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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2001-2002 MATHEMATICS COLLOQUIUM SERIES 04/22/02 Colloquium DR. K. R. RAJAGOPAL Department of Mechanical Engineering Texas A & M University ON THE EXISTENCE OF A HOTNESS MANIFOLD Abstract:   The concept of temperature is central to the development of thermodynamics and in mathematical treatments of the subject, the existence of a hotness manifold, i.e., the notion of temperature is a primitive assumption. Here, I shall show that the zeroth law of thermodynamics and other physically reasonable assumptions concerning the notion of "heat transfer" leads naturally to the existence of a manifold of dimension one, namely temperature. Thus, the notion of temperature is a derived notion and need not be assumed apriori as primitive.