Post on 19-Dec-2015
Kinetic Theory of Gases
Physics 202Professor Lee
CarknerLecture 15
PAL #14 Heat Transfer Heat transfer in a cylinder No conduction through vacuum
No convection through iron or vacuum
No radiation through iron
What is a Gas?
A gas is made up of molecules (or atoms)
The pressure is a measure of the force the molecules exert when bouncing off a surface
We need to know something about the microscopic properties of a gas to understand its behavior
Mole When thinking about molecules it sometimes is helpful
to use the mole
6.02 x 1023 is called Avogadro’s number (NA)
M = mNA Where m is the mass per molecule or atom
Gasses with heavier atoms have larger molar masses
Ideal Gas
Specifically 1 mole of any gas held at constant temperature and constant volume will have the almost the same pressure
Gases that obey this relation are called ideal gases
Ideal Gas Law
The temperature, pressure and volume of an ideal gas is given by:
Where:
R is the gas constant 8.31 J/mol K
Work and the Ideal Gas Law
We can use the ideal gas law to solve this equation
Vf
VipdVW
Vf
VidVV1
nRTW
Isothermal Process
If we hold the temperature constant in the work equation:
W = nRT ln(Vf/Vi)
Work for ideal gas in isothermal process
Isothermal Work
Isotherms From the ideal gas law we can get an
expression for the temperature
For an isothermal process temperature is constant so:
If P goes up, V must go down
Lines of constant temperature
Isotherms
Constant Volume or Pressure
In a constant volume process no work is done so:
In a constant pressure process the work
equation becomes
W = pV For situations where T, V or P are not
constant, we must solve the integral
Random Gas Motions
Gas Speed
The molecules bounce around inside a box and exert a pressure on the walls via collisions
The pressure is a force and so is related to velocity by
Newton’s second law F=d(mv)/dt
A bigger box means fewer collisions
The final result is:
Where M is the molar mass (mass contained in 1 mole)
RMS Speed Not all the molecules have the same speed even if the
temperature is constant
We take as a typical value the root-mean-squared velocity (vrms)
We can find an expression for vrms from the pressure and ideal gas equations
vrms = (3RT/M)½
For a given type of gas, velocity depends only on temperature
Maxwell’sDistribution
Maxwellian Distribution and the Sun
The vrms of protons is not large enough for them to combine in hydrogen fusion
There are enough protons in the high-speed tail of the distribution for fusion to occur
Translational Kinetic Energy
If the molecules have a velocity then they also have kinetic energy (K=½mv2)
Kave = ½mvrms
2
Kave = (3/2)kT
Where k = (R/NA) = 1.38 X 10-23 J/K and is called the Boltzmann constant