Work In Simple Systems

Physics 313Professor Lee

CarknerLecture 7

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

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

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