1. Work Physics 313 Professor Lee Carkner Lecture 6

2. 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 

3. 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

4. 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?

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

6. 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)

8. 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

9. 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

10. 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

12. 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

14. 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) 

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

16. Sign of Work    Move to left = expansion = negative work

17. Procedures  From equations:      From PV diagram:  Find area 