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