{"id":30855,"date":"2021-07-03T13:00:40","date_gmt":"2021-07-03T13:00:40","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=30855"},"modified":"2025-01-02T04:29:10","modified_gmt":"2025-01-02T04:29:10","slug":"the-first-law-of-thermodynamics","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/","title":{"rendered":"The First Law of Thermodynamics"},"content":{"rendered":"<style>\n\tp, ul, ol {\n\t\ttext-align: justify;\n\t}\n\th1, h2 {\n\t\ttext-align: center;\n\t}\n<\/style>\n<h1>The First Law of Thermodynamics<\/h1>\n<p style=\"text-align:center;\">\n\t<em><br \/>\n\t\tThe First Law of Thermodynamics is the foundation that links fundamental concepts such as heat, work, and internal energy, establishing that energy is neither created nor destroyed, only transformed. This material explores how this law applies to closed systems, delving into the analysis of thermodynamic work, heat capacities, and the statistical properties of gases. Through a combination of mathematical formulations and physical reasoning, you will discover essential tools for understanding energy processes in complex systems.<br \/>\n\t<\/em>\n<\/p>\n<p style=\"text-align:center;\"><strong>Learning Objectives:<\/strong><\/p>\n<p>By the end of this class, students will be able to:<\/p>\n<ol>\n<li><strong>Justify<\/strong> the First Law of Thermodynamics for closed systems, explaining the relationships between heat, work, and internal energy.<\/li>\n<li><strong>Analyze<\/strong> the concept of thermodynamic work in compression and expansion processes using differential formulas.<\/li>\n<li><strong>Calculate<\/strong> heat capacity under constant volume and pressure conditions, applying thermodynamic constraints.<\/li>\n<li><strong>Explain<\/strong> the Maxwell-Boltzmann distribution and the equipartition of energy principle in molecular systems.<\/li>\n<li><strong>Demonstrate<\/strong> specific relationships between heat capacities, the adiabatic index, and other thermodynamic properties for ideal gases.<\/li>\n<\/ol>\n<p style=\"text-align:center\"><strong><u>TABLE OF CONTENTS<\/u>:<\/strong><br \/>\n\t<a href=\"#1\">Formulation of the First Law of Thermodynamics<\/a><br \/>\n\t<a href=\"#2\">Thermodynamic Work<\/a><br \/>\n\t<a href=\"#3\">Heat Capacity<\/a><br \/>\n\t<a href=\"#4\">Maxwell-Boltzmann Distribution and the Equipartition of Energy<\/a><br \/>\n\t<a href=\"#5\">Exercises<\/a>\n<\/p>\n<p><center><br \/>\n\t<iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/T6K1Nizc5NE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><br \/>\n<\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>Formulation of the First Law of Thermodynamics<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=140s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>The First Law of Thermodynamics<\/strong><br \/>\n\t<\/a> states that:\n<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"background-color: #c0ffc0;\">\n\t<span style=\"color: #000080;\"><br \/>\n\t\t<strong>FIRST LAW OF THERMODYNAMICS<\/strong><br \/>\n\t\tEnergy is neither created nor destroyed; moreover, heat and work are forms of energy (emitted, absorbed, or used by a process).<br \/>\n\t<\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Internal energy <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> is a state function because it has a well-defined value for each equilibrium state of the system. The internal energy of the system can be changed by applying heat <span class=\"katex-eq\" data-katex-display=\"false\">Q<\/span> or performing work <span class=\"katex-eq\" data-katex-display=\"false\">W<\/span>; however, work and heat are not state functions. This is because both depend on the process by which energy is added or removed, and once the process is completed, it is impossible to determine the exact amount of heat or work involved in achieving that equilibrium state.<\/p>\n<p>The change in the internal energy of a system can be expressed as:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta U = \\Delta Q + \\Delta W<\/span><\/span><\/p>\n<p>Where <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> is the amount of heat supplied, and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> is the amount of work done on the system. By convention, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> is positive when heat is supplied to the system; if <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta Q<\/span><\/span> is negative, heat is being removed from the system. Similarly, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\Delta W<\/span><\/span> is positive for work done on the system and negative when the system does work on the surroundings.<\/p>\n<p>The relationship between work, heat, and internal energy can also be expressed differentially as:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU = \\delta Q + \\delta W<\/span><\/span>.<\/p>\n<p>Here, the symbol <span class=\"katex-eq\" data-katex-display=\"false\">\\delta<\/span> is used to denote inexact differentials.<\/p>\n<p>A thermally isolated system is defined as one that cannot exchange heat with its surroundings. In this case, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU = \\delta W<\/span><\/span>. This represents the <strong>First Law of Thermodynamics<\/strong> applied to an adiabatic system.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Heat Capacity<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=677s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>Let us now<\/strong><br \/>\n\t<\/a> aim to understand in greater detail how the internal energy of a system changes when heat is added. Generally, internal energy is a function of temperature and volume, which allows us to write <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=U(T,V)<\/span><\/span>. Since energy is an exact differential, the change in <span class=\"katex-eq\" data-katex-display=\"false\">U<\/span> with respect to <span class=\"katex-eq\" data-katex-display=\"false\">T<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">V<\/span> can be expressed as:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle dU = \\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left(\\frac{\\partial U}{\\partial V}\\right)_T dV<\/span><\/span>.\n<\/p>\n<p>Now, using the relations <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=\\delta Q + \\delta W<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta W=-PdV<\/span><\/span>, we can reformulate the <strong>First Law of Thermodynamics<\/strong> as follows:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\delta Q &amp;= dU + PdV\\\\ \\\\\n\n&amp; \\displaystyle  =\\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left(\\frac{\\partial U}{\\partial V}\\right)_T dV + PdV\\\\ \\\\\n\n&amp; \\displaystyle =\\left(\\frac{\\partial U}{\\partial T}\\right)_V dT + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]dV \\\\ \\\\\n\n\\displaystyle  \\frac{\\delta Q}{dT} &amp; \\displaystyle  =\\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]\\frac{dV}{dT}.\n\n\\end{array}\n\n<\/span>\n<p>This is a general relation valid for any change in temperature and volume.<\/p>\n<p>Using this result, we can determine the amount of heat required to produce a temperature change under specific constraints.<\/p>\n<h3>Constant Volume Constraint<\/h3>\n<p>To analyze what happens under constant volume, recall the definition of heat capacity at constant volume: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V=(\\partial Q\/ \\partial T)_V<\/span><\/span>. By restricting the analysis to constant volume, we nullify the term <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dV\/dT<\/span><\/span> in the expression for <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\delta Q\/dT<\/span><\/span>. This leads to:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V = \\left(\\frac{\\partial U}{\\partial T} \\right)_V<\/span><\/span>.\n<\/p>\n<h3>Constant Pressure Constraint<\/h3>\n<p>If we keep the pressure constant, then:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle C_p =\\left(\\frac{\\partial Q}{\\partial T}\\right)_P=\\left(\\frac{\\partial U}{\\partial T}\\right)_V + \\left[\\left(\\frac{\\partial U}{\\partial V}\\right)_T + P\\right]\\left(\\frac{\\partial V}{\\partial T}\\right)_p<\/span><\/span>.\n<\/p>\n<h3>Heat Capacity of a Monatomic Gas<\/h3>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=974s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>When considering<\/strong><br \/>\n\t<\/a> a monatomic gas, the internal energy due to the kinetic energy of its particles is of the form <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\n\n\tU=\\frac{3}{2}Nk_BT<\/span>. This result is justified by the equipartition of energy principle, which can be studied from a statistical perspective of particle motion.\n<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Maxwell-Boltzmann Distribution and the Equipartition of Energy<\/h2>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>Since the energy of a system<\/strong><br \/>\n\t<\/a> is proportional to its <strong>Boltzmann Factor<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-E\/(k_BT)}<\/span><\/span>, reasoning from this and considering that the kinetic energy of particles has the form <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle E_{cin}=\\frac{1}{2}mv^2<\/span><\/span>, we can infer that the energy associated with particle motion projected along one of the three coordinate axes (let\u2019s focus on the <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span> axis for now) will correspond to a velocity distribution <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> proportional to <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">e^{-mv_x^2\/(2k_BT)}<\/span><\/span>. In other words:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)= A e^{-mv_x^2\/(2k_BT)}<\/span><\/span>,\n<\/p>\n<p>where <span class=\"katex-eq\" data-katex-display=\"false\">A<\/span> is a constant to be determined. Since <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">g(v_x)<\/span><\/span> is a distribution function, it must be normalized so that:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} g(v_x)dv_x= 1<\/span><\/span>.\n<\/p>\n<p>A useful result for analyzing this situation is the Gaussian integral:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle\\int_{-\\infty}^{+\\infty} e^{-x^2}dx= \\sqrt{\\pi}<\/span><\/span>.\n<\/p>\n<p>From this, we deduce that:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 1= \\int_{-\\infty}^{+\\infty} Ae^{\\frac{-mv_x^2}{2k_BT}}dv_x= A\\sqrt{\\frac{\\pi}{m\/(2k_BT)}} = A\\sqrt{\\frac{2\\pi k_BT}{m}}<\/span><\/span>.\n<\/p>\n<p>Thus:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  g(v_x) = \\sqrt{\\frac{m}{2\\pi k_BT}}e^{-mv_x^2\/(2k_BT)}<\/span><\/span>.\n<\/p>\n<p>With this result, we can now calculate the average squared velocity projected along the <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\hat{x}<\/span><\/span> axis, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left\\lt v_x^2\\right\\gt<\/span><\/span>. Its result is:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt v_x^2\\right\\gt = \\int_{-\\infty}^{+\\infty} v_x^2 g(v_x) dv_x = \\sqrt{\\frac{m}{2\\pi k_BT}} \\int_{-\\infty}^{+\\infty} v_x^2 e^{-mv_x^2\/(2k_BT)} = \\frac{k_BT}{m} <\/span><\/span>.\n<\/p>\n<p>And since the root mean square velocity can be decomposed as <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt v^2\\right\\gt = \\left\\lt v_x^2\\right\\gt + \\left\\lt v_y^2\\right\\gt + \\left\\lt v_z^2\\right\\gt<\/span><\/span>, and each component has the same development and result, the average kinetic energy of the system of particles can be written as:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt E_{cin}\\right\\gt =\\frac{1}{2}m\\left\\lt v^2\\right\\gt  = \\frac{1}{2}m \\cdot 3\\frac{k_BT}{m}= \\frac{3}{2}k_BT<\/span><\/span>.\n<\/p>\n<p>This is known as the \u00abequipartition of energy principle.\u00bb From this, we can conclude that if the system consists of <span class=\"katex-eq\" data-katex-display=\"false\">N<\/span> particles with an average kinetic energy <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left\\lt E_{cin}\\right\\gt<\/span><\/span>, and the system&#8217;s total energy is purely kinetic, then not only is the internal energy of the system <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle U=3Nk_BT\/2<\/span> (as predicted), but it also becomes evident that the internal energy only depends on the system&#8217;s temperature, which implies:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\left(\\frac{\\partial U}{\\partial V}\\right)_T = 0<\/span><\/span>.\n<\/p>\n<h3>Development for the Ideal Gas<\/h3>\n<p>\n\t<a href=\"https:\/\/www.youtube.com\/watch?v=T6K1Nizc5NE&amp;t=1027s\" target=\"_blank\" rel=\"noopener\"><br \/>\n\t\t<strong>Now, recalling the ideal gas law<\/strong><br \/>\n\t<\/a>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">PV=Nk_BT =nRT<\/span><\/span>, solving for the volume gives:\n<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  V= \\frac{nRT}{P}<\/span><\/span>.\n<\/p>\n<p>Therefore:<\/p>\n<p style=\"text-align: center;\">\n\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  \\left(\\frac{\\partial V}{\\partial T} \\right)_P = \\frac{nR}{P}<\/span><\/span>.\n<\/p>\n<p>Using the expressions for <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span>, we find:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nC_P - C_V &amp; \\displaystyle = \\left[\\left(\\frac{\\partial U}{\\partial V} \\right)_T + P \\right]\\left(\\frac{\\partial V}{\\partial T} \\right)_P = P\\cdot \\frac{nR}{P} = nR\n\n\\end{array}\n\n<\/span>\n<p>Since <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle  C_V=(\\partial U \/ \\partial T)_V<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=3Nk_BT\/2=3nRT\/2<\/span><\/span>, we have:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\displaystyle  C_V = \\frac{3}{2}nR\n\n<\/span>\n<p>And therefore:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\nC_P = C_V + nR = \\displaystyle  \\frac{3}{2}nR + nR = \\frac{5}{2}nR\n\n<\/span>\n<h3>The Adiabatic Index<\/h3>\n<p>A commonly used quantity is the ratio of <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> to <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span>, which is given a special name. The <strong>adiabatic index<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\gamma<\/span> is defined as:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\gamma = \\displaystyle  \\frac{C_P}{C_V}\n\n<\/span>\n<p>For ideal gases, the adiabatic index has an exact value:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\gamma = \\displaystyle \\frac{5}{3}\n\n<\/span>\n<p><a name=\"5\"><\/a><\/p>\n<h2>Exercises<\/h2>\n<ol>\n<li>\n\t\tIs it always true that <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dU=C_VdT<\/span><\/span>? Compare the general case with that of ideal gases and justify your answer.\n\t<\/li>\n<li>\n\t\tAssuming that for an ideal gas it holds that <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">U=C_VT<\/span><\/span>, calculate:<\/p>\n<ol>\n<li>The internal energy per unit mass.<\/li>\n<li>The internal energy per unit volume.<\/li>\n<\/ol>\n<\/li>\n<li>\n\t\tOne mole of a monatomic ideal gas is confined in a cylinder by a piston and kept at constant temperature <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">T_0<\/span><\/span> through thermal contact with a reservoir. The gas is slowly expanded from a volume <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_1<\/span><\/span> to another volume <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">V_2<\/span><\/span>, maintaining constant temperature throughout the process. <\/p>\n<ol>\n<li>Does the internal energy of the gas change?<\/li>\n<li>Calculate the work done by the gas and the heat flow into the gas.<\/li>\n<\/ol>\n<\/li>\n<li>\n\t\tShow that, for an ideal gas, the following relations hold:<\/p>\n<p style=\"text-align: center;\">\n\t\t\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{C_V} = \\gamma - 1<\/span><\/span>\n\t\t<\/p>\n<p style=\"text-align: center;\">\n\t\t\t<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{R}{C_P} = \\frac{\\gamma - 1}{\\gamma}<\/span><\/span>\n\t\t<\/p>\n<p>Where <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_V<\/span><\/span> and <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">C_P<\/span><\/span> are molar heat capacities.<\/p>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>The First Law of Thermodynamics The First Law of Thermodynamics is the foundation that links fundamental concepts such as heat, work, and internal energy, establishing that energy is neither created nor destroyed, only transformed. This material explores how this law applies to closed systems, delving into the analysis of thermodynamic work, heat capacities, and the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":30854,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":1,"footnotes":""},"categories":[635,919],"tags":[],"class_list":["post-30855","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 v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The First Law of Thermodynamics - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Discover how the First Law of Thermodynamics connects heat, work, and internal energy, as well as its application to closed systems and ideal gases.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\" \/>\n<meta property=\"og:locale\" content=\"es_ES\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The First Law of Thermodynamics\" \/>\n<meta property=\"og:description\" content=\"Discover how the First Law of Thermodynamics connects heat, work, and internal energy, as well as its application to closed systems and ideal gases.\" \/>\n<meta property=\"og:url\" content=\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\" \/>\n<meta property=\"og:site_name\" content=\"toposuranos.com\/material\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/groups\/toposuranos\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-03T13:00:40+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-01-02T04:29:10+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/primeraley-1024x585.jpg\" \/>\n<meta name=\"author\" content=\"giorgio.reveco\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:title\" content=\"The First Law of Thermodynamics\" \/>\n<meta name=\"twitter:description\" content=\"Discover how the First Law of Thermodynamics connects heat, work, and internal energy, as well as its application to closed systems and ideal gases.\" \/>\n<meta name=\"twitter:image\" content=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/primeraley.jpg\" \/>\n<meta name=\"twitter:creator\" content=\"@topuranos\" \/>\n<meta name=\"twitter:site\" content=\"@topuranos\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"giorgio.reveco\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tiempo de lectura\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minuto\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/#article\",\"isPartOf\":{\"@id\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\"},\"author\":{\"name\":\"giorgio.reveco\",\"@id\":\"http:\/\/toposuranos.com\/material\/#\/schema\/person\/e15164361c3f9a2a02cf6c234cf7fdc1\"},\"headline\":\"The First Law of Thermodynamics\",\"datePublished\":\"2021-07-03T13:00:40+00:00\",\"dateModified\":\"2025-01-02T04:29:10+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\"},\"wordCount\":1733,\"commentCount\":0,\"publisher\":{\"@id\":\"http:\/\/toposuranos.com\/material\/#organization\"},\"image\":{\"@id\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/01\/primeraley.jpg\",\"articleSection\":[\"Physics\",\"Thermodynamics\"],\"inLanguage\":\"es\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\",\"url\":\"http:\/\/toposuranos.com\/material\/en\/the-first-law-of-thermodynamics\/\",\"name\":\"The First Law of Thermodynamics - 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