable to use at constant volume
6 Absorption of Heat According to the First Law, E = q + w = q  P V, assuming PV work is the only kind that can occur. Therefore, E = q V. The subscript means that the process occurs at constant volume.
More informationk is change in kinetic energy and E
Energy Balances on Closed Systems A system is closed if mass does not cross the system boundary during the period of time covered by energy balance. Energy balance for a closed system written between two
More informationA k 1. At equilibrium there is no net change in [A] or [B], namely d[a] dt
Chapter 15: Chemical Equilibrium Key topics: Equilibrium Constant Calculating Equilibrium Concentrations The Concept of Equilibrium Consider the reaction A k 1 k 1 B At equilibrium there is no net change
More informationPHASE CHEMISTRY AND COLLIGATIVE PROPERTIES
PHASE CHEMISTRY AND COLLIGATIVE PROPERTIES Phase Diagrams Solutions Solution Concentrations Colligative Properties Brown et al., Chapter 10, 385 394, Chapter 11, 423437 CHEM120 Lecture Series Two : 2011/01
More informationChemistry B11 Chapter 4 Chemical reactions
Chemistry B11 Chapter 4 Chemical reactions Chemical reactions are classified into five groups: A + B AB Synthesis reactions (Combination) H + O H O AB A + B Decomposition reactions (Analysis) NaCl Na +Cl
More informationType: Double Date: Kinetic Energy of an Ideal Gas II. Homework: Read 14.3, Do Concept Q. # (15), Do Problems # (28, 29, 31, 37)
Type: Double Date: Objective: Kinetic Energy of an Ideal Gas I Kinetic Energy of an Ideal Gas II Homework: Read 14.3, Do Concept Q. # (15), Do Problems # (8, 9, 31, 37) AP Physics Mr. Mirro Kinetic Energy
More informationApplied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur
Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture  7 Ideal Gas Laws, Different Processes Let us continue
More information(b) Explain how the principle of conservation of momentum is a natural consequence of Newton s laws of motion. [3]
Physics A Unit: G484: The Newtonian World 1(a) State Newton s second law of motion. The resultant force on an object is proportional to the rate of change of momentum of the object In part (a) the candidate
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationExample 1. Solution: Diagram: Given: m = 1 kg P 1 = P 2 = 0.8 MPa = constant v 1 = m 3 /kg v 2 = m 3 /kg. Find:
Example 1 Problem Statement: A piston/cylinder device contains one kilogram of a substance at 0.8 MPa with a specific volume of 0.2608 m 3 /kg. The substance undergoes an isobaric process until its specific
More informationEquilibrium Notes Ch 14:
Equilibrium Notes Ch 14: Homework: E q u i l i b r i u m P a g e 1 Read Chapter 14 Work out sample/practice exercises in the sections, Bonus Chapter 14: 23, 27, 29, 31, 39, 41, 45, 51, 57, 63, 77, 83,
More informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationGases. States of Matter. Molecular Arrangement Solid Small Small Ordered Liquid Unity Unity Local Order Gas High Large Chaotic (random)
Gases States of Matter States of Matter Kinetic E (motion) Potential E(interaction) Distance Between (size) Molecular Arrangement Solid Small Small Ordered Liquid Unity Unity Local Order Gas High Large
More informationThermodynamics. Chapter 13 Phase Diagrams. NC State University
Thermodynamics Chapter 13 Phase Diagrams NC State University Pressure (atm) Definition of a phase diagram A phase diagram is a representation of the states of matter, solid, liquid, or gas as a function
More informationTheory of Chromatography
Theory of Chromatography The Chromatogram A chromatogram is a graph showing the detector response as a function of elution time. The retention time, t R, for each component is the time needed after injection
More information9231 FURTHER MATHEMATICS
CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2012 series 9231 FURTHER MATHEMATICS 9231/21 Paper 2, maximum raw mark 100
More informationUnit G484: The Newtonian World
Define linear momentum (and appreciate the vector nature of momentum) net force on a body impulse of a force a perfectly elastic collision an inelastic collision the radian gravitational field strength
More informationWave Structures on A Jet Entering the Bulk Liquid. He Yijun; Li Youxi: Zhu Zijia; Lin Liang; Corkill Ashley Christine
Wave Structures on A Jet Entering the Bulk Liquid He Yijun; Li Youxi: Zhu Zijia; Lin Liang; Corkill Ashley Christine Introduction The formation of capillary waves on fluid pipes Our goal is to describe
More informationMass and Energy Analysis of Control Volumes
MAE 320Chapter 5 Mass and Energy Analysis of Control Volumes Objectives Develop the conservation of mass principle. Apply the conservation of mass principle to various systems including steady and unsteadyflow
More informationChapter 18. The Micro/Macro Connection
Chapter 18. The Micro/Macro Connection Heating the air in a hotair balloon increases the thermal energy of the air molecules. This causes the gas to expand, lowering its density and allowing the balloon
More informationChapter Biography of J. C. Maxwell Derivation of the Maxwell Speed Distribution Function
Chapter 10 10.1 Biography of J. C. Maxwell 10.2 Derivation of the Maxwell Speed Distribution Function The distribution of molecular speeds was first worked out by Maxwell before the development of statistical
More informationThermal Properties of Matter
Chapter 18 Thermal Properties of Matter PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 18 To relate the
More informationDevelopment of a Model for Wet Scrubbing of Carbon Dioxide by Chilled Ammonia
Development of a Model for Wet Scrubbing of Carbon Dioxide by Chilled Ammonia John Nilsson Department of Chemical Engineering, Lund University, P. O. Box 124, SE221 00 Lund, Sweden In this paper, the
More information