Download LECT 10

Department of Mechanical Engineering
ME 322 – Mechanical Engineering
Thermodynamics
Lecture 10
Work as an Energy Transport Mode
What is Work?
From Physics 211 …
dW   Fby the system  Fon the system   d s
Questions … Is work a vector or a scalar?
When you integrate dW do you get W2 – W1?
What is the significance of dW ?
In ME 322 …work can occur in several different ways.
However, they are all analogous to a ‘force’ through a
‘distance’.
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Possible Work Modes
Mechanical
Work
Other types
of Work
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Department of Mechanical Engineering
ME 322 – Mechanical Engineering
Thermodynamics
Moving Boundary Work
P(dV) Work
Moving Boundary Work
Example: Expansion of a fluid in a piston-cylinder assembly
The work done can be found by
integration,
dW  Fd x
dW   pA d x
dV
dW   pA 
A
dW  pdV
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
2
dW 
1
W12 


V2
pdV
V1
V2
pdV
V1
In order to find the work done, the
pressure-volume relationship
needs to be known. Work is a path
function!
Boundary Work is a Path Function
W12 
p

V2
pdV
V1
p
Process A
1
1
W12,A
2
W12,B
V
W12,A  W12,B
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Process B
2
V
The Polytropic Process
This process is common in many thermodynamic analyses.
A polytropic process obeys the following relationship,
p
pV n  constant
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 W12 
W12

2
V2
V1
pdV 

V2
V1
constant
dV
n
V
V
The constant can be evaluated anywhere on the process
curve. Therefore,
V2
V2
p1V1 n
p2 V2 n
W12 
dV 
dV
n
n
V
V
V1
V1

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
The Polytropic Process
Evaluation of the integral results in,
W12 

V2
V1
p1V1 n
p2 V2  p1V1
dV 
n
V
1 n
for n  1
For the case where n = 1,
W12 

The polytropic process
defines a relationship
between end states,
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V2
V1
p1V1
V2
dV  p1V1 ln
V
V1
pV  constant
n
p1 V1 n  p2 V2 n
p2  V1 
 
p1  V2 
n
The Polytropic Process – Ideal Gas
The previous relationship is valid,
independent of the fluid,
p2  V1 
 
p1  V2 
n
If the fluid is an ideal gas,
n
p2  V1   mRT1 / p1 
  

p1  V2   mRT2 / p2 
This leads to two additional relationships for ideal gases,
T2  p2 
 
T1  p1 
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 n 1 / n
1 n
and
T2  V2 
 
T1  V1 
The Polytropic Process – Ideal Gas
The work done during a polytropic process is,
W12 

V2
V1
p1V1 n
p2 V2  p1V1
dV 
n
V
1 n
for n  1
If the fluid is an ideal gas,
W12 
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mR T2  T1 
1 n
for n  1
Some New Terminology ...
• An aergonic process
– A process that occurs without any work modes
– Example: A process in a closed, rigid
container
• An adiabatic process
– A process that occurs without any heat transfer
modes
– Example: An process that occurs in an
insulated container
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