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Thermal Properties of MatterThermal Properties of Matter
April 5, 2012ChapterChapter
18
April 5, 2012 Physics 221 1
Equations of State
State variables for a particular materialPressurePressureVolumeTemperatureTemperatureQuantityOther properties needed to describe theOther properties needed to describe the “state” of the material
April 5, 2012 Physics 221 2
Measurements of Ideal Gasses Show
Volume proportional to the number of moles of materialnumber of moles of material.The volume varies inversely with absolute pressurewith absolute pressure.The pressure is proportional to th b l t t tthe absolute temperature
April 5, 2012 Physics 221 3
The Ideal Gas Equation
theisMandmolesofnumbertheisnWhere = Mnmtotal
:Then mass.molar theisMandmolesofnumber theisn Where
= nRTpV
KJ/mol8 314RWherestate. ofequation gas" ideal" theasknown is
= nRTpV
KJ/mol8.314RWhere =
April 5, 2012 Physics 221 4
pV - Diagrams
Ideal Gas
Non Ideal Gas
April 5, 2012 Physics 221 5
Non-Ideal Gas
Molecular Properties of Matter
April 5, 2012 Physics 221 6
Avogadro’s Number
One mole of a substance contains as many elementary entities as there aremany elementary entities as there are atoms in 0.012 kg of carbon-12.N =6 022 X 1023 molecules/moleNA =6.022 X 10 molecules/mole
April 5, 2012 Physics 221 7
Kinetic Theory of an Ideal GasOur container with volume V of material contains a large number N of identical particles each with a mass mmass, m.The molecules behave as point particles and their size is small compared to the distance between pparticles as well as the dimensions of the container.The molecules are in constant motion, obeying N t ’ L f ti d tt i f tlNewton’s Laws of motion and scattering perfectly elastically with the container walls.The container walls are infinitely massive and
April 5, 2012 Physics 221 8
The container walls are infinitely massive and perfectly rigid.
Elastic Collisions with the walls of the container
April 5, 2012 Physics 221 9
Calculating Gas Pressure from these Collisions
| dt)(A|vVN
x
2
wall. the towardheading themof halfithcylinder wewithin thmoleculesofnumber the
VdtNAmv|m|v| dt)(A|v
VNdP x
xxx ==2
dttimetheduringchangemomentumtotaltheis
)2(21
pV
NAmvdt
dP xx ==2
dt.timetheduringchange momentumtotaltheis
April 5, 2012 Physics 221 10
Vdt
Pressure and Molecular KE++= zyx vvvv
find. wemolecules theof allover averaging
2222
++= avezaveyavexave vvvv
So.
)()()( )( 2222
= aveavex vv )(31)(
So.
22
⎤⎡NNV )(12)(1Yielding
22
April 5, 2012 Physics 221 11
⎥⎦⎤
⎢⎣⎡== aveave vmNvNmpV )(23
)(3
22
Connecting to the Ideal Gas Equation
)(21
32 2 =⎥⎦
⎤⎢⎣⎡= nRTvmNpV ave
1hf
, 23)(
21 2 =
NN
nRTvmN ave
where,23)(
21
so,1then ,for
2 =
==
kTvm
nNN
ave
A
K J/molecule 10 x 3811
2)(
223−== .k
NR
ave
April 5, 2012 Physics 221 12ConstantBoltzmann the
N A
Average Translational KE
kTvm ave 23)(
21 2 =
ofenergy kinetic onal translatiaverage the22
:ofmoleculestheseofvelocityaveragesquared"-mean-root" a yielding molecule, gas a
RTkTvv 33)(
:ofmoleculestheseof velocity average
2 ===
April 5, 2012 Physics 221 13
Mmvv averms )(
