{"title":"Systems of Interacting Particles","authors":"D. V. Schroeder","doi":"10.1093/OSO/9780192895547.003.0008","DOIUrl":"https://doi.org/10.1093/OSO/9780192895547.003.0008","url":null,"abstract":"This chapter presents two examples of the application of Boltzmann statistics to systems with nontrivial interactions between particles. The first example is a nonideal gas, treated approximately using a series expansion that we can visualize in terms of simple diagrams. The second example is a model of a ferromagnet as a collection of two-state particles interacting with their nearest neighbors. It is easy to solve this model exactly in one dimension, and to gain a semi-quantitative understanding of why the system magnetizes below a critical temperature in two or three dimensions. The most powerful tool for studying this model, however, is numerical simulation on a computer using a random-sampling algorithm based on the Boltzmann distribution.","PeriodicalId":348442,"journal":{"name":"An Introduction to Thermal Physics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123888656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Boltzmann Statistics","authors":"D. V. Schroeder","doi":"10.1093/oso/9780192895547.003.0006","DOIUrl":"https://doi.org/10.1093/oso/9780192895547.003.0006","url":null,"abstract":"When a system is held at a fixed temperature, its higher-energy states are less probable than its lower energy states by an amount that depends on how the energy compares to the temperature. The formula that quantifies this idea is called the Boltzmann distribution. This chapter derives the Boltzmann distribution and shows how to use it to predict the thermal behavior of any system whose microscopic states we can enumerate. The examples go beyond the three simple model systems studied already in Chapters 2 and 3 to include detailed properties of gases, stellar spectra, and paramagnetic materials.","PeriodicalId":348442,"journal":{"name":"An Introduction to Thermal Physics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129552579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Second Law","authors":"D. V. Schroeder","doi":"10.1093/OSO/9780192895547.003.0002","DOIUrl":"https://doi.org/10.1093/OSO/9780192895547.003.0002","url":null,"abstract":"Why are so many large-scale processes irreversible, happening in one direction but not the other as time passes? This chapter answers that question using three simple model systems: a collection of two-state particles such as flipped coins or elementary magnetic dipoles; the Einstein model of a solid as a collection of identical quantum oscillators; and a monatomic ideal gas such as helium or argon. For each system we learn to calculate the multiplicity: the number of possible microscopic arrangements. Taking the logarithm of the multiplicity gives the entropy. And the laws of probability then imply the second law of thermodynamics: Entropy tends to increase.","PeriodicalId":348442,"journal":{"name":"An Introduction to Thermal Physics","volume":"39 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120918833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}