kinetic theory of gases
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Kinetic Theory of Gases. Physics 313 Professor Lee Carkner Lecture 11. Exercise #10 Ideal Gas. 8 kmol of ideal gas Compressibility factors Z m = S y i Z i y CO2 = 6/8 = 0.75 V = ZnRT/P = (0.48)(1.33) = 0.638 m 3 Error from experimental V = 0.648 m 3 Compressibility factors: 1.5% - PowerPoint PPT PresentationTRANSCRIPT
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Kinetic Theory of Gases
Physics 313Professor Lee
CarknerLecture 11
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Exercise #10 Ideal Gas 8 kmol of ideal gas
Compressibility factors
Zm = yiZi
yCO2 = 6/8 = 0.75 V = ZnRT/P = (0.48)(1.33) = 0.638 m3
Error from experimental V = 0.648 m3
Compressibility factors: 1.5% Most of the deviation comes from CO2
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Ideal Gas At low pressure all gases approach an ideal
state
The internal energy of an ideal gas depends only on the temperature:
The first law can be written in terms of the
heat capacities:dQ = CVdT +PdV dQ = CPdT -VdP
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Heat Capacities Heat capacities defined as:
CV = (dQ/dT)V = (dU/dT)V
Heat capacities are a function of T only for
ideal gases: Monatomic gas
Diatomic gas
= cP/cV
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Adiabatic Process
For adiabatic processes, no heat enters of leaves system
For isothermal, isobaric and isochoric processes, something remains constant
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Adiabatic Relations
dQ = CVdT + PdV
VdP =CPdT
(dP/P) = - (dV/V)
. Can use with initial and final P and V of
adiabatic process
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Adiabats Plotted on a PV diagram adibats have a
steeper slope than isotherms
If different gases undergo the same
adiabatic process, what determines the final properties?
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Ruchhardt’s Method
How can be found experimentally?
Ruchhardt used a jar with a small oscillating ball suspended in a tube
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Finding
Also related to PV and Hooke’s law
Modern method uses a magnetically
suspended piston (very low friction)
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Microscopic View
Classical thermodynamics deals with macroscopic properties
The microscopic properties of a gas
are described by the kinetic theory of gases
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Kinetic Theory of Gases The macroscopic properties of a gas are
caused by the motion of atoms (or molecules)
Pressure is the momentum transferred by atoms colliding with a container
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Assumptions Any sample has
large number of particles (N)
Atoms have no internal structure
No forces except collision
Atoms distributed randomly in space and velocity direction
Atoms have speed distribution
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Particle Motions
The pressure a gas exerts is due to the momentum change of particles striking the container wall
We can rewrite this in similar form to the ideal equation of state:
PV = (Nm/3) v2
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Applications of Kinetic Theory
We then use the ideal gas law to find T:PV = nRT
T = (N/3nR)mv2
We can also solve for the velocity:
For a given sample of gas v depends only on the temperature
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Kinetic Energy
Since kinetic energy = ½mv2, K.E. per particle is:
where NA is Avogadro’s number
and k is the Boltzmann constant