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12 November 2004 What is heat? George E. Hrabovsky, President MAST Where We Have Been Last time I explained how to develop a theory library. I also described how to learn theory, as opposed to mathematics. I then explained that I was going to investigate an area in which I am not an expert, namely the matter of what heat is. I also began a notebook for this project, a bound sketchbook. Session 1: What is heat? One of the first places I go when I am unsure of a topic in science is the "McGraw-Hill Encyclopedia of Science and Technology on CD-ROM" [1]. I looked up heat and discovered this article: Harold W. Weber and William A. Steele, "Heat" [2]. In essence this article states that heat is the flow of energy due to a temperature difference from the source of the energy to a sink of energy. Heat only exists when this energy flows. This explanation raises many questions: 1. What is energy? 2. What does it mean for energy to flow? 3. What is temperature? 4. What constitutes a difference in temperature? 5. How does a difference in temperature come about? 6. Why does this cause heat? 7. What is a source of energy? 8. What is a sink of energy? What is energy? According to Brian de Falco [3], energy can be defined as the ability of one system to do work on another system. We can insert this definition into our definition of heat. Heat then is the flow of the ability of one system to do work on another system due to a temperature difference from the one system to the other system. Heat only exists when this the ability of one system to do work on another system flows. This implies that the one system is the source and the other system is the sink. This answer raises a couple more questions: 9. What is a system? 10. What is work? What is a system? I was unable to find an article suitable to systems in the encyclopedia, so I looked in the dictionary of scientific and technical terms [4]. Here is what I found there: "A region of space or a portion of matter that has a certain amount of one or more substances ordered in one or more phases." A lot of questions were raised by this definition: 11. What is a region? 12. What is space? 13. What is matter? 14. What is a substance? 15. How can matter have an amount of more than one substance? 16. What is a phase? 17. What does it mean to be ordered into one or more phases? What is a region? Again looking in the dictionary I was referred to the entry for domain, where I found, "A nonempty open connected set in euclidean space" [4]. Several questions come to mind: 18. What is a set? 19. What is a connected set? 20. What is an open set? 21. What is a connected open set? 12. What is a space? 22. What is a euclidean space? What is a set? I made the following discovery while reading: A set is a collection of objects called elements [5]. For a set
Inserting this notion into our definition of a region gives us, "A nonempty open connected collection of objects in euclidean space." What is a connected set? Again using the dictionary, as no significant or relevant article was under that name in the encyclopedia, I found this: "A set in a topological space that is not in the union of two nonempty sets Inserting this notion into our definition of a region gives us, "A nonempty open set in a topological space that is not in the union of two nonempty sets This also raised many questions: 23. What are the properties of sets? 12. What is a space? 24. What is a topological space? 25. What is a union? 26. What is an intersection? 27. What is a closure? 28. What is an empty set? More about sets Using reference 5, we find answers to several questions. We can declare that a set
This is called set-builder notation. We can use this to define certain principles of set theory. The union between two sets is defined as,
The intersection between two sets is defined as,
The empty set is a set with no elements. This set is denoted with the symbol Book Review: "The McGraw-Hill Encyclopedia of Science and Technology" on CD-ROM Mark Licker, "The Multimedia Encyclopedia of Science and Technology," McGraw-Hill Professional Book Group (2000). This is a remarkable CD-ROM. It contains the entire 26-volume encyclopedia (8th edition) on one disk. It also has the complete "McGraw-Hill Dictionary of Scientific and Technical Terms" (5th edition). Each article appears in its own window. Equations appear in an acceptable format. Diagrams appear as part of the text and, sometimes, as extra windows. There are animations, too. Articles are cross-referenced and hyperlinked within the text. Taking the article above as an example, while you read there are references to these other articles: "Energy," "Internal Energy," "Work," "Temperature," and "Thermodynamic Principles." By clicking on the hyperlink to, "Energy," I am taken to that article. The articles are written by some of the top experts in their fields. Many articles have a list of references that allow you to delve deeper that the articles can. The cost is rather high, over $1,000 when I purchased it. I consider it worthwhile. If you have few other resources, this contains at least something (and usually a lot) about any topic in science and technology. References 1. Mark Licker, "The Multimedia Encyclopedia of Science and Technology," McGraw-Hill Professional Book Group (2000). 2. Harold W. Weber and William A. Steele, "Heat" [1]. 3. Brian de Falco, "Energy" [1]. 4. "McGraw-Hill Dictionary of Scientific and Technical Terms," 5th Edition [1]. 5. R. H. Bing, "Set Theory" [1]. ----------------------------------------------------------------------------------------- Created by Mathematica (October 17, 2004) | |||||
Copyright 2004 by Society for Amateur Scientists |
, the fact that 
is a member of the set is written,
and 
for which both the intersection of the closure of 
and 
and the intersection of the closure of 
and 
are empty." We have been seeing the word empty a lot, I hope to find that definition soon.
and 
for which both the intersection of the closure of 
and 
and the intersection of the closure of 
and 
are empty in euclidean space."
is composed of elements 
such that every 
meets some requirement 
. We can write this in shorthand,
.