Extended Work-Energy Theorem
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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� -
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. -
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. -
Feeling Joules and Watts
FEELING JOULES AND WATTS OVERVIEW & PURPOSE Power was originally measured in horsepower – literally the number of horses it took to do a particular amount of work. James Watt developed this term in the 18th century to compare the output of steam engines to the power of draft horses. This allowed people who used horses for work on a regular basis to have an intuitive understanding of power. 1 horsepower is about 746 watts. In this lab, you’ll learn about energy, work and power – including your own capacity to do work. Energy is the ability to do work. Without energy, nothing would grow, move, or change. Work is using a force to move something over some distance. work = force x distance Energy and work are measured in joules. One joule equals the work done (or energy used) when a force of one newton moves an object one meter. One newton equals the force required to accelerate one kilogram one meter per second squared. How much energy would it take to lift a can of soda (weighing 4 newtons) up two meters? work = force x distance = 4N x 2m = 8 joules Whether you lift the can of soda quickly or slowly, you are doing 8 joules of work (using 8 joules of energy). It’s often helpful, though, to measure how quickly we are doing work (or using energy). Power is the amount of work (or energy used) in a given amount of time. http://www.rdcep.org/demo-collection page 1 work power = time Power is measured in watts. One watt equals one joule per second. -
Lecture 8: Maximum and Minimum Work, Thermodynamic Inequalities
Lecture 8: Maximum and Minimum Work, Thermodynamic Inequalities Chapter II. Thermodynamic Quantities A.G. Petukhov, PHYS 743 October 4, 2017 Chapter II. Thermodynamic Quantities Lecture 8: Maximum and Minimum Work, ThermodynamicA.G. Petukhov,October Inequalities PHYS 4, 743 2017 1 / 12 Maximum Work If a thermally isolated system is in non-equilibrium state it may do work on some external bodies while equilibrium is being established. The total work done depends on the way leading to the equilibrium. Therefore the final state will also be different. In any event, since system is thermally isolated the work done by the system: jAj = E0 − E(S); where E0 is the initial energy and E(S) is final (equilibrium) one. Le us consider the case when Vinit = Vfinal but can change during the process. @ jAj @E = − = −Tfinal < 0 @S @S V The entropy cannot decrease. Then it means that the greater is the change of the entropy the smaller is work done by the system The maximum work done by the system corresponds to the reversible process when ∆S = Sfinal − Sinitial = 0 Chapter II. Thermodynamic Quantities Lecture 8: Maximum and Minimum Work, ThermodynamicA.G. Petukhov,October Inequalities PHYS 4, 743 2017 2 / 12 Clausius Theorem dS 0 R > dS < 0 R S S TA > TA T > T B B A δQA > 0 B Q 0 δ B < The system following a closed path A: System receives heat from a hot reservoir. Temperature of the thermostat is slightly larger then the system temperature B: System dumps heat to a cold reservoir. Temperature of the system is slightly larger then that of the thermostat Chapter II. -
Entropy: Is It What We Think It Is and How Should We Teach It?
Entropy: is it what we think it is and how should we teach it? David Sands Dept. Physics and Mathematics University of Hull UK Institute of Physics, December 2012 We owe our current view of entropy to Gibbs: “For the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the system that do not alter its energy, the variation of its entropy shall vanish or be negative.” Equilibrium of Heterogeneous Substances, 1875 And Maxwell: “We must regard the entropy of a body, like its volume, pressure, and temperature, as a distinct physical property of the body depending on its actual state.” Theory of Heat, 1891 Clausius: Was interested in what he called “internal work” – work done in overcoming inter-particle forces; Sought to extend the theory of cyclic processes to cover non-cyclic changes; Actively looked for an equivalent equation to the central result for cyclic processes; dQ 0 T Clausius: In modern thermodynamics the sign is negative, because heat must be extracted from the system to restore the original state if the cycle is irreversible . The positive sign arises because of Clausius’ view of heat; not caloric but still a property of a body The transformation of heat into work was something that occurred within a body – led to the notion of “equivalence value”, Q/T Clausius: Invented the concept “disgregation”, Z, to extend the ideas to irreversible, non-cyclic processes; TdZ dI dW Inserted disgregation into the First Law; dQ dH TdZ 0 Clausius: Changed the sign of dQ;(originally dQ=dH+AdL; dL=dI+dW) dHdQ Derived; dZ 0 T dH Called; dZ the entropy of a body. -
Lecture 6: Entropy
Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic. -
Maximum Frictional Dissipation and the Information Entropy of Windspeeds
J. Non-Equilib. Thermodyn. 2002 Vol. 27 pp. 229±238 Á Á Maximum Frictional Dissipation and the Information Entropy of Windspeeds Ralph D. Lorenz Lunar and Planetary Lab, University of Arizona, Tucson, AZ, USA Communicated by A. Bejan, Durham, NC, USA Registration Number 926 Abstract A link is developed between the work that thermally-driven winds are capable of performing and the entropy of the windspeed history: this information entropy is minimized when the minimum work required to transport the heat by wind is dissipated. When the system is less constrained, the information entropy of the windspeed record increases as the windspeed ¯uctuates to dissipate its available work. Fluctuating windspeeds are a means for the system to adjust to a peak in entropy production. 1. Introduction It has been long-known that solar heating is the driver of winds [1]. Winds represent the thermodynamic conversion of heat into work: this work is expended in accelerat- ing airmasses, with that kinetic energy ultimately dissipated by turbulent drag. Part of the challenge of the weather forecaster is to predict the speed and direction of wind. In this paper, I explore how the complexity of wind records (and more generally, of velocity descriptions of thermally-driven ¯ow) relates to the available work and the frictional or viscous dissipation. 2. Zonal Energy Balance Two linked heat ¯uxes drive the Earth's weather ± the vertical transport of heat upwards, and the transport of heat from low to high latitudes. In the present paper only horizontal transport is considered, although the concepts may be extended by analogy into the vertical dimension. -
Work-Energy for a System of Particles and Its Relation to Conservation Of
Conservation of Energy, the Work-Energy Principle, and the Mechanical Energy Balance In your study of engineering and physics, you will run across a number of engineering concepts related to energy. Three of the most common are Conservation of Energy, the Work-Energy Principle, and the Mechanical Engineering Balance. The Conservation of Energy is treated in this course as one of the overarching and fundamental physical laws. The other two concepts are special cases and only apply under limited conditions. The purpose of this note is to review the pedigree of the Work-Energy Principle, to show how the more general Mechanical Energy Bal- ance is developed from Conservation of Energy, and finally to describe the conditions under which the Mechanical Energy Balance is preferred over the Work-Energy Principle. Work-Energy Principle for a Particle Consider a particle of mass m and velocity V moving in a gravitational field of strength g sub- G ject to a surface force Rsurface . Under these conditions, writing Conservation of Linear Momen- tum for the particle gives the following: d mV= R+ mg (1.1) dt ()Gsurface Forming the dot product of Eq. (1.1) with the velocity of the particle and rearranging terms gives the rate form of the Work-Energy Principle for a particle: 2 dV⎛⎞ d d ⎜⎟mmgzRV+=() surfacei G ⇒ () EEWK += GP mech, in (1.2) dt⎝⎠2 dt dt Gravitational mechanical Kinetic potential power into energy energy the system Recall that mechanical power is defined as WRmech, in= surfaceiV G , the dot product of the surface force with the velocity of its point of application. -
Work-Force Ageing in OECD Countries
CHAPTER 4 Work-force ageing in OECD countries A. INTRODUCTION AND MAIN FINDINGS force ageing, but offset part of the projected fall in labour force growth. 1. Introduction OECD labour markets have adapted to signi®- cant shifts in the age structure of the labour force in Expanding the range and quality of employ- the past. However, the ageing projected over the ment opportunities available to older workers will next several decades is outside the range of recent become increasingly important as populations age historical experience. Hence, it is uncertain how eas- in OECD countries. Accordingly, there is a need to ily such a large increase in the supply of older work- understand better the capacity of labour markets to ers can be accommodated, including the implica- adapt to ageing work forces, including how it can be tions for the earnings and employment of older enhanced. workers. Both the supply and demand sides of the There is only weak evidence that the earnings labour market will be important. It is likely that pen- of older workers are lower relative to younger work- sion programmes and social security systems in ers in countries where older workers represent a many OECD countries will be reformed so that larger share of total employment. This may indicate existing incentives for early retirement will be that workers of different ages are close substitutes reduced or eliminated. Strengthening ®nancial in production, so that an increased supply of older incentives to extend working life, together with a workers can be employed without a signi®cant fall in large increase in the older population and improve- their relative wages. -
3. Energy, Heat, and Work
3. Energy, Heat, and Work 3.1. Energy 3.2. Potential and Kinetic Energy 3.3. Internal Energy 3.4. Relatively Effects 3.5. Heat 3.6. Work 3.7. Notation and Sign Convention In these Lecture Notes we examine the basis of thermodynamics – fundamental definitions and equations for energy, heat, and work. 3-1. Energy. Two of man's earliest observations was that: 1)useful work could be accomplished by exerting a force through a distance and that the product of force and distance was proportional to the expended effort, and 2)heat could be ‘felt’ in when close or in contact with a warm body. There were many explanations for this second observation including that of invisible particles traveling through space1. It was not until the early beginnings of modern science and molecular theory that scientists discovered a true physical understanding of ‘heat flow’. It was later that a few notable individuals, including James Prescott Joule, discovered through experiment that work and heat were the same phenomenon and that this phenomenon was energy: Energy is the capacity, either latent or apparent, to exert a force through a distance. The presence of energy is indicated by the macroscopic characteristics of the physical or chemical structure of matter such as its pressure, density, or temperature - properties of matter. The concept of hot versus cold arose in the distant past as a consequence of man's sense of touch or feel. Observations show that, when a hot and a cold substance are placed together, the hot substance gets colder as the cold substance gets hotter. -
Chemistry 130 Gibbs Free Energy
Chemistry 130 Gibbs Free Energy Dr. John F. C. Turner 409 Buehler Hall [email protected] Chemistry 130 Equilibrium and energy So far in chemistry 130, and in Chemistry 120, we have described chemical reactions thermodynamically by using U - the change in internal energy, U, which involves heat transferring in or out of the system only or H - the change in enthalpy, H, which involves heat transfers in and out of the system as well as changes in work. U applies at constant volume, where as H applies at constant pressure. Chemistry 130 Equilibrium and energy When chemical systems change, either physically through melting, evaporation, freezing or some other physical process variables (V, P, T) or chemically by reaction variables (ni) they move to a point of equilibrium by either exothermic or endothermic processes. Characterizing the change as exothermic or endothermic does not tell us whether the change is spontaneous or not. Both endothermic and exothermic processes are seen to occur spontaneously. Chemistry 130 Equilibrium and energy Our descriptions of reactions and other chemical changes are on the basis of exothermicity or endothermicity ± whether H is negative or positive H is negative ± exothermic H is positive ± endothermic As a description of changes in heat content and work, these are adequate but they do not describe whether a process is spontaneous or not. There are endothermic processes that are spontaneous ± evaporation of water, the dissolution of ammonium chloride in water, the melting of ice and so on. We need a thermodynamic description of spontaneous processes in order to fully describe a chemical system Chemistry 130 Equilibrium and energy A spontaneous process is one that takes place without any influence external to the system.