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
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