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MASSACHUSETTS INSTITUTE OF TECHNOLOGY SPRING 2007 5 92 Energy Environment and Society a Project Based First Year Subject supported by the d Arbeloff Program Session 1 4 Energy Basics continued 1 Discussion of team projects and project selections 2 Summary of thermodynamics concepts and applications Readings and Assignments D Goodstein Out of Gas Norton 2004 Chapter 2 Energy Myths and a Brief History of Energy pp 41 56 Practice Problems on First and Second Laws of Thermodynamics due Feb 21 Supplementary recommended text on library reserve J B Fenn Engines Energy and Entropy W H Freeman and Co 1982 Thermodynamics is about the flow of energy Thermodynamics was first developed to explain how much heat could be used to do work eventually we learned that these laws apply to every material and energy transformation everywhere in the universe Describes macroscopic properties of equilibrium systems you don t need to know anything about atoms and molecules but it helps Entirely Empirical cannot be proven logically but can be derived using statistical mechanics Built on Four Laws and simple mathematics but we will not assume you have had 18 02 0th Law Defines Temperature T The common sense Law 1st Law Defines Energy U Heat q Work w You can break even but you can t win 2nd Law Defines Entropy S You have to go to 0 K to break even Everything wants to be as imperfect as possible 3rd Law Gives Numerical Value to Entropy You can t get to 0 K so you can never break even These laws are UNIVERSALLY VALID they cannot be circumvented 1 From BTU s and calories Producing foot pounds ergs and joules Heat Engines must to serve our needs Obey inexorable rules J B Fenn Engines Energy and Entropy Definitions System The part of the Universe that we are interested in everything inside the boundary Surroundings The rest of the Universe everything else outside the boundary Boundary The surface dividing the System from the Surroundings SURROUNDINGS SYSTEM BOUNDARY 2 In order to describe a system we have to specify a small number of macroscopic properties state variables such as Pressure p Energy U or E Volume V Enthalpy H Entropy S Temperature T Temperature is defined by the Zeroth Law of Thermodynamics Thermal Equilibrium when heat stops flowing A B A B A When a hot object is placed in thermal contact with a cold object heat flows from the warmer to the cooler object This continues until they are in thermal equilibrium no more heat flow We say at this point that both bodies have the same temperature This intuitively straightforward idea is formalized in the 0th Law of thermodynamics and is made practical through the development of thermometers and temperature scales ZERO th LAW of Thermodynamics If then B A and B are in thermal equilibrium and B A and C C are in thermal equilibrium and are in thermal equilibrium acts like is a thermometer and same temperature A B and C are all at the For thermodynamics calculations we have to use the Absolute Kelvin temperature scale T K T C 273 15 3 B Work Heat and the First Law w F l Work distance l applied constant force pext Expansion work pext F pext A w pextA l pext V convention w 0 means that the surroundings do work to the system compression V 0 If the system does work on the surroundings expansion V 0 then w 0 Work is not a property of the state of the system w pext dV means not an exact differential which means that 2 the integral w 1 pext dV depends on the path See Non Lecture 1 for an example calculation of the path dependence of w Heat q The quantity that flows between the system and the surroundings which results in a change of temperature of the system and or the surroundings Sign convention Remember this If heat enters the system then q is positive w 0 if work done on system q 0 if heat added to system w and q are both forms of energy Units of q and w 1 calorie heat needed to raise 1 g H2O by 1 C at T 15 C 1 Joule 4 184 calories 1 BTU 252 calories 1 055 Joules 1 quad 1015 BTU 1 055 exaJoules Heat capacity amount of q needed to raise a substance s temperature by T heat capacity of water 1 cal K 1 g 1 4 184 J K 1 g 1 75 3 J K 1 mole 1 4 Non Lecture 1 Path dependence of work Example assume a reversible process so that pext p p same as pext everywhere and at all times inside the system Ar g p1 V1 Ar g p2 V2 Compression V1 V2 and p1 p2 pext p1 pext p2 p1 V1 compression p2 V2 initial Two paths 1 First then final V1 V2 at p p1 p1 p2 at V V2 First p1 p2 at V V1 then V1 V2 at p p2 2 Ar g p1 V1 Ar g p1 V2 Ar g p2 V2 path 1 Ar g p1 V1 Ar g p2 V1 Ar g p2 V2 path 2 p p2 final p1 path 1 path 2 initial V V2 w 1 V pext dV V pext dV V2 V2 1 2 V p1dV p1 V2 V1 V2 1 V1 w 2 V pext dV V pext dV V1 V2 1 1 V p2dV p2 V2 V1 V2 1 w 1 p1 V1 V2 w 2 p2 V1 V2 Note w 0 work is done on system to compress it w 1 w 2 because p1 p2 Note for the closed cycle path 1 path 2 d w 0 closed cycle w is not a state function you cannot write w f p V 5 The equivalence of work and heat was demonstrated by Joule s experiments on raising the temperature of a known amount of water see Goodstein Chapter 2 for detail Graphics QuickTime are needed d T1 T2 a with only heat b with only work weight falls propeller rotates viscous friction heats water are Graphics QuickTime needed dec to T1 T2 The First Law of Thermodynamics Conservation of Energy dU d q d w or Mathematical statement U q w or d q d w U system q w U surroundings q w U universe U system U surroundings 0 U is a state function value depends only on properties of system p V T etc Enthalpy H U pV useful to measure energy changes in processes taking place at constant pressure For example the H of vaporization of water at p 1 atmosphere 2400 J gram 43 2 kJ mole 6 Clausius statement of 1st Law The energy of the universe is conserved The First Law tells us that a properly designed engine can run in a cycle by converting heat into useful work The work obtained cannot exceed the heat But can all of the heat be converted into work A very large system of uniform T This T of the reservoir does not change regardless …


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MIT 5 92 - Energy Basics

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