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Work Physics 313 Professor Lee Carkner Lecture 6

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Exercise #4 Stretched Wire Change in tension with temperature (d /dT) L = -(d /dL) T (dL/dT) = -(AY/L)( L) Frequency of guitar string f = ( ) ½ (1/ ) = ( / ) ½ (1/2L) f = (8.8/0.00005) ½ [1/(2)(0.8)] = Change in tension (d /d )L = -aAY = -(2X10 -5 )(0.0001)(2.1X10 6 )(20) = -0.084 f = [(8.8-0.084)/0.00005) ] ½ [1/(2)(0.8)] = 260.95 Hz Difference ~ 1 Hz

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Work Work is force times displacement In thermodynamics we will only consider external work Internal work involves one part of the system acting on another Measured in joules

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Sign Conventions Work by the system is negative Work done on the system is positive Note that this is the opposite of the engineering convention (e.g. Halliday and Resnick) Does the system gain or lose energy?

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Work and Hydrostatic Systems Work is not a property of the system Work is a transfer of energy due to a volume change

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Work, Pressure and Volume dW = F dx dW = -P dV If dV is positive (increase in V) then W is negative (work by the system)

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Total Work To find the total work, integrate dW between the initial and final states: Need to know P as a function of V W depends on both the change of volume and how the volume changed

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Isothermal Process Final expression for work in terms of constants and V i and V f PV = nRT W = - (nRT/V) dV W = -nRT (1/V) dV

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PV Diagram The process by which the volume changes is a line or curve connecting the two points For different processes, different curves, different amounts of work Even if the initial and final points are the same

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Closed Cycle If the same path is traveled in both directions, W=0 Cyclic processes are important for engines Repeat the same process over and over, extract work each cycle

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Path Dependence What are the paths? Isothermal: keep constant T (add or subtract heat) Isobaric: constant P (add or subtract heat) horizontal choric: keep constant volume (rigid container, W=0)

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P-V Diagram p V Isobaric (p=const.) Isochoric (V=const) Isothermal (T=const) Adiabatic (Q=0)

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Sign of Work Move to left = expansion = negative work

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Procedures From equations: From PV diagram: Find area

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