Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Lecture 3 – The First Law (Ch. 1)Lecture 3 – The First Law (Ch. 1)Friday January 11Friday January 11thth•Test of the clickers (HiTT remotes)•I will not review the previous class•Usually I will (certainly after Ch. 2)•Internal energy•The equivalence of work and heat•The first law (conservation of energy)•Functions of state•Reversible workReading: Reading: All of chapter 1 (pages 1 - 23)All of chapter 1 (pages 1 - 23)1st homework set due next Friday 1st homework set due next Friday (18th).(18th).Homework assignment available on web Homework assignment available on web page.page.Assigned problems: 2, 6, 8, 10, 12Assigned problems: 2, 6, 8, 10, 12Functions of state: internal energy Functions of state: internal energy UUJoule’s paddle wheelexperiment Work = Ugrav W = (mgh) = mghGravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.AdiabaticMeasured as a change Measured as a change in temperature, in temperature, Functions of state: internal energy Functions of state: internal energy UUJoule’s paddle wheelexperimentGravitational energy is lost. 1st law is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.Ufluid = W = mgh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!AdiabaticMeasured as a change Measured as a change in temperature, in temperature, Functions of state: internal energy Functions of state: internal energy UUStirringU = W = torque × angular displacement = d AdiabaticRise in Rise in (temperature)(temperature)Functions of state: internal energy Functions of state: internal energy UUElectricalworkU = W = i 2RRRiiAdiabaticRise in Rise in (temperature)(temperature)Functions of state: internal energy Functions of state: internal energy UUReversibleworkU = W = Force × distance = P VAdiabaticRise in Rise in (temperature)(temperature)Force, FEquivalence of work and heatEquivalence of work and heatHeat, QU = QAdiabaticSame rise in Same rise in (temperature)(temperature)The First Law of ThermodynamicsThe First Law of ThermodynamicsThese ideas lead to the first law of thermodynamics (a fundamental postulate):“The change in internal energy of a system is equal to the heat supplied plus the work done on the system. Energy is conserved if the heat is taken into account.”Note that đQ and đW are not functions of state. However, dU is, i.e. the correct combination of đQ and đW which, by themselves are not functions of state, lead to the differential internal energy, dU, which is a function of state.U = Q U = Q ++ W W oror dUdU = = đđQQ đđW WHow to know if quantity is a function of How to know if quantity is a function of statestateU1U2area under curveW PdV= =�( )UD =�đQ + đWHow can U be state function, but not W?Heat is involved (not adiabatic).Significantheat flows inHow to know if quantity is a function of How to know if quantity is a function of statestateThere is a mathematical basis.....There is a mathematical basis.....Consider the function F = f(x,y):yxf fdF dx dyx y� �� �� �= +� �� �� �� �� �zyxdSdrdF��In general, F is a state function if the differential dF is ‘exact’. dF dF ((= Adx = Adx Bdy Bdy) is exact if:1.2. 03. is independent of pathbaA By xdFdF� �=� �=���See also: See also: •Appendix EAppendix E•PHY3513 notesPHY3513 notes•Appendix A in Carter bookAppendix A in Carter book•In thermodynamics, all state variables are by definition exact. However, differential work and heat are not.How to know if quantity is a function of How to know if quantity is a function of statestateThere is a mathematical basis.....There is a mathematical basis.....Consider the function F = f(x,y):yxf fdF dx dyx y� �� �� �= +� �� �� �� �� �Differentials satisfying the following condition are said to be ‘exact’:0dF =��This condition also guarantees that any integration of dF will not depend on the path of integration, i.e. only the limits of integration matter.This is by no means true for any function!If integration does depend on path, then the differential is said to be ‘inexact’, i.e. it cannot be integrated unless a path is also specified. An example is the following:đF = ydx xdy.Note: is a differential đF is inexact, this implies that it cannot be integrated to yield a function F.How to know if quantity is a function of How to know if quantity is a function of
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