Download Unit 61: Engineering Thermodynamics

Unit 61: Engineering
Thermodynamics
Lesson 5: Work
Objective
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• The purpose of this lesson is to consider the
concepts of work and heat.
Work
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• Work is often defined as the product of force and
the distance moved in the direction of the force.
This is the mechanical definition of work.
• A more general definition of work is the
thermodynamic one: Work, an interaction
between a system and its surroundings, is done
by a system if the sole external effect on the
surroundings could be the raising of a weight.
Work
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Piston
Cylinder
Velocity
W
Gas
Work being done by expanding gas in a cylinder
Work
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• The convention chosen for positive work is
that if the system performs work on the
surroundings it is positive.
• A piston compressing a fluid is doing negative
work, whereas a fluid expanding against a
piston is doing positive work.
• The units of work are force x distance i.e. N.m
or J or lb-ft
Power
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• The rate of doing work, designated W is called
power.
• The units of power are J.s-1 or Watts or ft.lbf.s1.
• Sometimes power is measure in horsepower
defined as 1 hp = 0.746kW = 550 ft-lbf.s-1.
Power
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Resistor
battery
Note: if no energy were to cross the system
boundary, then no work would be done. It is
therefore important to determine the system
boundary in thermodynamics
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• There are a number of modes of work that occur
in engineering for example…
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–
–
–
the work needed to stretch a wire, or
to rotate a shaft, or
to move against friction, or
To cause a current to flow through a resistor or to
charge a capacitor
• In thermodynamics we are primarily concerned
with the work required to move a boundary
against a pressure force.
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• Consider the piston-cylinder arrangement
from previous. Consider that there is a seal to
contain the gas in the cylinder, that the
pressure is uniform throughout and that there
are no gravity effects, magnetic or electric
effects.
• This assures us of a quasiequilibrium process,
one in which the gas is assumed to pass
through a series of equilibrium states.
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• Now allow an expansion of the gas to occur
that sees the piston move a small distance, ds.
• The force acting on the piston is the pressure
times the area of the piston.
• This pressure is expressed as absolute
pressure since pressure is a result of
molecular activity – any molecular activity will
yield a pressure which will result in work being
done when the boundary moves.
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• The infinitesimal work which the system (the
gas) does on the surroundings (the piston) is
then the force multiplied by the distance…
δW = PAdS but Ads is dV (differential volume)
• Thus as the piston moves from some position
s1 to another position s2, the above expression
can be integrated to give…
V
W1-2 = PdV
2
V1
Quasiequilibrium Work
due to a Moving Boundary
NDGTA
• This assumes that the pressure is known for each
position as the piston moves from volume V1 to V2.
The work W1-2 is the crosshatched area under the
P-V curve
P
P
1
1
PdV
PdV
2
V1
V2
2
V
V1
V2
V
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• Note 1: the area representing the work is very
dependent upon the path – i.e. the states 1
and 2 are the same in both diagrams yet the
areas are different. Thus work is a function of
path. The differential of a path function is
called an inexact differential.
• Note 2: the pressure P is assumed to be
constant throughout the volume at each
intermediate position.
Quasi-equilibrium Work
due to a Moving Boundary
NDGTA
• Example: 1-kg of steam with a quality of 20%
is heated at a constant pressure of 200kPa
until the temperature reaches 400oC.
Calculate the work done by the steam.
V2
PdV = P(V2 – V1) = mP(v1 – v2)
W1-2 =
V1