// Numbas version: finer_feedback_settings
{"name": "Chemical Thermodynamics: 2nd Law of Thermodynamics", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Chemical Thermodynamics: 2nd Law of Thermodynamics", "tags": [], "metadata": {"description": "<p>Public</p>", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "statement": "", "advice": "<p><strong>Bonus Information (you don't need to know this)</strong>:</p>\n<p></p>\n<p></p>\n<p></p>\n<p>You may be wondering how the two versions of the second law are equivalent to eachother; after all, they seem quite different at first glance:</p>\n<p></p>\n<p></p>\n<p>\"<strong>Heat never flows from a cold body to a hot body</strong>.\" ,</p>\n<p></p>\n<p></p>\n<p>\"<strong>Any spontaneous heat transfer must be accompanied by an increase in the entropy of the Universe</strong>.\" .</p>\n<p></p>\n<p></p>\n<p></p>\n<p>The key to understanding their equivalence is the final formula we covered in this question:</p>\n<p>$\\mathrm{\\Delta S=\\frac{\\Delta Q}{T}}$ ,</p>\n<p></p>\n<p>as it provides a mathematical link between <strong>heat transfer</strong> and <strong>entropy change</strong>.</p>\n<p></p>\n<p></p>\n<p>Let's consider a <strong>hot body</strong> and a <strong>cold body</strong>, at temperatures $\\mathrm{T_{H}}$ and $\\mathrm{T_C}$ respectively, with a heat transfer occurring between them - assume this heat transfer is small enough such that the temperature of each body remains effectively unchanged (this assumption is alright to make, as all macroscopic heat transfers can be viewed as a series of microscopic heat transfers).</p>\n<p>If this heat $\\mathrm{\\Delta Q}$ is transferred <strong>from the hot body to the cold body</strong>, then the <strong>hot body</strong> experiences a heat change of $\\mathrm{-\\Delta Q}$ whilst the <strong>cold body</strong> experiences a heat change of $\\mathrm{+\\Delta Q}$. Thus, the entropy changes for each body are given by:</p>\n<p>$\\mathrm{\\Delta S_H=\\frac{-\\Delta Q}{T_H}}$&nbsp; (a negative entropy change),</p>\n<p></p>\n<p>$\\mathrm{\\Delta S_C=\\frac{+\\Delta Q}{T_C}}$ (a positive entropy change).</p>\n<p></p>\n<p>The temperature of the hot body is trivially greater than that of the cold body, i.e. $\\mathrm{T_H&gt;T_C}$, so dividing by $\\mathrm{T_H}$ will give a smaller result than dividing by $\\mathrm{T_C}$. Thus, the magnitude of the entropy <strong>decrease</strong> for the hot body is <strong>less than</strong> that of the entropy <strong>increase</strong> for the cold body:</p>\n<p>$\\mathrm{\\mid\\Delta S_H\\mid=\\mid\\frac{-\\Delta Q}{T_H}\\mid=\\frac{\\Delta Q}{T_H}\\space &gt;\\space \\mid\\Delta S_C\\mid=\\mid\\frac{+\\Delta Q}{T_C}\\mid=\\frac{\\Delta Q}{T_C}}$ .</p>\n<p></p>\n<p>Thus, because the entropy increase of the cold body outweighs the entropy decrease of the hot body, the <strong>overall</strong> entropy change of the system (the two bodies) must be <strong>positive</strong>.</p>\n<p></p>\n<p></p>\n<p>On the contrary, if we repeated the situation with the heat instead being transferred <strong>from the cold body to the hot body</strong>, then we would have the entropy changes:</p>\n<p>$\\mathrm{\\Delta S_H=\\frac{+\\Delta Q}{T_H}}$&nbsp; (a positive entropy change),</p>\n<p></p>\n<p>$\\mathrm{\\Delta S_C=\\frac{-\\Delta Q}{T_C}}$ (a negative entropy change).</p>\n<p></p>\n<p>Again,&nbsp;the magnitude of the entropy change for the hot body is <strong>less than</strong> that of the entropy change for the cold body; in this situation, that means the entropy decrease outweighs the entropy increase, so the <strong>overall</strong> entropy change of the system (the two bodies) must be <strong>nega</strong><strong>tive</strong>.</p>\n<p></p>\n<p></p>\n<p>So, finally, because of the facts we have just outlined, if we state that spontaneous heat transfers <strong>cannot occur from cold bodies to hot bodies</strong>, then they can <strong>only</strong> occur the other way around - <strong>from hot bodies to cold bodies</strong> - which must <strong>always</strong> be accompanied by an <strong>increase</strong> in the entropy of the Universe; i.e. stating our first version of the second law must <strong>imply</strong> the second version.</p>\n<p>Similarly, if we state that spontaneous heat transfers <strong>must</strong> be accompanied by an <strong>increase in the entropy of the Universe</strong>, then we can <strong>rule out</strong> the occurrence of spontaneous heat transfers <strong>from cold bodies to hot bodies</strong>, as these would be accompanied by <strong>decreases</strong> in the entropy of the Universe; i.e. stating our second version of the second law must imply the first version.</p>\n<p></p>\n<p>As our two versions of the second law <strong>imply eachother</strong>, this makes them effectively <strong>equivalent</strong> statements.</p>\n<p></p>\n<p></p>\n<p>Again, you do <strong>not</strong> need to know this; you should just remember the two versions of the second law themselves.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Complete the following description of the Second Law of Thermodynamics:</p>\n<p></p>\n<p>The 2nd Law of Thermodynamics states that [[0]] never flows from a [[1]] body to a [[2]] body.</p>\n<p></p>\n<p>Alternatively, the law states that any [[3]] heat transfer must be accompanied by [[4]] in the [[5]] of the Universe.</p>\n<p></p>\n<p>Entropy, $\\mathrm{S}$, is the quantitative measure of [[6]].</p>\n<p></p>\n<p>For a system gaining or losing heat, whilst maintaining a rougly fixed temperature, the change in its entropy is expressed by the formula:</p>\n<p></p>\n<p>[[7]]</p>\n<p></p>\n<p>where $\\mathrm{\\Delta Q}$ is the heat transferred [[8]] the system, and $\\mathrm{T}$ is the temperature of the system, measured on the [[9]] scale.</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["heat", "work", "water"], "matrix": ["1", 0, 0], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, 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