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Name: Rod
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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



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