Understanding Work in Simple Systems Physics Exam Review

1. Work In Simple Systems Physics 313 Professor Lee Carkner Lecture 7

2. Exam #1 • Monday, March 29th • Covers: • Lectures 1-9 • Chapters 1-4 • Format: • About 10 multiple choice (~25% weight) • About 4 problems (~75%weight) • Equations provided • Bring just pencil and calculator • Worth 20% of final grade

3. Exercise 5 - Shake Work • Find expression for P from equation of state and integrate • P = 15TV-3.4 • W = -  15TV-3.4 dV = -15T/-2.4V2.4 • W = (15)(265)/(2.4)(2)2.4 - (15)(265)/(2.4)(3)2.4 = • Trying to add to internal energy

4. Work and Systems • Thermodynamic systems are often designed to produce work … • or to add work to a system • Need to be able to compute the work • Even between same two states, work will vary (depends on path)

5. Force and Temperature • In general, work can be related as: dW = F dx • Need a “force” term • Need a “displacement” term • Force term often depends on T • Cannot compute work without understanding the heat transfer • For simplicity we will often discuss isothermal systems

6. Hydrostatic Systems W = - P dV • Can use ideal gas law, but need to limit T • Examples: • Isothermal: • Isobaric:

7. Polytropic Process • Often for compression and expansion of a gas, pressure and volume are related by: • Where C and n are constants • Called a polytropic process • Example:

8. Stretched Wire W =  t dL • how much energy does it take to cause a small increase in length? t = k L

9. Surface W =  g dA • how much energy does it take to cause a small increase in area? • Integral of force over length, area or volume

11. Shaft Work • When transmitting energy with a rotating shaft, work depends on the torque: T = Fr • The displacement is related to the number of revolutions, n • Work is then: • We can also write power as • Where (n/t) is the number of revolutions per second

12. Electrochemical Cell W = e dZ • how much energy does it take to cause a small movement of charge? • The movement of charge produces a current: W =  eI dt • Can measure current easier than charge

14. Dielectric Solid • Can place a dielectric solid between the plates of a capacitor that produces a uniform electric field W =  E dP • how much energy does it take to cause a small alignment of induced dipoles? • or else system is not in equilibrium

16. Paramagnetic Rod • Induce the magnetic field by wrapping the material in wire and run a current • Battery does work to move charge, induce a field and then induce small currents which produce magnetic dipoles W = m0 H dM • how much energy does it take to cause a small alignment of induced magnetic dipoles?

18. Composite Systems • Not just three dW = Y dX + Y’ dX’ + Y’’dX’’ … • The plots of XY become multidimensional

21. Work -- General Case • For a system specified by X, Y and Z, the work is the integral of one variable with respect to another • Since dW = F dx, the two variables are related to the force and the displacement • The displacement variable is extensive