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PETE 310
Lecture # 9
Ideal Gases
Ideal Gas
Characterized by 3 state variables: P, T, and V relationship among these from equations of state
Equations of State The Ideal Gas
Ideal gas propertiesVolume of gas molecules is negligible compared with gas volume
Forces of attraction or repulsion between molecules or walls of container are zero
No loss of internal energy due to collisions
Ideal Gas Laws from Experiments…
Boyle’s Law (at constant T)
Gay-Lussac’s ( or Charles ) law (at constant P)
PV
1
TV
Ideal Gas Laws
Avogadros’s Law At the same P and T equal volumes of gas contain the same # of molecules
Avogadro’s Number:
Na = 2. 73X1026 molecules/lb mole
Internet Lesson on Ideal Gas Behavior
Experimental instructions & Problems with solutions
Boyle
Can you Write this Law?
Boyles law
http://www.grc.nasa.gov/WWW/K-
12/airplane/aboyle.html (Public domain file)
Ideal Equation of State Construction
T2
T1
P1
P2
V1 Vx V2
2
2
1
211
T
V
T
V
VPVP
x
x
Step 2
Step 1
2
22
1
11
T
VP
T
VP
Combining
Jacques Charles (1746-1823)
Never published his results
Joseph Gay-Lussac (1778-1850)
Describing Gas Behavior
Evolution of Science - From ideal gases to real gases
Boyle & Charles laws
TPV
1 PTV
)/(
nVV
RT
PV
T
VP
T
VP
M
M
2
22
1
11
R = gas constant, depends upon units used
See page 95 McCain book
Ideal Gas Mixture
The pressure in a vessel containing an ideal gas mixture (n) or a single gas component (nk) is
t
kk
t
V
RTnP
V
nRTP
http://home.a-city.de/walter.fendt/phe/gaslaw.htm
Partial Pressure
Pk is the partial pressure of component k, and by definition
kkk y
n
n
P
P
cN
i
k PP1
P pk
T1
T1
n1
,n2
, nk
…, nk
Law of Partial Pressures John Dalton (1766-1844)
Law of Partial Pressures
Density of ideal gas
RT
P
VM
m
V
nRTP
twt
Watch out the units!
Mixtures of Ideal Gases
Dalton’s law of partial pressures
Amagat’s law of partial volumes
Specific gravity of a gas
Ideal Gas Laws & Exercises
Apparent Molecular Weight of a Gas Mixture
Determine the Mwa and density of a mixture of 30%C1, 40%C2, and 30%C3 at T=200oF and P=4000 psia