physics 231 lecture 26: ideal gases
DESCRIPTION
PHYSICS 231 Lecture 26: Ideal gases. Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom. Ideal Gas: properties. Collection of atoms/molecules that Exert no force upon each other - PowerPoint PPT PresentationTRANSCRIPT
PHY 2311
PHYSICS 231Lecture 26: Ideal gases
Remco ZegersWalk-in hour: Thursday 11:30-13:30 am
Helproom
PHY 2312
Ideal Gas: properties
Collection of atoms/molecules that• Exert no force upon each other
The energy of a system of two atoms/molecules cannot be
reduced by bringing them close to each other• Take no volume
The volume taken by the atoms/molecules
is negligible compared to the volume they
are sitting in
PHY 2313
R
Potential Energy
0-Emin
Rmin
Ideal gas: we are neglecting the potential energy betweenThe atoms/molecules
R
Potential Energy
0
Kinetic energy
PHY 2314
Number of particles: mol
1 mol of particles: 6.02 x 1023 particlesAvogadro’s number NA=6.02x1023 particles per mol
It doesn’t matter what kind of particles:1 mol is always NA particles
PHY 2315
What is the weight of 1 mol of atoms?
X
Z
A
Number of protons
molar mass
Name
PHY 2316
Weight of 1 mol of atoms
1 mol of atoms: A gram (A: mass number)
Example: 1 mol of Carbon = 12 g 1 mol of Zinc = 65.4 g
What about molecules?H2O 1 mol of water molecules:
2x 1 g (due to Hydrogen)1x 16 g (due to Oxygen)
Total: 18 g
PHY 2317
Example
A cube of Silicon (molar mass 28.1 g) is 250 g.A) How much Silicon atoms are in the cube? B) What would be the mass for the same number of gold atoms (molar mass 197 g)
PHY 2318
Boyle’s Law
P0 V0 T0
2P0 ½V0 T0
½P0 2V0 T0
At constant temperature: P ~ 1/V
PHY 2319
Charles’ law
P0 V0 T0
P0 2V0 2T0
If you want to maintain a constant pressure, the temperature must be increased linearly with the volume V~T
PHY 23110
Gay-Lussac’s law
P0 V0 T0 2P0 V0 2T0
If, at constant volume, the temperature is increased,the pressure will increase by the same factor
P ~ T
PHY 23111
Boyle & Charles & Gay-LussacIDEAL GAS LAW
PV/T = nR
n: number of particles in the gas (mol)R: universal gas constant 8.31 J/mol·K
If no molecules are extracted from or added to a system:
2
22
1
11 constant T
VP
T
VP
T
PV
PHY 23112
ExampleAn ideal gas occupies a volume of 1.0cm3 at 200C at1 atm. A) How many molecules are in the volume?B) If the pressure is reduced to 1.0x10-11 Pa, while thetemperature drops to 00C, how many molecules remainedin the volume?
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And another!An airbubble has a volume of 1.50 cm3at 950 m depth (T=7oC). What is its volume when it reaches the surface(water=1.0x103 kg/m3)?
PHY 23114
A small matter of definition
Ideal gas law: PV/T=nR PV/T=(N/NA)R
n (number of mols)=N (number of molecules)
NA (number of molecules in 1 mol)
Rewrite ideal gas law: PV/T = NkB
where kB=R/NA=1.38x10-23 J/K Boltzmann’s constant
PHY 23115
From macroscopic to microscopic descriptions: kinetic theory of gases
For derivations of the equations, see the textbook
1) The number of molecules is large (statistical model)2) Their average separation is large (take no volume)3) Molecules follow Newton’s laws4) Any particular molecule can move in any direction with a large distribution of velocities5) Molecules undergo elastic collision with each other6) Molecules make elastic collisions with the walls7) All molecules are of the same type
PHY 23116
Pressure
2
2
1
3
2vm
V
NP
Number of Molecules
Volume
Mass of 1 molecule
Averaged squared velocity
Average translation kinetic energy
Number of moleculesper unit volume
PHY 23117
M
RT
m
Tkvv
nRTTNkE
Tkvm
vmk
T
TNkPV
vmNPV
brms
Bkin
B
B
B
33
2
3
2
32
3
2
1
)2
1(
3
2
2
1
3
2
2
2
2
2
Microscopic
Macroscopic
Temperature ~ average molecular kinetic energy
Average molecular kinetic energy
Total kinetic energy
rms speed of a moleculeM=Molar mass (kg/mol)
PHY 23118
example
What is the rms speed of air at 1atm and room temperature? Assume it consist ofmolecular Nitrogen only (N2)?
PHY 23119
And another...
What is the total kinetic energy of the air molecules in thelecture room (assume only molecular nitrogen is present N2)?