Quantum Mechanics Enthalpy
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Equilibrium Thermodynamics
Equilibrium Thermodynamics Instructor: - Clare Yu (e-mail [email protected], phone: 824-6216) - office hours: Wed from 2:30 pm to 3:30 pm in Rowland Hall 210E Textbooks: - primary: Herbert Callen “Thermodynamics and an Introduction to Thermostatistics” - secondary: Frederick Reif “Statistical and Thermal Physics” - secondary: Kittel and Kroemer “Thermal Physics” - secondary: Enrico Fermi “Thermodynamics” Grading: - weekly homework: 25% - discussion problems: 10% - midterm exam: 30% - final exam: 35% Equilibrium Thermodynamics Material Covered: Equilibrium thermodynamics, phase transitions, critical phenomena (~ 10 first chapters of Callen’s textbook) Homework: - Homework assignments posted on course website Exams: - One midterm, 80 minutes, Tuesday, May 8 - Final, 2 hours, Tuesday, June 12, 10:30 am - 12:20 pm - All exams are in this room 210M RH Course website is at http://eiffel.ps.uci.edu/cyu/p115B/class.html The Subject of Thermodynamics Thermodynamics describes average properties of macroscopic matter in equilibrium. - Macroscopic matter: large objects that consist of many atoms and molecules. - Average properties: properties (such as volume, pressure, temperature etc) that do not depend on the detailed positions and velocities of atoms and molecules of macroscopic matter. Such quantities are called thermodynamic coordinates, variables or parameters. - Equilibrium: state of a macroscopic system in which all average properties do not change with time. (System is not driven by external driving force.) Why Study Thermodynamics ? - Thermodynamics predicts that the average macroscopic properties of a system in equilibrium are not independent from each other. Therefore, if we measure a subset of these properties, we can calculate the rest of them using thermodynamic relations. - Thermodynamics not only gives the exact description of the state of equilibrium but also provides an approximate description (to a very high degree of precision!) of relatively slow processes. -
Lecture 2 the First Law of Thermodynamics (Ch.1)
Lecture 2 The First Law of Thermodynamics (Ch.1) Outline: 1. Internal Energy, Work, Heating 2. Energy Conservation – the First Law 3. Quasi-static processes 4. Enthalpy 5. Heat Capacity Internal Energy The internal energy of a system of particles, U, is the sum of the kinetic energy in the reference frame in which the center of mass is at rest and the potential energy arising from the forces of the particles on each other. system Difference between the total energy and the internal energy? boundary system U = kinetic + potential “environment” B The internal energy is a state function – it depends only on P the values of macroparameters (the state of a system), not on the method of preparation of this state (the “path” in the V macroparameter space is irrelevant). T A In equilibrium [ f (P,V,T)=0 ] : U = U (V, T) U depends on the kinetic energy of particles in a system and an average inter-particle distance (~ V-1/3) – interactions. For an ideal gas (no interactions) : U = U (T) - “pure” kinetic Internal Energy of an Ideal Gas f The internal energy of an ideal gas U = Nk T with f degrees of freedom: 2 B f ⇒ 3 (monatomic), 5 (diatomic), 6 (polyatomic) (here we consider only trans.+rotat. degrees of freedom, and neglect the vibrational ones that can be excited at very high temperatures) How does the internal energy of air in this (not-air-tight) room change with T if the external P = const? f ⎡ PV ⎤ f U =Nin room k= T Bin⎢ N room = ⎥ = PV 2 ⎣ kB T⎦ 2 - does not change at all, an increase of the kinetic energy of individual molecules with T is compensated by a decrease of their number. -
Thermodynamics
ME346A Introduction to Statistical Mechanics { Wei Cai { Stanford University { Win 2011 Handout 6. Thermodynamics January 26, 2011 Contents 1 Laws of thermodynamics 2 1.1 The zeroth law . .3 1.2 The first law . .4 1.3 The second law . .5 1.3.1 Efficiency of Carnot engine . .5 1.3.2 Alternative statements of the second law . .7 1.4 The third law . .8 2 Mathematics of thermodynamics 9 2.1 Equation of state . .9 2.2 Gibbs-Duhem relation . 11 2.2.1 Homogeneous function . 11 2.2.2 Virial theorem / Euler theorem . 12 2.3 Maxwell relations . 13 2.4 Legendre transform . 15 2.5 Thermodynamic potentials . 16 3 Worked examples 21 3.1 Thermodynamic potentials and Maxwell's relation . 21 3.2 Properties of ideal gas . 24 3.3 Gas expansion . 28 4 Irreversible processes 32 4.1 Entropy and irreversibility . 32 4.2 Variational statement of second law . 32 1 In the 1st lecture, we will discuss the concepts of thermodynamics, namely its 4 laws. The most important concepts are the second law and the notion of Entropy. (reading assignment: Reif x 3.10, 3.11) In the 2nd lecture, We will discuss the mathematics of thermodynamics, i.e. the machinery to make quantitative predictions. We will deal with partial derivatives and Legendre transforms. (reading assignment: Reif x 4.1-4.7, 5.1-5.12) 1 Laws of thermodynamics Thermodynamics is a branch of science connected with the nature of heat and its conver- sion to mechanical, electrical and chemical energy. (The Webster pocket dictionary defines, Thermodynamics: physics of heat.) Historically, it grew out of efforts to construct more efficient heat engines | devices for ex- tracting useful work from expanding hot gases (http://www.answers.com/thermodynamics). -
Energetics and Thermochemistry
Energetics and 05 thermochemistry M05_CHE_SB_IBDIP_9755_U05.indd 210 27/01/2015 09:57 Essential ideas The burning of a fi rework increases the disorder in the 5.1 The enthalpy changes from chemical reactions can be calculated universe, as both energy and from their effect on the temperature of their surroundings. matter become dispersed. This is the natural direction of 5.2 In chemical transformations energy can neither be created nor change. destroyed (the fi rst law of thermodynamics). 5.3 Energy is absorbed when bonds are broken and is released when bonds are formed. 15.1 The concept of the energy change in a single step reaction being equivalent to the summation of smaller steps can be applied to changes involving ionic compounds. 15.2 A reaction is spontaneous if the overall transformation leads to an increase in total entropy (system plus surroundings). The direction of spontaneous change always increases the total entropy of the universe at the expense of energy available to do useful work. This is known as the second law of thermodynamics. All chemical reactions are accompanied by energy changes. Energy changes are vital. Our body’s processes are dependent on the energy changes which occur during respiration, when glucose reacts with oxygen. Modern lifestyles are dependent on the transfer of energy that occurs when fuels burn. As we explore the source of these energy changes, we will deepen our understanding of why bonds are broken and formed during a chemical reaction, and why electron transfer can lead to the formation of stable ionic compounds. The questions of why things change will lead to the development of the concept of entropy. -
Thermodynamic Stability: Free Energy and Chemical Equilibrium ©David Ronis Mcgill University
Chemistry 223: Thermodynamic Stability: Free Energy and Chemical Equilibrium ©David Ronis McGill University 1. Spontaneity and Stability Under Various Conditions All the criteria for thermodynamic stability stem from the Clausius inequality,cf. Eq. (8.7.3). In particular,weshowed that for anypossible infinitesimal spontaneous change in nature, d− Q dS ≥ .(1) T Conversely,if d− Q dS < (2) T for every allowed change in state, then the system cannot spontaneously leave the current state NO MATTER WHAT;hence the system is in what is called stable equilibrium. The stability criterion becomes particularly simple if the system is adiabatically insulated from the surroundings. In this case, if all allowed variations lead to a decrease in entropy, then nothing will happen. The system will remain where it is. Said another way,the entropyofan adiabatically insulated stable equilibrium system is a maximum. Notice that the term allowed plays an important role. Forexample, if the system is in a constant volume container,changes in state or variations which lead to a change in the volume need not be considered eveniftheylead to an increase in the entropy. What if the system is not adiabatically insulated from the surroundings? Is there a more convenient test than Eq. (2)? The answer is yes. To see howitcomes about, note we can rewrite the criterion for stable equilibrium by using the first lawas − d Q = dE + Pop dV − µop dN > TdS,(3) which implies that dE + Pop dV − µop dN − TdS >0 (4) for all allowed variations if the system is in equilibrium. Equation (4) is the key stability result. -
Statistical Thermodynamics - Fall 2009
1 Statistical Thermodynamics - Fall 2009 Professor Dmitry Garanin Thermodynamics September 9, 2012 I. PREFACE The course of Statistical Thermodynamics consist of two parts: Thermodynamics and Statistical Physics. These both branches of physics deal with systems of a large number of particles (atoms, molecules, etc.) at equilibrium. 3 19 One cm of an ideal gas under normal conditions contains NL =2.69 10 atoms, the so-called Loschmidt number. Although one may describe the motion of the atoms with the help of× Newton’s equations, direct solution of such a large number of differential equations is impossible. On the other hand, one does not need the too detailed information about the motion of the individual particles, the microscopic behavior of the system. One is rather interested in the macroscopic quantities, such as the pressure P . Pressure in gases is due to the bombardment of the walls of the container by the flying atoms of the contained gas. It does not exist if there are only a few gas molecules. Macroscopic quantities such as pressure arise only in systems of a large number of particles. Both thermodynamics and statistical physics study macroscopic quantities and relations between them. Some macroscopics quantities, such as temperature and entropy, are non-mechanical. Equilibruim, or thermodynamic equilibrium, is the state of the system that is achieved after some time after time-dependent forces acting on the system have been switched off. One can say that the system approaches the equilibrium, if undisturbed. Again, thermodynamic equilibrium arises solely in macroscopic systems. There is no thermodynamic equilibrium in a system of a few particles that are moving according to the Newton’s law. -
Szilard-1929.Pdf
In memory of Leo Szilard, who passed away on May 30,1964, we present an English translation of his classical paper ober die Enfropieuerminderung in einem thermodynamischen System bei Eingrifen intelligenter Wesen, which appeared in the Zeitschrift fur Physik, 1929,53,840-856. The publica- tion in this journal of this translation was approved by Dr. Szilard before he died, but he never saw the copy. At Mrs. Szilard’s request, Dr. Carl Eckart revised the translation. This is one of the earliest, if not the earliest paper, in which the relations of physical entropy to information (in the sense of modem mathematical theory of communication) were rigorously demonstrated and in which Max- well’s famous demon was successfully exorcised: a milestone in the integra- tion of physical and cognitive concepts. ON THE DECREASE OF ENTROPY IN A THERMODYNAMIC SYSTEM BY THE INTERVENTION OF INTELLIGENT BEINGS by Leo Szilard Translated by Anatol Rapoport and Mechthilde Knoller from the original article “Uber die Entropiever- minderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen.” Zeitschrift fur Physik, 1929, 65, 840-866. 0*3 resulting quantity of entropy. We find that The objective of the investigation is to it is exactly as great as is necessary for full find the conditions which apparently allow compensation. The actual production of the construction of a perpetual-motion ma- entropy in connection with the measure- chine of the second kind, if one permits an ment, therefore, need not be greater than intelligent being to intervene in a thermo- Equation (1) requires. dynamic system. When such beings make F(J measurements, they make the system behave in a manner distinctly different from the way HERE is an objection, already historical, a mechanical system behaves when left to Tagainst the universal validity of the itself. -
Thermodynamic Processes: the Limits of Possible
Thermodynamic Processes: The Limits of Possible Thermodynamics put severe restrictions on what processes involving a change of the thermodynamic state of a system (U,V,N,…) are possible. In a quasi-static process system moves from one equilibrium state to another via a series of other equilibrium states . All quasi-static processes fall into two main classes: reversible and irreversible processes . Processes with decreasing total entropy of a thermodynamic system and its environment are prohibited by Postulate II Notes Graphic representation of a single thermodynamic system Phase space of extensive coordinates The fundamental relation S(1) =S(U (1) , X (1) ) of a thermodynamic system defines a hypersurface in the coordinate space S(1) S(1) U(1) U(1) X(1) X(1) S(1) – entropy of system 1 (1) (1) (1) (1) (1) U – energy of system 1 X = V , N 1 , …N m – coordinates of system 1 Notes Graphic representation of a composite thermodynamic system Phase space of extensive coordinates The fundamental relation of a composite thermodynamic system S = S (1) (U (1 ), X (1) ) + S (2) (U-U(1) ,X (2) ) (system 1 and system 2). defines a hyper-surface in the coordinate space of the composite system S(1+2) S(1+2) U (1,2) X = V, N 1, …N m – coordinates U of subsystems (1 and 2) X(1,2) (1,2) S – entropy of a composite system X U – energy of a composite system Notes Irreversible and reversible processes If we change constraints on some of the composite system coordinates, (e.g. -
Thermodynamic Temperature
Thermodynamic temperature Thermodynamic temperature is the absolute measure 1 Overview of temperature and is one of the principal parameters of thermodynamics. Temperature is a measure of the random submicroscopic Thermodynamic temperature is defined by the third law motions and vibrations of the particle constituents of of thermodynamics in which the theoretically lowest tem- matter. These motions comprise the internal energy of perature is the null or zero point. At this point, absolute a substance. More specifically, the thermodynamic tem- zero, the particle constituents of matter have minimal perature of any bulk quantity of matter is the measure motion and can become no colder.[1][2] In the quantum- of the average kinetic energy per classical (i.e., non- mechanical description, matter at absolute zero is in its quantum) degree of freedom of its constituent particles. ground state, which is its state of lowest energy. Thermo- “Translational motions” are almost always in the classical dynamic temperature is often also called absolute tem- regime. Translational motions are ordinary, whole-body perature, for two reasons: one, proposed by Kelvin, that movements in three-dimensional space in which particles it does not depend on the properties of a particular mate- move about and exchange energy in collisions. Figure 1 rial; two that it refers to an absolute zero according to the below shows translational motion in gases; Figure 4 be- properties of the ideal gas. low shows translational motion in solids. Thermodynamic temperature’s null point, absolute zero, is the temperature The International System of Units specifies a particular at which the particle constituents of matter are as close as scale for thermodynamic temperature. -
INTRODUCTION to Thermodynamic Properties Introduction to Thermodynamic Properties
INTRODUCTION TO Thermodynamic Properties Introduction to Thermodynamic Properties © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,219,373; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates •COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community •Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM021603 Contents The Thermodynamic Properties Data Base . -
Thermodynamics Cycle Analysis and Numerical Modeling of Thermoelastic Cooling Systems
international journal of refrigeration 56 (2015) 65e80 Available online at www.sciencedirect.com ScienceDirect www.iifiir.org journal homepage: www.elsevier.com/locate/ijrefrig Thermodynamics cycle analysis and numerical modeling of thermoelastic cooling systems Suxin Qian, Jiazhen Ling, Yunho Hwang*, Reinhard Radermacher, Ichiro Takeuchi Center for Environmental Energy Engineering, Department of Mechanical Engineering, University of Maryland, 4164 Glenn L. Martin Hall Bldg., College Park, MD 20742, USA article info abstract Article history: To avoid global warming potential gases emission from vapor compression air- Received 3 October 2014 conditioners and water chillers, alternative cooling technologies have recently garnered Received in revised form more and more attentions. Thermoelastic cooling is among one of the alternative candi- 3 March 2015 dates, and have demonstrated promising performance improvement potential on the Accepted 2 April 2015 material level. However, a thermoelastic cooling system integrated with heat transfer fluid Available online 14 April 2015 loops have not been studied yet. This paper intends to bridge such a gap by introducing the single-stage cycle design options at the beginning. An analytical coefficient of performance Keywords: (COP) equation was then derived for one of the options using reverse Brayton cycle design. Shape memory alloy The equation provides physical insights on how the system performance behaves under Elastocaloric different conditions. The performance of the same thermoelastic cooling cycle using NiTi Efficiency alloy was then evaluated based on a dynamic model developed in this study. It was found Nitinol that the system COP was 1.7 for a baseline case considering both driving motor and Solid-state cooling parasitic pump power consumptions, while COP ranged from 5.2 to 7.7 when estimated with future improvements. -
Thermodynamics: First Law, Calorimetry, Enthalpy
Thermodynamics: First Law, Calorimetry, Enthalpy Monday, January 23 CHEM 102H T. Hughbanks Calorimetry Reactions are usually done at either constant V (in a closed container) or constant P (open to the atmosphere). In either case, we can measure q by measuring a change in T (assuming we know heat capacities). Calorimetry: constant volume ∆U = q + w and w = -PexΔV If V is constant, then ΔV = 0, and w = 0. This leaves ∆U = qv, again, subscript v indicates const. volume. Measure ΔU by measuring heat released or taken up at constant volume. Calorimetry Problem When 0.2000 g of quinone (C6H4O2) is burned with excess oxygen in a bomb (constant volume) calorimeter, the temperature of the calorimeter increases by 3.26°C. The heat capacity of the calorimeter is known to be 1.56 kJ/°C. Find ΔU for the combustion of 1 mole of quinone. Calorimetry: Constant Pressure Reactions run in an open container will occur at constant P. Calorimetry done at constant pressure will measure heat: qp. How does this relate to ∆U, etc.? qP & ΔU ∆U = q + w = q - PΔV At constant V, PΔV term was zero, giving ∆U = qv. If P is constant and ΔT ≠ 0, then ΔV ≠ 0. – In particular, if gases are involved, PV = nRT wp ≠ 0, so ∆U ≠ qp Enthalpy: A New State Function It would be nice to have a state function which is directly related to qp: ∆(?) = qp We could then measure this function by calorimetry at constant pressure. Call this function enthalpy, H, defined by: H = U + PV Enthalpy Enthalpy: H = U + PV U, P, V all state functions, so H must also be a state function.