kinetic theory of gases physics 313 professor lee carkner lecture 11
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Kinetic Theory of Gases
Physics 313Professor Lee
CarknerLecture 11
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
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
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
Adiabatic Process
For adiabatic processes, no heat enters of leaves system
For isothermal, isobaric and isochoric processes, something remains constant
Adiabatic Relations
dQ = CVdT + PdV
VdP =CPdT
(dP/P) = - (dV/V)
. Can use with initial and final P and V of
adiabatic process
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?
Ruchhardt’s Method
How can be found experimentally?
Ruchhardt used a jar with a small oscillating ball suspended in a tube
Finding
Also related to PV and Hooke’s law
Modern method uses a magnetically
suspended piston (very low friction)
Microscopic View
Classical thermodynamics deals with macroscopic properties
The microscopic properties of a gas
are described by the kinetic theory of gases
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
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
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
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
Kinetic Energy
Since kinetic energy = ½mv2, K.E. per particle is:
where NA is Avogadro’s number
and k is the Boltzmann constant