Lecture 3 Lecture 3 ––The First Law (Ch. 1)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 All of chapter 1 (pages 1 --23)23)1st homework set due next Friday (18th).1st homework set due next Friday (18th).Homework assignment available on web page.Homework assignment available on web 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 wheelexperimentWork = −ΔUgravW = −(−mgh)= mghGravitational energy is lost. 1stlaw 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, θθFunctions of state: internal energy Functions of state: internal energy UUJoule’s paddle wheelexperimentGravitational energy is lost. 1stlaw is about conservation of energy. This energy goes into thermal (‘internal’) energy associated with the fluid.ΔUfluid= W = mgh!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!AdiabaticMeasured as a change Measured as a change in temperature, in temperature, θθFunctions of state: internal energy Functions of state: internal energy UUStirringΔU = W = torque × angular displacement = τdφAdiabaticRise in Rise in θθ(temperature)(temperature)Functions of state: internal energy Functions of state: internal energy UUElectricalworkΔU = W = i2RRRiiAdiabaticRise in Rise in θθ(temperature)(temperature)Functions of state: internal energy Functions of state: internal energy UUReversibleworkΔU = W = Force × distance = −P ΔVAdiabaticRise in Rise in θθ(temperature)(temperature)Force, FEquivalence of work and heatEquivalence of work and heatHeat, QΔU = QAdiabaticSame rise in Same rise in θθ(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 notfunctions 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.ΔΔU = Q U = Q ++W W orordUdU= = đđQQ++đđWWHow to know if quantity is a function of stateHow to know if quantity is a function of stateU1U2area under curveWPdV==∫()UΔ=∫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 stateHow to know if quantity is a function of stateThere is a mathematical basis.....There is a mathematical basis.....Consider the function F = f(x,y):yxffdF dx dyxy⎛⎞∂∂⎛⎞=+⎜⎟⎜⎟∂∂⎝⎠⎝⎠zyxdSdrdF∫vIn general, F is a state function if the differential dF is ‘exact’. dFdF((= = AdxAdx++BdyBdy) is exact if:1.2. 03. is independent of pathbaAByxdFdF∂∂=∂∂=∫∫vSee 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 stateHow to know if quantity is a function of stateThere is a mathematical basis.....There is a mathematical basis.....Consider the function F = f(x,y):yxffdF dx dyxy⎛⎞∂∂⎛⎞=+⎜⎟⎜⎟∂∂⎝⎠⎝⎠Differentials satisfying the following condition are said to be ‘exact’:0dF=∫vThis condition also guarantees that any integration of dFwill 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 stateHow to know if quantity is a function of
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