Work

Physics 313Professor Lee

CarknerLecture 6

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)(2.1X106)(20) = -0.084 f = [(8.8-0.084)/0.00005) ]½[1/(2)(0.8)] = 260.95

Hz Difference ~ 1 Hz

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

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?

Work and Hydrostatic Systems

Work is not a property of the system

Work is a transfer of energy due to a volume change

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)

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

Isothermal Process

Final expression for work in terms of constants and Vi and Vf

PV = nRT

W = - (nRT/V) dVW = -nRT (1/V) dV

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

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

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)

P-V Diagram

p

V

Isobaric (p=const.)

Isochoric (V=const)

Isothermal (T=const)

Adiabatic (Q=0)

Sign of Work

Move to left = expansion = negative work

Procedures

From equations:

From PV diagram: Find area