thermo & stat mech - spring 2006 class 4 1 thermodynamics and statistical mechanics does the...
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![Page 1: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/1.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
1
Thermodynamics and Statistical Mechanics
Does the Internal Energy of a Real Gas Depend Only on Temperature?
![Page 2: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/2.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
2
Change of Phase
First Law is: du = đq – Pdv
For a finite change at constant temperature
u = q – Pv
At transition, u2 – u1 = l12 – P(v2 – v1)
l12 = (u2 + Pv2) – (u1 + P v1)
l12 = h2 – h1
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Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy and Latent Heat
on)(sublimati vapor tosolid
ion)(vaporizat vapor toliquid
(fusion) liquid tosolid
13
23
12
hh
hh
hh
Enthalpy is defined as: h = u + Pv
![Page 4: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/4.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy is a State Function
![Page 5: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/5.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Does u depend on Volume?
If u = u(T, v), then,
dvvu
dTTu
duTv
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Thermo & Stat Mech - Spring 2006 Class 4
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From Cyclical Relation
uv
T
v
T
v
T
u
vT
cvu
cvu
Tuvu
vT
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Thermo & Stat Mech - Spring 2006 Class 4
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Gay-Lussac–Joule Experiment
![Page 8: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/8.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Gay-Lussac–Joule Results
3-m kilomoleK 001.0
0
u
u
vT
vT
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Thermo & Stat Mech - Spring 2006 Class 4
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Joule-Thompson Throttling Process
A gas passes through a constriction from a region where it is at high pressure to a region where it is at lower pressure. The gas expands, and the temperature of the gas can be lowered. This is an important tool in low temperature physics.
![Page 10: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/10.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Joule-Thompson Throttling Process
![Page 11: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/11.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Joule-Thompson Throttling Process
On high pressure side: Wi = – PiVi
On low pressure side: Wf = + PfVf
Total work: W = PfVf – PiVi
Q = 0 = U + W0 = Uf – Ui + PfVf – PiVi
0 = (Uf + PfVf ) – (Ui + PiVi )
![Page 12: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/12.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy
vdPdhqd
VdPQddH
QdPdVdU
PdVQddU
VdPPdVdUdH
PVUH
so
law)(First
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Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy
PPP
cdTdh
dTqd
vdPdhqd
![Page 14: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/14.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy
hP
TThP
TP
TP
dPdT
cPh
Ph
dPdT
c
dh
dPPh
dTcdPPh
dTTh
dh
PThh
or 0
,0For
),(For
![Page 15: Thermo & Stat Mech - Spring 2006 Class 4 1 Thermodynamics and Statistical Mechanics Does the Internal Energy of a Real Gas Depend Only on Temperature?](https://reader035.vdocuments.us/reader035/viewer/2022062515/56649c745503460f94927168/html5/thumbnails/15.jpg)
Thermo & Stat Mech - Spring 2006 Class 4
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Enthalpy
)( 0, If
t coefficienThomson -Joule
Phh
cPh
dPdT
PT
h
True for ideal gas.
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Thermo & Stat Mech - Spring 2006 Class 4
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Ideal Gas
dTdu
c
dTdh
dTdh
c
V
PP
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Thermo & Stat Mech - Spring 2006 Class 4
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Joule-Thompson Throttling Process