{"id":30544,"date":"2021-03-31T13:00:57","date_gmt":"2021-03-31T13:00:57","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30544"},"modified":"2024-12-30T07:38:56","modified_gmt":"2024-12-30T07:38:56","slug":"exercises-moles-combinatorics-and-large-numbers","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/en\/exercises-moles-combinatorics-and-large-numbers\/","title":{"rendered":"Exercises: Moles, Combinatorics, and Large Numbers"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\ttext-align:center;\n\t}\n<\/style>\n<h1>Exercises: Moles, Combinatorics, and Large Numbers<\/h1>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/qgsJbPd-www\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>Now is the time to apply what you have learned with practical exercises that will help you master essential thermodynamic concepts, such as moles, combinatorics, and calculations with large numbers. If you haven\u2019t done so already, I recommend reviewing the previous lessons, as they contain the necessary foundations to approach these problems with confidence.<\/p>\n<ol style=\"text-align: left; color: #000000;\">\n<li>What is the mass of 3 moles of carbon dioxide <span class=\"katex-eq\" data-katex-display=\"false\">(CO_2)<\/span>? <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=33s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">[SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>A typical bacterium has a mass of <span class=\"katex-eq\" data-katex-display=\"false\">10^{-12}[g].<\/span> Calculate the mass of one mole of bacteria. <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=222s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>Estimate the number of water molecules in your own body. <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=322s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><\/li>\n<li>A thermodynamic system has <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> atoms, each capable of having up to a single quantum of energy. How many different ways can <span class=\"katex-eq\" data-katex-display=\"false\">k<\/span> quanta of energy be distributed when:<br \/>\na) <span class=\"katex-eq\" data-katex-display=\"false\">n=2<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">k=1,<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=703s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><br \/>\nb) <span class=\"katex-eq\" data-katex-display=\"false\">n=20<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">k=10,<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=739s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><br \/>\nc) <span class=\"katex-eq\" data-katex-display=\"false\">n=2\\cdot 10^{23}<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">k=10^{23},<\/span> <a href=\"https:\/\/www.youtube.com\/watch?v=qgsJbPd-www&amp;t=939s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\"> [SOLUTION]<\/span><\/strong><\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Exercises: Moles, Combinatorics, and Large Numbers Now is the time to apply what you have learned with practical exercises that will help you master essential thermodynamic concepts, such as moles, combinatorics, and calculations with large numbers. If you haven\u2019t done so already, I recommend reviewing the previous lessons, as they contain the necessary foundations to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30543,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":12,"footnotes":""},"categories":[635,919],"tags":[],"class_list":["post-30544","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physics","category-thermodynamics"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Exercises: Moles, Combinatorics, and Large Numbers - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Master Moles, Combinatorics, and Large Numbers with practical exercises and step-by-step solutions. 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