Transcript kinetic theory of gases

Kinetic Theory of Gases
Physics 313
Professor Lee Carkner
Lecture 11
Exercise #10 Ideal Gas
8 kmol of ideal gas

Compressibility factors
Zm = SyiZi

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
g = 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) = -g (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 g be found experimentally?

Ruchhardt used a jar with a small
oscillating ball suspended in a tube


Finding g

Also related to PVg 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
