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