3. Energy, Heat, and Work
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Lecture 4: 09.16.05 Temperature, Heat, and Entropy
3.012 Fundamentals of Materials Science Fall 2005 Lecture 4: 09.16.05 Temperature, heat, and entropy Today: LAST TIME .........................................................................................................................................................................................2� State functions ..............................................................................................................................................................................2� Path dependent variables: heat and work..................................................................................................................................2� DEFINING TEMPERATURE ...................................................................................................................................................................4� The zeroth law of thermodynamics .............................................................................................................................................4� The absolute temperature scale ..................................................................................................................................................5� CONSEQUENCES OF THE RELATION BETWEEN TEMPERATURE, HEAT, AND ENTROPY: HEAT CAPACITY .......................................6� The difference between heat and temperature ...........................................................................................................................6� Defining heat capacity.................................................................................................................................................................6� -
AST242 LECTURE NOTES PART 3 Contents 1. Viscous Flows 2 1.1. the Velocity Gradient Tensor 2 1.2. Viscous Stress Tensor 3 1.3. Na
AST242 LECTURE NOTES PART 3 Contents 1. Viscous flows 2 1.1. The velocity gradient tensor 2 1.2. Viscous stress tensor 3 1.3. Navier Stokes equation { diffusion 5 1.4. Viscosity to order of magnitude 6 1.5. Example using the viscous stress tensor: The force on a moving plate 6 1.6. Example using the Navier Stokes equation { Poiseuille flow or Flow in a capillary 7 1.7. Viscous Energy Dissipation 8 2. The Accretion disk 10 2.1. Accretion to order of magnitude 14 2.2. Hydrostatic equilibrium for an accretion disk 15 2.3. Shakura and Sunyaev's α-disk 17 2.4. Reynolds Number 17 2.5. Circumstellar disk heated by stellar radiation 18 2.6. Viscous Energy Dissipation 20 2.7. Accretion Luminosity 21 3. Vorticity and Rotation 24 3.1. Helmholtz Equation 25 3.2. Rate of Change of a vector element that is moving with the fluid 26 3.3. Kelvin Circulation Theorem 28 3.4. Vortex lines and vortex tubes 30 3.5. Vortex stretching and angular momentum 32 3.6. Bernoulli's constant in a wake 33 3.7. Diffusion of vorticity 34 3.8. Potential Flow and d'Alembert's paradox 34 3.9. Burger's vortex 36 4. Rotating Flows 38 4.1. Coriolis Force 38 4.2. Rossby and Ekman numbers 39 4.3. Geostrophic flows and the Taylor Proudman theorem 39 4.4. Two dimensional flows on the surface of a planet 41 1 2 AST242 LECTURE NOTES PART 3 4.5. Thermal winds? 42 5. -
Energy Literacy Essential Principles and Fundamental Concepts for Energy Education
Energy Literacy Essential Principles and Fundamental Concepts for Energy Education A Framework for Energy Education for Learners of All Ages About This Guide Energy Literacy: Essential Principles and Intended use of this document as a guide includes, Fundamental Concepts for Energy Education but is not limited to, formal and informal energy presents energy concepts that, if understood and education, standards development, curriculum applied, will help individuals and communities design, assessment development, make informed energy decisions. and educator trainings. Energy is an inherently interdisciplinary topic. Development of this guide began at a workshop Concepts fundamental to understanding energy sponsored by the Department of Energy (DOE) arise in nearly all, if not all, academic disciplines. and the American Association for the Advancement This guide is intended to be used across of Science (AAAS) in the fall of 2010. Multiple disciplines. Both an integrated and systems-based federal agencies, non-governmental organizations, approach to understanding energy are strongly and numerous individuals contributed to the encouraged. development through an extensive review and comment process. Discussion and information Energy Literacy: Essential Principles and gathered at AAAS, WestEd, and DOE-sponsored Fundamental Concepts for Energy Education Energy Literacy workshops in the spring of 2011 identifies seven Essential Principles and a set of contributed substantially to the refinement of Fundamental Concepts to support each principle. the guide. This guide does not seek to identify all areas of energy understanding, but rather to focus on those To download this guide and related documents, that are essential for all citizens. The Fundamental visit www.globalchange.gov. Concepts have been drawn, in part, from existing education standards and benchmarks. -
HEAT and TEMPERATURE Heat Is a Type of ENERGY. When Absorbed
HEAT AND TEMPERATURE Heat is a type of ENERGY. When absorbed by a substance, heat causes inter-particle bonds to weaken and break which leads to a change of state (solid to liquid for example). Heat causing a phase change is NOT sufficient to cause an increase in temperature. Heat also causes an increase of kinetic energy (motion, friction) of the particles in a substance. This WILL cause an increase in TEMPERATURE. Temperature is NOT energy, only a measure of KINETIC ENERGY The reason why there is no change in temperature at a phase change is because the substance is using the heat only to change the way the particles interact (“stick together”). There is no increase in the particle motion and hence no rise in temperature. THERMAL ENERGY is one type of INTERNAL ENERGY possessed by an object. It is the KINETIC ENERGY component of the object’s internal energy. When thermal energy is transferred from a hot to a cold body, the term HEAT is used to describe the transferred energy. The hot body will decrease in temperature and hence in thermal energy. The cold body will increase in temperature and hence in thermal energy. Temperature Scales: The K scale is the absolute temperature scale. The lowest K temperature, 0 K, is absolute zero, the temperature at which an object possesses no thermal energy. The Celsius scale is based upon the melting point and boiling point of water at 1 atm pressure (0, 100o C) K = oC + 273.13 UNITS OF HEAT ENERGY The unit of heat energy we will use in this lesson is called the JOULE (J). -
Estimation of the Dissipation Rate of Turbulent Kinetic Energy: a Review
Chemical Engineering Science 229 (2021) 116133 Contents lists available at ScienceDirect Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces Review Estimation of the dissipation rate of turbulent kinetic energy: A review ⇑ Guichao Wang a, , Fan Yang a,KeWua, Yongfeng Ma b, Cheng Peng c, Tianshu Liu d, ⇑ Lian-Ping Wang b,c, a SUSTech Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology, Shenzhen 518055, PR China b Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China c Department of Mechanical Engineering, 126 Spencer Laboratory, University of Delaware, Newark, DE 19716-3140, USA d Department of Mechanical and Aeronautical Engineering, Western Michigan University, Kalamazoo, MI 49008, USA highlights Estimate of turbulent dissipation rate is reviewed. Experimental works are summarized in highlight of spatial/temporal resolution. Data processing methods are compared. Future directions in estimating turbulent dissipation rate are discussed. article info abstract Article history: A comprehensive literature review on the estimation of the dissipation rate of turbulent kinetic energy is Received 8 July 2020 presented to assess the current state of knowledge available in this area. Experimental techniques (hot Received in revised form 27 August 2020 wires, LDV, PIV and PTV) reported on the measurements of turbulent dissipation rate have been critically Accepted 8 September 2020 analyzed with respect to the velocity processing methods. Traditional hot wires and LDV are both a point- Available online 12 September 2020 based measurement technique with high temporal resolution and Taylor’s frozen hypothesis is generally required to transfer temporal velocity fluctuations into spatial velocity fluctuations in turbulent flows. -
Turbulence Kinetic Energy Budgets and Dissipation Rates in Disturbed Stable Boundary Layers
4.9 TURBULENCE KINETIC ENERGY BUDGETS AND DISSIPATION RATES IN DISTURBED STABLE BOUNDARY LAYERS Julie K. Lundquist*1, Mark Piper2, and Branko Kosovi1 1Atmospheric Science Division Lawrence Livermore National Laboratory, Livermore, CA, 94550 2Program in Atmospheric and Oceanic Science, University of Colorado at Boulder 1. INTRODUCTION situated in gently rolling farmland in eastern Kansas, with a homogeneous fetch to the An important parameter in the numerical northwest. The ASTER facility, operated by the simulation of atmospheric boundary layers is the National Center for Atmospheric Research (NCAR) dissipation length scale, lε. It is especially Atmospheric Technology Division, was deployed to important in weakly to moderately stable collect turbulence data. The ASTER sonic conditions, in which a tenuous balance between anemometers were used to compute turbulence shear production of turbulence, buoyant statistics for the three velocity components and destruction of turbulence, and turbulent dissipation used to estimate dissipation rate. is maintained. In large-scale models, the A dry Arctic cold front passed the dissipation rate is often parameterized using a MICROFRONTS site at approximately 0237 UTC diagnostic equation based on the production of (2037 LST) 20 March 1995, two hours after local turbulent kinetic energy (TKE) and an estimate of sunset at 1839 LST. Time series spanning the the dissipation length scale. Proper period 0000-0600 UTC are shown in Figure 1.The parameterization of the dissipation length scale 6-hr time period was chosen because it allows from experimental data requires accurate time for the front to completely pass the estimation of the rate of dissipation of TKE from instrumented tower, with time on either side to experimental data. -
Toolkit 1: Energy Units and Fundamentals of Quantitative Analysis
Energy & Society Energy Units and Fundamentals Toolkit 1: Energy Units and Fundamentals of Quantitative Analysis 1 Energy & Society Energy Units and Fundamentals Table of Contents 1. Key Concepts: Force, Work, Energy & Power 3 2. Orders of Magnitude & Scientific Notation 6 2.1. Orders of Magnitude 6 2.2. Scientific Notation 7 2.3. Rules for Calculations 7 2.3.1. Multiplication 8 2.3.2. Division 8 2.3.3. Exponentiation 8 2.3.4. Square Root 8 2.3.5. Addition & Subtraction 9 3. Linear versus Exponential Growth 10 3.1. Linear Growth 10 3.2. Exponential Growth 11 4. Uncertainty & Significant Figures 14 4.1. Uncertainty 14 4.2. Significant Figures 15 4.3. Exact Numbers 15 4.4. Identifying Significant Figures 16 4.5. Rules for Calculations 17 4.5.1. Addition & Subtraction 17 4.5.2. Multiplication, Division & Exponentiation 18 5. Unit Analysis 19 5.1. Commonly Used Energy & Non-energy Units 20 5.2. Form & Function 21 6. Sample Problems 22 6.1. Scientific Notation 22 6.2. Linear & Exponential Growth 22 6.3. Significant Figures 23 6.4. Unit Conversions 23 7. Answers to Sample Problems 24 7.1. Scientific Notation 24 7.2. Linear & Exponential Growth 24 7.3. Significant Figures 24 7.4. Unit Conversions 26 8. References 27 2 Energy & Society Energy Units and Fundamentals 1. KEY CONCEPTS: FORCE, WORK, ENERGY & POWER Among the most important fundamentals to be mastered when studying energy pertain to the differences and inter-relationships among four concepts: force, work, energy, and power. Each of these terms has a technical meaning in addition to popular or colloquial meanings. -
Work and Energy Summary Sheet Chapter 6
Work and Energy Summary Sheet Chapter 6 Work: work is done when a force is applied to a mass through a displacement or W=Fd. The force and the displacement must be parallel to one another in order for work to be done. F (N) W =(Fcosθ)d F If the force is not parallel to The area of a force vs. the displacement, then the displacement graph + W component of the force that represents the work θ d (m) is parallel must be found. done by the varying - W d force. Signs and Units for Work Work is a scalar but it can be positive or negative. Units of Work F d W = + (Ex: pitcher throwing ball) 1 N•m = 1 J (Joule) F d W = - (Ex. catcher catching ball) Note: N = kg m/s2 • Work – Energy Principle Hooke’s Law x The work done on an object is equal to its change F = kx in kinetic energy. F F is the applied force. 2 2 x W = ΔEk = ½ mvf – ½ mvi x is the change in length. k is the spring constant. F Energy Defined Units Energy is the ability to do work. Same as work: 1 N•m = 1 J (Joule) Kinetic Energy Potential Energy Potential energy is stored energy due to a system’s shape, position, or Kinetic energy is the energy of state. motion. If a mass has velocity, Gravitational PE Elastic (Spring) PE then it has KE 2 Mass with height Stretch/compress elastic material Ek = ½ mv 2 EG = mgh EE = ½ kx To measure the change in KE Change in E use: G Change in ES 2 2 2 2 ΔEk = ½ mvf – ½ mvi ΔEG = mghf – mghi ΔEE = ½ kxf – ½ kxi Conservation of Energy “The total energy is neither increased nor decreased in any process. -
Heat Energy a Science A–Z Physical Series Word Count: 1,324 Heat Energy
Heat Energy A Science A–Z Physical Series Word Count: 1,324 Heat Energy Written by Felicia Brown Visit www.sciencea-z.com www.sciencea-z.com KEY ELEMENTS USED IN THIS BOOK The Big Idea: One of the most important types of energy on Earth is heat energy. A great deal of heat energy comes from the Sun’s light Heat Energy hitting Earth. Other sources include geothermal energy, friction, and even living things. Heat energy is the driving force behind everything we do. This energy gives us the ability to run, dance, sing, and play. We also use heat energy to warm our homes, cook our food, power our vehicles, and create electricity. Key words: cold, conduction, conductor, convection, energy, evaporate, fire, friction, fuel, gas, geothermal heat, geyser, heat energy, hot, insulation, insulator, lightning, liquid, matter, particles, radiate, radiant energy, solid, Sun, temperature, thermometer, transfer, volcano Key comprehension skill: Cause and effect Other suitable comprehension skills: Compare and contrast; classify information; main idea and details; identify facts; elements of a genre; interpret graphs, charts, and diagram Key reading strategy: Connect to prior knowledge Other suitable reading strategies: Ask and answer questions; summarize; visualize; using a table of contents and headings; using a glossary and bold terms Photo Credits: Front cover: © iStockphoto.com/Julien Grondin; back cover, page 5: © iStockphoto.com/ Arpad Benedek; title page, page 20 (top): © iStockphoto.com/Anna Ziska; pages 3, 9, 20 (bottom): © Jupiterimages Corporation; -
Middle School Physical Science: Kinetic Energy and Potential Energy
MIDDLE SCHOOL PHYSICAL SCIENCE: KINETIC ENERGY AND POTENTIAL ENERGY Standards Bundle Standards are listed within the bundle. Bundles are created with potential instructional use in mind, based upon potential for related phenomena that can be used throughout a unit. MS-PS3-1 Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. [Clarification Statement: Emphasis is on descriptive relationships between kinetic energy and mass separately from kinetic energy and speed. Examples could include riding a bicycle at different speeds, rolling different sizes of rocks downhill, and getting hit by a wiffle ball versus a tennis ball.] MS-PS3-2 Develop a model to describe that when the arrangement of objects interacting at a distance changes, different amounts of potential energy are stored in the system. [Clarification Statement: Emphasis is on relative amounts of potential energy, not on calculations of potential energy. Examples of objects within systems interacting at varying distances could include: the Earth and either a roller coaster cart at varying positions on a hill or objects at varying heights on shelves, changing the direction/orientation of a magnet, and a balloon with static electrical charge being brought closer to a classmate’s hair. Examples of models could include representations, diagrams, pictures, and written descriptions of systems.] [Assessment Boundary: Assessment is limited to two objects and electric, magnetic, and gravitational interactions.] MS-PS3-5. Engage in argument from evidence to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object. -
TEMPERATURE, HEAT, and SPECIFIC HEAT INTRODUCTION Temperature and Heat Are Two Topics That Are Often Confused
TEMPERATURE, HEAT, AND SPECIFIC HEAT INTRODUCTION Temperature and heat are two topics that are often confused. Temperature measures how hot or cold an object is. Commonly this is measured with the aid of a thermometer even though other devices such as thermocouples and pyrometers are also used. Temperature is an intensive property; it does not depend on the amount of material present. In scientific work, temperature is most commonly expressed in units of degrees Celsius. On this scale the freezing point of water is 0oC and its boiling point is 100oC. Heat is a form of energy and is a phenomenon that has its origin in the motion of particles that make up a substance. Heat is an extensive property. The unit of heat in the metric system is called the calorie (cal). One calorie is defined as the amount of heat necessary to raise 1 gram of water by 1oC. This means that if you wish to raise 7 g of water by 4oC, (4)(7) = 28 cal would be required. A somewhat larger unit than the calorie is the kilocalorie (kcal) which equals 1000 cal. The definition of the calorie was made in reference to a particular substance, namely water. It takes 1 cal to raise the temperature of 1 g of water by 1oC. Does this imply perhaps that the amount of heat energy necessary to raise 1 g of other substances by 1oC is not equal to 1 cal? Experimentally we indeed find this to be true. In the modern system of international units heat is expressed in joules and kilojoules. -
Kinetic Energy and Work
Kinetic Energy and Work 8.01 W06D1 Today’s Readings: Chapter 13 The Concept of Energy and Conservation of Energy, Sections 13.1-13.8 Announcements Problem Set 4 due Week 6 Tuesday at 9 pm in box outside 26-152 Math Review Week 6 Tuesday at 9 pm in 26-152 Kinetic Energy • Scalar quantity (reference frame dependent) 1 K = mv2 ≥ 0 2 • SI unit is joule: 1J ≡1kg ⋅m2/s2 • Change in kinetic energy: 1 2 1 2 1 2 2 2 1 2 2 2 ΔK = mv f − mv0 = m(vx, f + vy, f + vz, f ) − m(vx,0 + vy,0 + vz,0 ) 2 2 2 2 Momentum and Kinetic Energy: Single Particle Kinetic energy and momentum for a single particle are related by 2 1 2 p K = mv = 2 2m Concept Question: Pushing Carts Consider two carts, of masses m and 2m, at rest on an air track. If you push one cart for 3 seconds and then the other for the same length of time, exerting equal force on each, the kinetic energy of the light cart is 1) larger than 2) equal to 3) smaller than the kinetic energy of the heavy car. Work Done by a Constant Force for One Dimensional Motion Definition: The work W done by a constant force with an x-component, Fx, in displacing an object by Δx is equal to the x- component of the force times the displacement: W = F Δx x Concept Q.: Pushing Against a Wall The work done by the contact force of the wall on the person as the person moves away from the wall is 1.