Temperature Upper Limit
Name: Jim S.
Date: Thursday, November 28, 2002
Given the fact that temperature is a measure of the
average internal kinetic energy and kinetic energy appears to me to be
limited due to constraints imposed by the Theory of Relativity, why is
there no upper limit to temperature?
The Theory of Relativity does not limit kinetic energy. What it limits is
velocity. However, as an object's velocity approaches the speed of light,
its mass approaches infinity. Thus, its kinetic energy can still increase
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Relativity does not impose an upper limit on kinetic energy. As particles
move faster, their kinetic energy is no longer given by the expression
(m*v^2)/2, but by
As v approaches c, the value of this expression approaches infinity.
I am not sure that the theory of relativity puts any constraints on kinetic
energy in a practical sense. I suppose you could say that an upper limit
would be that if the entire universe was so hot that the speed of the entire
mass approached the speed of light that it would set an upper limit.
However, we have no guarantee that the rules of physics, as we know them,
would apply to such conditions.
There is no upper limit to kinetic energy because the formula we normally
use is not exact. (1/2)*(rest mass)*(speed)^2 is correct so long as size
is not on the order of individual molecules and speed is not approaching the
speed of light. As the speed of an object increases, so does its mass (in
our reference frame). Kinetic energy begins to increase faster as mass
begins to increase. It must reach an infinite mass to reach the speed of
light. An infinite amount of energy must be put into a massive object's
motion to make it reach the speed of light. An object moving at the speed
of light (provided it has mass) has an infinite amount of kinetic energy (as
we see it).
Dr. Ken Mellendorf
Illinois Central College
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