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8/3/2019 2 - Thermodynamics
http://slidepdf.com/reader/full/2-thermodynamics 1/15
Thermodynamics
1
8/3/2019 2 - Thermodynamics
http://slidepdf.com/reader/full/2-thermodynamics 2/15
• To tell us the relationshi between the ressure, tem erature and
density of a gas as it moves.
• Altogether there are 6 variables we need to describe the state of a
gas…• p pressure (Pa)
• density (kg/m3), or specific volume v =1/
• T temperature (K)
• h enthalpy ( ), he+ p/
• s entropy ( )
•
1. The Kinetic Theory of Gases,
2. The 1st Law of Thermodynamics, 3. S eci ic Heats
4. The 2nd Law of Thermodynamics
2
8/3/2019 2 - Thermodynamics
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.
•
• Gas is
a collection
of
molecules
in
random
motion
• Molecules bounce of each other like hard spheres
• Gives two sets of relations… Neglects forces
between molecules
Gas constant
R = 287 J/kg/K
for air
• Gases that obey these relations are called “Thermally
3Perfect”
8/3/2019 2 - Thermodynamics
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•
class, but
this
isn’t
always
true…
Ceases
to
be
valid
.
Why?
4
8/3/2019 2 - Thermodynamics
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st.
“Energy is Conserved”W
E QChange in
Amount of work
W Q E
Collection of identified
gas molecules
(System)
energymoun o
heat addedone y pressure
and viscous forces
Work =
p V (<0)
Surface area S
5
8/3/2019 2 - Thermodynamics
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…
pdvdedq
6
8/3/2019 2 - Thermodynamics
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.
• Specific heat – amount of heat needed to raise the
temperature of 1kg by 1 Kelvin
• Two kinds: T
q
T
q
C
• Specific heat at constant volume
• Specific heat at constant pressure
vv q
p p
T qC ) / (
7Pratt and
Whitney
JT58
Test
(Powered
SR71)
8/3/2019 2 - Thermodynamics
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vdpdhdq pdvdedq
…
8
8/3/2019 2 - Thermodynamics
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dT
dhC p
dT
deC v
•
A gas that is thermally perfect and for which the…
… , …
• We will assume calorically perfect gases in this class, but…
9
8/3/2019 2 - Thermodynamics
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nd. Shock in a Converging Diverging Nozzle
10Bourgoing &
Benay
(2005),
ONERA,
France Schlieren
visualization
Sensitive to in‐plane index of ref. gradient
8/3/2019 2 - Thermodynamics
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• ‐ .
• Reversible Process
– no
dissipative
phenomena
occur.
• –
•nd –
Constant entropy.
Entropy – measure of disorder in the gas molecules.
increase entropy, but adding or removing heat may
increase or decrease entropy by an amount Q/T
• So…
11
8/3/2019 2 - Thermodynamics
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…
dqTds For a reversible process…
pdvdedq 1st Law
e v
v RT p /
T erma y
perfect
gas
12
8/3/2019 2 - Thermodynamics
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v p C C R v p C C /
…
13
8/3/2019 2 - Thermodynamics
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1
1212
T ss
21 T C
e
v
2 – 1 …
14
8/3/2019 2 - Thermodynamics
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SummaryAll gases Thermally perfect
perfect
)(T ee
• 1st Law pdvdedq )(T hh
•
Specific
dT deC v / vv
T eC ) / ( T C e v
• 2nd Law
p p p p
1
1212 log
T sse
• 2nd Law
21v
1
1
22 T 1
22
T p
15
11 T 11 T p