Mathematically, the definition of entropy is:
\n\n$\\mathrm{dS=\\frac{dQ}{T}}$,
\n\nwhere $\\mathrm{dS}$ is an infinitesimal entropy change; $\\mathrm{dQ}$ is an infinitesimal heat transfer to the system being described (i.e. it has negative value if heat is removed from the system); and $\\mathrm{T}$ is the temperature of the system, in $\\mathrm{K}$.
\n\nThis equation works because the temperature of the system effectively remains constant during an infinitesimal heat transfer, whereas it generally does not work for any macroscopic heat transfer, as the temperature will change due to the heat transfer (the equation would effectively change as we added heat) - however, if the system is large enough, to distribute the heat over a large enough number of particles, then its temperature will remain effectively constant for fairly small heat transfers. This allows us to integrate the formula whilst treating $\\mathrm{T}$ as a constant:
\n$\\mathrm{\\Delta S=\\int dS=\\int \\frac{dQ}{T}=\\frac{\\Delta Q}{T}}$ .
\n\nYou don't need to remember that explanation; just that if a system is large enough to assume a constant temperature, then the entropy change corresponding to a given heat transfer to the system is given by:
\n$\\mathrm{\\Delta S=\\frac{\\Delta Q}{T}}$ .
\n\nNote: If you are asked a question of this type and are not told that the system is large enough to assume constant temperature, but you are only told the heat transfer and one temperature, and expected to come to an answer, then it's probably safe to make the assumption yourself that the temperature remains constant and the entropy change will be given by the above formula.
\n\nWe want to calculate the entropy change of some zinc when $\\mathrm{\\var{heat}\\space kJ}$ of heat is transferred to it at $\\mathrm{\\var{ctemp}°C}$. Let's convert our heat transfer to $\\mathrm{J}$ by multiplying by one thousand, and convert our temperature to $\\mathrm{K}$ by adding $\\mathrm{273.15}$ to it. This gives us a heat transfer of $\\mathrm{\\var{trueheat}\\space J}$ at a temperature of $\\mathrm{\\var{ktemp}\\space K}$.
\n\nWe can now substitute our values into our equation to calculate the entropy change:
\n$\\mathrm{\\Delta S=\\frac{\\Delta Q}{T}}$
\n\n$\\mathrm{\\Rightarrow\\space\\space\\space \\Delta S=\\frac{\\var{trueheat}}{\\var{ktemp}}=\\var{sigformat(entro,3)}\\space J\\space K^{-1}}$ .
", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"entro": {"name": "entro", "group": "Ungrouped variables", "definition": "trueheat/ktemp", "description": "", "templateType": "anything", "can_override": false}, "trueheat": {"name": "trueheat", "group": "Ungrouped variables", "definition": "heat*1000", "description": "", "templateType": "anything", "can_override": false}, "ktemp": {"name": "ktemp", "group": "Ungrouped variables", "definition": "ctemp+273.15", "description": "", "templateType": "anything", "can_override": false}, "heat": {"name": "heat", "group": "Ungrouped variables", "definition": "random(11 .. 75#0.1)", "description": "", "templateType": "randrange", "can_override": false}, "ctemp": {"name": "ctemp", "group": "Ungrouped variables", "definition": "random(5 .. 49#0.1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["entro", "trueheat", "ktemp", "heat", "ctemp"], "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": "Calculate the change in entropy when $\\mathrm{\\var{heat}\\space kJ}$ of energy is transferred to a piece of zinc at $\\mathrm{\\var{ctemp}°C}$ (assume that the mass of zinc is sufficiently large such that its temperature can be considered constant):
\n\n[[0]] $\\mathrm{J\\space K^{-1}}$ .
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "entro-(entro/200)", "maxValue": "entro+(entro/200)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": "50", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en", "scientific"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Frances Docherty", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4059/"}, {"name": "Tess Lynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16608/"}, {"name": "Michael McFadden", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18132/"}], "resources": []}]}], "contributors": [{"name": "Frances Docherty", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4059/"}, {"name": "Tess Lynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16608/"}, {"name": "Michael McFadden", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18132/"}]}