Temperature Upper Limit ```Name: Jim S. Status: educator Age: 40s Location: N/A Country: N/A Date: Thursday, November 28, 2002 ``` Question: 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? Replies: 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 without bound. 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 ``` mc^2 ---------------. sqrt(1-v^2/c^2) ``` As v approaches c, the value of this expression approaches infinity. Tim Mooney 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. Vince Calder Jim, 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 Physics Instructor Illinois Central College Click here to return to the Physics Archives

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