{"id":13171,"date":"2026-05-13T07:48:16","date_gmt":"2026-05-13T07:48:16","guid":{"rendered":"https:\/\/www.vedprep.com\/exams\/?p=13171"},"modified":"2026-05-13T08:41:12","modified_gmt":"2026-05-13T08:41:12","slug":"equipartition-of-energy","status":"publish","type":"post","link":"https:\/\/www.vedprep.com\/exams\/iit-jam\/equipartition-of-energy\/","title":{"rendered":"Equipartition of Energy: Master IIT JAM 2027"},"content":{"rendered":"<p><strong>Equipartition of energy<\/strong> is a fundamental concept in thermodynamics that states that in a closed system, the total energy is equally distributed among its degrees of freedom, leading to an equilibrium state. Understanding this concept is essential for IIT JAM and other competitive exams.<\/p>\n<h2><strong>Equipartition of Energy For IIT JAM: Understanding the Concept<\/strong><\/h2>\n<p data-path-to-node=\"1\">Let\u2019s talk about something that sounds heavy but is actually pretty intuitive once you peel back the layers: the <b data-path-to-node=\"1\" data-index-in-node=\"113\">equipartition of energy.<\/b>\u00a0If you&#8217;re prepping for the IIT JAM, you know thermodynamics is a huge chunk of the syllabus. This concept is basically the &#8220;fairness doctrine&#8221; of the molecular world.<\/p>\n<p data-path-to-node=\"2\">At its heart, the theorem says that if a system is in thermal equilibrium, the total energy doesn&#8217;t just hang out in one place. Instead, it gets split up equally among all the different ways a molecule can move. We call these &#8220;ways to move&#8221; <b data-path-to-node=\"2\" data-index-in-node=\"241\">degrees of freedom<\/b>.<\/p>\n<p data-path-to-node=\"3\">Think of it like a group of friends ordering a giant pizza. If everyone is equally hungry and the group is in &#8220;equilibrium,&#8221; each person (or degree of freedom) gets an equal number of slices. In the world of physics, each &#8220;slice&#8221; of energy is exactly \u00bd kT.<\/p>\n<p data-path-to-node=\"4\"><strong>Key Characteristics:<\/strong><\/p>\n<ul data-path-to-node=\"5\">\n<li>\n<p data-path-to-node=\"5,0,0\">Every single degree of freedom grabs \u00bd kT of energy (k\u00a0is the Boltzmann constant, <span class=\"math-inline\" data-math=\"T\" data-index-in-node=\"93\">T<\/span>\u00a0is temperature).<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,1,0\">The energy is spread out like a perfectly divided bill at dinner.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"5,2,0\">This only works when things have settled down into thermal equilibrium.<\/p>\n<\/li>\n<\/ul>\n<h2><strong>Syllabus &#8211; Thermodynamics\u00a0<\/strong><\/h2>\n<p data-path-to-node=\"8\">At <b data-path-to-node=\"8\" data-index-in-node=\"3\">VedPrep<\/b>, we\u2019ve noticed that students often breeze past this topic, thinking it\u2019s just one formula. But in the <a href=\"https:\/\/jam2026.iitb.ac.in\/files\/syllabus_CY.pdf\" rel=\"nofollow noopener\" target=\"_blank\"><strong>IIT JAM syllabus<\/strong><\/a> section, it\u2019s the backbone of understanding heat capacities (<span class=\"math-inline\" data-math=\"C_p\" data-index-in-node=\"201\">C<sub>p<\/sub><\/span> and <span class=\"math-inline\" data-math=\"C_v\" data-index-in-node=\"209\">C<sub>v<\/sub><\/span>).<\/p>\n<p data-path-to-node=\"9\">You\u2019ll find this in the classic &#8220;holy grail&#8221; books like Atkins to cover areas such as <strong>equipartition of energy<\/strong>. The core idea you need to grasp for the exam is how internal energy (<span class=\"math-inline\" data-math=\"U\" data-index-in-node=\"228\">U<\/span>) connects to these degrees of freedom. It\u2019s the bridge between the tiny world of atoms and the big world of temperature readings.<\/p>\n<h2><strong>Equipartition of Energy For IIT JAM: Key Formulas and Equations<\/strong><\/h2>\n<p>Alright, let&#8217;s get into the math, but we&#8217;ll keep it simple. If a system has <span class=\"math-inline\" data-math=\"n\" data-index-in-node=\"76\">$n$<\/span> degrees of freedom, the total energy <span class=\"math-inline\" data-math=\"E\" data-index-in-node=\"115\">E<\/span>\u00a0is:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15978 aligncenter\" src=\"https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/n-degrees-of-freedom.png\" alt=\"n degrees of freedom\" width=\"200\" height=\"82\" \/><\/p>\n<p>If you\u2019re looking at a single degree of freedom (let&#8217;s call it \u03b5<sub><span class=\"math-inline\" data-math=\"\\epsilon_i\" data-index-in-node=\"63\">i<\/span><\/sub>), its average energy is:<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-15979 aligncenter\" src=\"https:\/\/www.vedprep.com\/exams\/wp-content\/uploads\/average-energy.png\" alt=\"average energy\" width=\"192\" height=\"87\" \/><\/p>\n<p data-path-to-node=\"16\"><strong>Let\u2019s break down the degrees of freedom (DOF):<\/strong><\/p>\n<ol start=\"1\" data-path-to-node=\"17\">\n<li>\n<p data-path-to-node=\"17,0,0\"><b data-path-to-node=\"17,0,0\" data-index-in-node=\"0\">Monatomic Gas (like Helium):<\/b> It\u2019s just a tiny dot. It can move up\/down, left\/right, and forward\/backward. That\u2019s 3 translational DOFs. Total energy = <span class=\"math-inline\" data-math=\"\\frac{3}{2} kT\" data-index-in-node=\"150\">3\/2 kT<\/span>.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"17,1,0\"><b data-path-to-node=\"17,1,0\" data-index-in-node=\"0\">Diatomic Gas (like <span class=\"math-inline\" data-math=\"O_2\" data-index-in-node=\"19\">O<sub>2<\/sub><\/span>):<\/b> Imagine a dumbbell. It can move in 3 directions, but it can also rotate like a spinning baton. That adds 2 rotational DOFs. Total energy = <span class=\"math-inline\" data-math=\"\\frac{5}{2} kT\" data-index-in-node=\"164\">5\/2 kT<\/span>.<\/p>\n<\/li>\n<\/ol>\n<h2><strong>Worked Example: Equipartition of Energy for IIT JAM<\/strong><\/h2>\n<p>Imagine you have a container filled with <span class=\"math-inline\" data-math=\"N = 10^{20}\" data-index-in-node=\"41\">N = 10<sup>20<\/sup><\/span><sup>\u00a0<\/sup>molecules of a specific gas. Let\u2019s say this gas is diatomic, so it has 5 degrees of freedom (3 translational + 2 rotational). If the room is at a comfortable 300 K, how much energy are we talking about?<\/p>\n<ol start=\"1\" data-path-to-node=\"21\">\n<li>\n<p data-path-to-node=\"21,0,0\"><b data-path-to-node=\"21,0,0\" data-index-in-node=\"0\">Identify the bits:<\/b> <span class=\"math-inline\" data-math=\"f = 5\" data-index-in-node=\"19\">f = 5<\/span>, <span class=\"math-inline\" data-math=\"N = 10^{20}\" data-index-in-node=\"26\">N = 10<sup>20<\/sup><\/span>, <span class=\"math-inline\" data-math=\"T = 300\\text{ K}\" data-index-in-node=\"39\">T = 300 K<\/span>, and <span class=\"math-inline\" data-math=\"k = 1.38 \\times 10^{-23}\\text{ J\/K}\" data-index-in-node=\"61\">k = 1.38 \u00d7 10-<sup>23<\/sup> J\/K<\/span>.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"21,1,0\"><b data-path-to-node=\"21,1,0\" data-index-in-node=\"0\">Plug it in:<\/b> <span class=\"math-inline\" data-math=\"E = \\frac{f}{2} NkT\" data-index-in-node=\"12\">E = f\/2 NkT<\/span><\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"21,2,0\"><b data-path-to-node=\"21,2,0\" data-index-in-node=\"0\">Do the math:<\/b> <span class=\"math-inline\" data-math=\"E = \\frac{5}{2} \\times 10^{20} \\times 1.38 \\times 10^{-23} \\times 300\" data-index-in-node=\"13\">E = 5\/2 \u00d7 10<sup>20<\/sup> \u00d7 1.38 \u00d7 10<sup>-23<\/sup> \u00d7 300<\/span><\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"21,3,0\"><b data-path-to-node=\"21,3,0\" data-index-in-node=\"0\">Result:<\/b> You get about <b data-path-to-node=\"21,3,0\" data-index-in-node=\"22\">5.175 Joules<\/b>.<\/p>\n<\/li>\n<\/ol>\n<p data-path-to-node=\"22\">It doesn&#8217;t sound like much, but for <span class=\"math-inline\" data-math=\"10^{20}\" data-index-in-node=\"36\">10<sup>20<\/sup><\/span>\u00a0tiny molecules, that&#8217;s a lot of microscopic dancing!<\/p>\n<h2><strong>Misconception: Equipartition of Energy vs. Conservation of Energy<\/strong><\/h2>\n<p data-path-to-node=\"25\">This is a classic trap. We\u2019ve seen plenty of smart students at <b data-path-to-node=\"25\" data-index-in-node=\"63\">VedPrep<\/b> get these two mixed up.<\/p>\n<p data-path-to-node=\"26\"><b data-path-to-node=\"26\" data-index-in-node=\"0\">Conservation of energy<\/b> is the old &#8220;energy can\u2019t be created or destroyed&#8221; rule. It\u2019s about the total amount staying the same. <b data-path-to-node=\"26\" data-index-in-node=\"125\">Equipartition of energy<\/b> is about the <i data-path-to-node=\"26\" data-index-in-node=\"162\">distribution<\/i>.<\/p>\n<p data-path-to-node=\"27\"><b data-path-to-node=\"27\" data-index-in-node=\"0\">The Coffee Shop Scenario:<\/b> &gt; Imagine a fictional scenario where you and four friends go to a coffee shop. Conservation of energy says that if the group brings $50, the group still has $50 after they walk inside. Equipartition says that once you sit down to order, you\u2019ll likely decide to split that $50 so everyone has exactly $10 to spend. One is about the <i>total;<\/i>\u00a0the other is about the <i data-path-to-node=\"27\" data-index-in-node=\"387\">split<\/i>.<\/p>\n<p data-path-to-node=\"28\">Equipartition tells us how the energy likes to &#8220;settle&#8221; once the system finds its groove, or equilibrium.<\/p>\n<h2><strong>Exam Strategy: Tips for Solving Equipartition of Energy Questions<\/strong><\/h2>\n<p data-path-to-node=\"31\">When you\u2019re staring down a JAM paper, the questions usually hide the degrees of freedom. They won\u2019t always tell you &#8220;this molecule has 5 DOFs.&#8221; They\u2019ll say, &#8220;Nitrogen at room temperature. &#8221; You have to know that nitrogen is diatomic and, at room temperature, its vibrations haven&#8217;t &#8220;woken up&#8221; yet.<\/p>\n<p data-path-to-node=\"32\"><strong>Quick Tips:<\/strong><\/p>\n<ul data-path-to-node=\"33\">\n<li>\n<p data-path-to-node=\"33,0,0\"><b data-path-to-node=\"33,0,0\" data-index-in-node=\"0\">Check the Temperature:<\/b> Vibrational degrees of freedom usually only count at very high temperatures. For most JAM problems, stick to translation and rotation unless the question says otherwise.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"33,1,0\"><b data-path-to-node=\"33,1,0\" data-index-in-node=\"0\">now your <span class=\"math-inline\" data-math=\"C_v\" data-index-in-node=\"10\">C<sub>v<\/sub><\/span>:<\/b> Remember that <span class=\"math-inline\" data-math=\"C_v = \\left(\\frac{\\partial U}{\\partial T}\\right)_v\" data-index-in-node=\"29\">C<sub>v<\/sub> = (\u2202U\/\u2202T)<sub>v<\/sub><\/span>. Since <span class=\"math-inline\" data-math=\"U = \\frac{f}{2} RT\" data-index-in-node=\"87\">U = f\/2 RT<\/span> (for one mole), <span class=\"math-inline\" data-math=\"C_v = \\left(\\frac{\\partial U}{\\partial T}\\right)_v\" data-index-in-node=\"29\">C<sub>v<\/sub><\/span> is just <span class=\"math-inline\" data-math=\"\\frac{f}{2} R\" data-index-in-node=\"134\">f\/2 R<\/span>.<\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"33,2,0\"><b data-path-to-node=\"33,2,0\" data-index-in-node=\"0\">Practice:<\/b> We always tell our students that seeing the formula isn&#8217;t the same as using it. Try applying it to different gases like <span class=\"math-inline\" data-math=\"CO_2\" data-index-in-node=\"130\">CO<sub>2<\/sub><\/span> (linear) vs <span class=\"math-inline\" data-math=\"H_2O\" data-index-in-node=\"147\">H<sub>2<\/sub>O<\/span>\u00a0(non-linear).<\/p>\n<\/li>\n<\/ul>\n<p><strong><a href=\"https:\/\/www.vedprep.com\/online-courses\/iit-jam\">VedPrep<\/a> <\/strong>provides students with access to practice problems and solutions, allowing them to assess their knowledge and identify areas for improvement. By following these tips and practicing consistently, students can develop a strong grasp of <strong>equipartition of energy<\/strong> and excel in their exams.<\/p>\n<h2><strong>Solved Problems: Equipartition of Energy For IIT JAM<\/strong><\/h2>\n<p data-path-to-node=\"36\">Let&#8217;s look at something a bit more advanced\u2014spins in a magnetic field.<\/p>\n<p data-path-to-node=\"37\">If you have a bunch of non-interacting &#8220;spins&#8221; (think of them as tiny magnets), they can either point up or down. In a magnetic field, these two states have different energies (<span class=\"math-inline\" data-math=\"+\\mu B\" data-index-in-node=\"177\">+\u03bcB$<\/span> and <span class=\"math-inline\" data-math=\"-\\mu B\" data-index-in-node=\"188\">-\u03bcB<\/span>).<\/p>\n<p data-path-to-node=\"38\">While the math involves something called a <b>partition function<\/b>\u00a0(<span class=\"math-inline\" data-math=\"Z\" data-index-in-node=\"63\">Z<\/span>), the big takeaway is how the energy behaves at high temperatures. When things get really hot, the energy distribution tries to even out, following the spirit of the equipartition theorem. At high <span class=\"math-inline\" data-math=\"T\" data-index-in-node=\"262\">T<\/span>, the average energy ends up being nearly zero because the &#8220;ups&#8221; and &#8220;downs&#8221; cancel each other out in the chaos.<\/p>\n<h2 data-path-to-node=\"3\"><strong>Conclusion<\/strong><\/h2>\n<p data-path-to-node=\"41\">Getting a handle on the <b data-path-to-node=\"41\" data-index-in-node=\"24\">equipartition of energy<\/b> is a major win for your IIT JAM 2027 prep. It\u2019s the secret sauce that explains why different gases heat up at different rates. Once you get used to counting degrees of freedom, you\u2019ll start seeing these problems as easy points on the board.<\/p>\n<p data-path-to-node=\"42\">Just remember: the &#8220;law&#8221; isn&#8217;t perfect. When things get super cold, quantum mechanics steps in and ruins the party (we call this the &#8220;freezing&#8221; of degrees of freedom). But for most of your exam prep, just remember the &#8220;equal split&#8221; rule and you&#8217;ll be golden.<\/p>\n<p data-path-to-node=\"5\">To know more in detail from our faculty, watch our YouTube video:<\/p>\n<p class=\"responsive-video-wrap clr\"><iframe title=\"Thermodynamics | Internal Energy | Degree of Freedom | Equipartition of Energy | Chem Academy\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/KCmqlfmlOy4?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/p>\n<section>\n<h2><strong>Frequently Asked Questions<\/strong><\/h2>\n<\/section>\n<style>#sp-ea-13920 .spcollapsing { height: 0; overflow: hidden; transition-property: height;transition-duration: 300ms;}#sp-ea-13920.sp-easy-accordion>.sp-ea-single {margin-bottom: 10px; border: 1px solid #e2e2e2; }#sp-ea-13920.sp-easy-accordion>.sp-ea-single>.ea-header a {color: #444;}#sp-ea-13920.sp-easy-accordion>.sp-ea-single>.sp-collapse>.ea-body {background: #fff; color: #444;}#sp-ea-13920.sp-easy-accordion>.sp-ea-single {background: #eee;}#sp-ea-13920.sp-easy-accordion>.sp-ea-single>.ea-header a .ea-expand-icon { float: left; color: #444;font-size: 16px;}<\/style><div id=\"sp_easy_accordion-1777118304\">\n<div id=\"sp-ea-13920\" class=\"sp-ea-one sp-easy-accordion\" data-ea-active=\"ea-click\" data-ea-mode=\"vertical\" data-preloader=\"\" data-scroll-active-item=\"\" data-offset-to-scroll=\"0\">\n\n<!-- Start accordion card div. -->\n<div class=\"ea-card ea-expand sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139200\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139200\" aria-controls=\"collapse139200\" href=\"#\"  aria-expanded=\"true\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-minus\"><\/i> What is the law of equipartition of energy?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse collapsed show\" id=\"collapse139200\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139200\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>It states that for a system in thermal equilibrium, the total energy is distributed equally among all its independent degrees of freedom.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139201\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139201\" aria-controls=\"collapse139201\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What is a \"Degree of Freedom\" (f) in thermodynamics?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139201\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139201\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>It refers to the number of independent coordinates or ways a molecule can move (translate, rotate, or vibrate) in space.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139202\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139202\" aria-controls=\"collapse139202\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Who proposed the Equipartition Theorem?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139202\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139202\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>The theorem was primarily developed by James Clerk Maxwell and later refined by Ludwig Boltzmann.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139203\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139203\" aria-controls=\"collapse139203\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Is the equipartition of energy applicable to all systems?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139203\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139203\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>No, it is strictly applicable to classical systems in thermal equilibrium where the energy depends quadratically on the coordinates\/momenta.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139204\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139204\" aria-controls=\"collapse139204\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> How many degrees of freedom does a monatomic gas have?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139204\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139204\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>A monatomic gas (like Helium) has 3 degrees of freedom, all of which are translational (<span class=\"math-inline\" data-math=\"f = 3\" data-index-in-node=\"143\">f = 3<\/span>).<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139205\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139205\" aria-controls=\"collapse139205\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What are the degrees of freedom for a diatomic molecule at room temperature?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139205\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139205\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>It typically has 5 degrees of freedom: 3 translational and 2 rotational (<span class=\"math-inline\" data-math=\"f = 5\" data-index-in-node=\"150\">f = 5<\/span>).<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139206\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139206\" aria-controls=\"collapse139206\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Why are vibrational degrees of freedom ignored at room temperature?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139206\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139206\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>Vibrational modes require higher energy levels to be \"excited.\" At room temperature, <span class=\"math-inline\" data-math=\"k_B T\" data-index-in-node=\"153\">k<sub>B<\/sub> T<\/span>\u00a0is usually insufficient to activate these modes.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139207\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139207\" aria-controls=\"collapse139207\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> How many degrees of freedom does a non-linear polyatomic molecule have?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139207\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139207\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>It has 6 degrees of freedom: 3 translational and 3 rotational.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139208\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139208\" aria-controls=\"collapse139208\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What is the formula for the total internal energy (U) using this theorem?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139208\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139208\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>The formula is <span class=\"math-inline\" data-math=\"U = \\frac{f}{2} nRT\" data-index-in-node=\"89\">U = (f\/2) nRT$<\/span>, where <span class=\"math-inline\" data-math=\"n\" data-index-in-node=\"116\">n<\/span>\u00a0is the number of moles and <span class=\"math-inline\" data-math=\"f\" data-index-in-node=\"145\">$f$<\/span> is the degrees of freedom.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-139209\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse139209\" aria-controls=\"collapse139209\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Why does the equipartition theorem fail at very low temperatures?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse139209\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-139209\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>At low temperatures, quantum effects become dominant, and energy levels become discrete (quantized), leading to \"frozen\" degrees of freedom.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-1392010\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse1392010\" aria-controls=\"collapse1392010\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What is the difference between Equipartition and Conservation of Energy?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse1392010\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-1392010\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>Equipartition describes the <i data-path-to-node=\"9,1,0\" data-index-in-node=\"101\">distribution<\/i> of energy at equilibrium, while Conservation states that total energy remains constant in an isolated system.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-1392011\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse1392011\" aria-controls=\"collapse1392011\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> What is the most common mistake students make in JAM questions on this topic?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse1392011\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-1392011\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>Students often forget to check if the molecule is linear or non-linear before assigning rotational degrees of freedom.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-1392012\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse1392012\" aria-controls=\"collapse1392012\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> Does the equipartition theorem apply to potential energy?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse1392012\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-1392012\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>Yes, but only if the potential energy is a quadratic function of the coordinates (like a simple harmonic oscillator).<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<!-- Start accordion card div. -->\n<div class=\"ea-card  sp-ea-single\">\n\t<!-- Start accordion header. -->\n\t<h3 class=\"ea-header\">\n\t\t<!-- Add anchor tag for header. -->\n\t\t<a class=\"collapsed\" id=\"ea-header-1392013\" role=\"button\" data-sptoggle=\"spcollapse\" data-sptarget=\"#collapse1392013\" aria-controls=\"collapse1392013\" href=\"#\"  aria-expanded=\"false\" tabindex=\"0\">\n\t\t<i aria-hidden=\"true\" role=\"presentation\" class=\"ea-expand-icon eap-icon-ea-expand-plus\"><\/i> How does temperature affect the degrees of freedom?\t\t<\/a> <!-- Close anchor tag for header. -->\n\t<\/h3>\t<!-- Close header tag. -->\n\t<!-- Start collapsible content div. -->\n\t<div class=\"sp-collapse spcollapse \" id=\"collapse1392013\" data-parent=\"#sp-ea-13920\" role=\"region\" aria-labelledby=\"ea-header-1392013\">  <!-- Content div. -->\n\t\t<div class=\"ea-body\">\n\t\t<p>As temperature increases, more degrees of freedom (like vibration) \"unlock\" or contribute to the specific heat.<\/p>\n\t\t<\/div> <!-- Close content div. -->\n\t<\/div> <!-- Close collapse div. -->\n<\/div> <!-- Close card div. -->\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Equipartition of energy is a fundamental concept in thermodynamics that states that in a closed system, the total energy is equally distributed among its degrees of freedom. Understanding this concept is essential for IIT JAM and other competitive exams.<\/p>\n","protected":false},"author":11,"featured_media":13170,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","rank_math_seo_score":88},"categories":[23],"tags":[2923,7273,7274,8538,7275,2922],"class_list":["post-13171","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-iit-jam","tag-competitive-exams","tag-equipartition-of-energy-for-iit-jam","tag-equipartition-of-energy-for-iit-jam-notes","tag-equipartition-of-energy-for-iit-jam-practice","tag-equipartition-of-energy-for-iit-jam-questions","tag-vedprep","entry","has-media"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/13171","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/comments?post=13171"}],"version-history":[{"count":6,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/13171\/revisions"}],"predecessor-version":[{"id":15983,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/posts\/13171\/revisions\/15983"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media\/13170"}],"wp:attachment":[{"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/media?parent=13171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/categories?post=13171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vedprep.com\/exams\/wp-json\/wp\/v2\/tags?post=13171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}