Work In Simple Systems Physics 313 Professor Lee Carkner Lecture 7

Exam #1  Monday, March 29 th  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

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

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)

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

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

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:

Stretched Wire  W =   dL  how much energy does it take to cause a small increase in length?   = k L

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

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

Electrochemical Cell  W =   dZ  how much energy does it take to cause a small movement of charge?   The movement of charge produces a current: W =   I dt   Can measure current easier than charge

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

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 =  0  H dM   how much energy does it take to cause a small alignment of induced magnetic dipoles?

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

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 