 |
 |
Molecular Kinetic Energy
Name: Rod
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
An earlier answer on kinetic energy,
in part: "...temperature is a measure of the average
kinetic energy of a particle/substance. BUT, your
definition of kinetic energy is incomplete. Translational
(linear) motion is only one part of kinetic energy--
rotational and vibrational energy also feed into kinetic
energy as a whole..." Is ALL of the kinetic energy used
to calculate temperature ala 3/2kT (or some other factor)?
In other words does vibrational or rotation kinetic energy
effect the temperature?
Replies:
You make a good point. Both rotational motions and
vibrational motions of molecules have a kinetic energy
component. The formula 3/2kT applies to the translational
component only -- that is because the energy levels of
translational motion are so closely spaced that they behave
"classically" contributing 1/2kT for each motion in the X,Y,Z
directions. The rotational and vibrational energy levels do
not behave classically, and their contribution to the
"temperature" only becomes evident at low temperatures. In
fact, historically the decrease in the heat capacity of solids
at low temperatures (from 3/2k) was one of the early hints
that the classical model for internal motions of molecules
did not obey the classical mechanical model. Einstein used
Planck's rules of quantized levels to "explain" the drop of
in heat capacity as the temperature is reduced. A good way
to look at this is to consider that molecular vibrations and
rotations act as a 'heat sink' as the temperature decreases.
The heat capacity decreases, where the "classical" model
predicts no such decrease.
Vince Calder
Rod,
Temperature is due to "internal" kinetic energy, the vibrational and
rotational parts. Actually, translational kinetic energy per molecule
is not significant in most cases. The random motions due to the
bouncing around, due to the forces within and between individual
molecules, are what we measure as temperature. Although heat energy
needed to raise the temperature of a material also contributes to
potential energy, temperature is an expression of only the kinetic
energy.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
The 'kinetic' definition of temperature, the one that comes from the 3/2 kT
definition of temperature, is useful for monatomic gases ("pure hard
spheres"), but becomes less useful when you have complex molecules with
several types of degrees of freedom. The 3/2 kT definition is not accurate
for complex molecules. The definition given ("...average kinetic energy...")
is a reasonable working definition, but there are plenty of situations where
a more precise definition is useful.
Chemical engineers (and physicists too I presume) often turn to
thermodynamics, such as the partial derivative of entropy with respect to
internal energy holding volume and system size the same is equal to the
inverse of temperature [(delS/delU|V,N)= 1/T ]. Every thermodynamics
textbook will have several pages or more on thermodynamic identities and
functions such as these that allow you to use temperature. If this is where
you are headed, I encourage you to find a thermodynamics text and read these
sections. Unfortunately, thermodynamics definitions are not very intuitive -- at
least not for me.
Instead, you may want to have a more operational-style definition, such as
"temperature is the tendency of a body to give off heat to its
surroundings." This definition does not give much insight into the nature of
temperature, but it sure is very intuitive.
There is a pretty good article I found on the subject of temperature, beyond
the kinetic definition:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper2.html
It explains various definitions of temperature, and some better ways to
define temperature in complex systems. Rather than re-summarize the whole
article here, go read it and email me back if there are things you would
like to discuss or clarify further.
Hope this helps,
Burr Zimmerman
Click here to return to the Physics Archives
| |
Update: June 2012
|
|
