// Numbas version: finer_feedback_settings
{"name": "Balancing heating in materials", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "parts": [{"prompt": "<p>Calculate the total heat absorbed by the water through this process, <strong>in kJ</strong>, to three significant figures. </p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "type": "numberentry", "maxValue": "siground(Q_water_kj,3)+siground(abs(Q_water_kj/100),3)", "marks": "1", "scripts": {}, "minValue": "siground(Q_water_kj,3)-siground(abs(Q_water_kj/100),3)", "variableReplacements": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"prompt": "<p>Calculate the change in temperature of the {Mat_string} in the water, to three significant figures.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "type": "numberentry", "maxValue": "siground(d_temp2,3)+siground(abs(d_temp2/100),3)", "marks": "2", "scripts": {}, "minValue": "siground(d_temp2,3)-siground(abs(d_temp2/100),3)", "variableReplacements": [{"variable": "q_water", "must_go_first": true, "part": "p0"}], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"prompt": "<p>Calculate the starting temperature of the {mat_string}.</p>", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "type": "numberentry", "maxValue": "siground(temp2,3)+siground(abs(temp2/100),3)", "marks": "2", "scripts": {}, "minValue": "siground(temp2,3)-siground(abs(temp2/100),3)", "variableReplacements": [{"variable": "d_temp2", "must_go_first": true, "part": "p1"}], "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "variables": {"water_heatcap": {"description": "", "group": "Material values", "definition": "4200", "templateType": "anything", "name": "water_heatcap"}, "phase1_temp": {"description": "", "group": "Material values", "definition": "fusion_temp_list[wat_mat]", "templateType": "anything", "name": "phase1_temp"}, "mass2": {"description": "", "group": "Random variables", "definition": "random(2.0..9.9#0.1)", "templateType": "anything", "name": "mass2"}, "mass_string": {"description": "", "group": "kg or g", "definition": "if(mass<1,dpformat(mass*1000,0)+' g',dpformat(mass,2)+' kg')", "templateType": "anything", "name": "mass_string"}, "mat_string": {"description": "", "group": "Material values", "definition": "material_list[wat_mat]", "templateType": "anything", "name": "mat_string"}, "d_temp2": {"description": "", "group": "Q values", "definition": "Q_water_kj*(-1000)/(mass*solid_heatcap)", "templateType": "anything", "name": "d_temp2"}, "wavelength": {"description": "", "group": "Q values", "definition": "kw/temp2", "templateType": "anything", "name": "wavelength"}, "solid_hc_list": {"description": "", "group": "Lists of values", "definition": "[240,900,450,390,130]", "templateType": "anything", "name": "solid_hc_list"}, "mass": {"description": "", "group": "Random variables", "definition": "random(0.01..0.99#0.01)", "templateType": "anything", "name": "mass"}, "mass2_string": {"description": "", "group": "kg or g", "definition": "if(mass2<1,dpformat(mass2*1000,0)+' g',dpformat(mass2,2)+' kg')", "templateType": "anything", "name": "mass2_string"}, "temp0": {"description": "", "group": "Random variables", "definition": "random(1.0..40.0#0.1)", "templateType": "anything", "name": "temp0"}, "Q_water": {"description": "", "group": "Q values", "definition": "mass2*water_heatcap*(temp1-temp0)", "templateType": "anything", "name": "Q_water"}, "temp2": {"description": "", "group": "Q values", "definition": "temp1+273.15-d_temp2", "templateType": "anything", "name": "temp2"}, "solid_heatcap": {"description": "", "group": "Material values", "definition": "solid_hc_list[wat_mat]", "templateType": "anything", "name": "solid_heatcap"}, "wat_mat": {"description": "", "group": "Random variables", "definition": "random(0..4)", "templateType": "anything", "name": "wat_mat"}, "fusion_temp_list": {"description": "", "group": "Lists of values", "definition": "[1235,933,1811,1357,1337]", "templateType": "anything", "name": "fusion_temp_list"}, "kw": {"description": "", "group": "Q values", "definition": "2898", "templateType": "anything", "name": "kw"}, "temp1": {"description": "", "group": "Random variables", "definition": "temp0+random(1.0..10.0#0.1)", "templateType": "anything", "name": "temp1"}, "material_list": {"description": "", "group": "Lists of values", "definition": "['Silver','Aluminium','Iron','Copper','Gold']", "templateType": "anything", "name": "material_list"}, "Q_water_kj": {"description": "", "group": "Q values", "definition": "Q_water/1000", "templateType": "anything", "name": "Q_water_kj"}}, "ungrouped_variables": [], "statement": "<p></p>\n<p style=\"text-align: center;\"><strong>A room is in complete thermal equilibrium at {temp0} &deg;C. A {mass_string} lump of {Mat_string} is heated in a flame for several minutes. The {Mat_string} is then transferred quickly into {mass2_string} of water, and the water and {Mat_string} both reach {temp1} &deg;C.&nbsp;</strong></p>\n<p></p>\n<table style=\"margin-left: auto; margin-right: auto;\" border=\"1\">\n<tbody>\n<tr>\n<td></td>\n<td>Solid {Mat_string}</td>\n<td>Liquid water</td>\n</tr>\n<tr>\n<td>Specific heat capacity</td>\n<td>{solid_heatcap} JK&lt;sup&gt;-1&lt;/sup&gt;kg&lt;sup&gt;-1&lt;/sup&gt;</td>\n<td>{water_heatcap} JK&lt;sup&gt;-1&lt;/sup&gt;kg&lt;sup&gt;-1&lt;/sup&gt;</td>\n</tr>\n</tbody>\n</table>", "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": "temp2 < phase1_temp"}, "extensions": ["jsxgraph"], "functions": {"onestep": {"language": "javascript", "type": "html", "parameters": [], "definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"\u00b0C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt = Numbas.jme.unwrapValue(scope.variables.phase_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-4,et+10,20,st-10],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\ndrawZero:true,\ndrawLabels: true,\nlabel: {offset: [20, 0]},\nminorTicks: 0\n});\n\n//\n//slope 1\nvar slope1 = board.create('line',[[4,st],[((pt-st)/((pt-st)+(et-pt))*8)+4,pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope2 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,pt],[16-((et-pt)/((pt-st)+(et-pt))*8),pt]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope3 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),pt],[16,et]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nvar dash1 = board.create('line',[[((pt-st)/((pt-st)+(et-pt))*8)+4,st-5],[((pt-st)/((pt-st)+(et-pt))*8)+4,et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash2 = board.create('line',[[16-((et-pt)/((pt-st)+(et-pt))*8),st-5],[16-((et-pt)/((pt-st)+(et-pt))*8),et+5]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\n  var label = board.create('text',[-2,(et+st)/2,k_c_str]);\n\n\n// and return the container div\nreturn div;"}, "twostep": {"language": "javascript", "type": "html", "parameters": [], "definition": "// Takes variables\n\n// showing K or C?\nk_c = Numbas.jme.unwrapValue(scope.variables.k_c_switch);\n\nif (k_c = 0) {\n    var k_c_corr =0;\n    var k_c_str=\"K\";\n} else {\n     var k_c_corr =-273;\n    var k_c_str=\"\u00b0C\";\n}\n\n//Set values\nst = Numbas.jme.unwrapValue(scope.variables.start_temp)+k_c_corr;\net = Numbas.jme.unwrapValue(scope.variables.end_temp)+k_c_corr;\npt1 = Numbas.jme.unwrapValue(scope.variables.phase1_temp)+k_c_corr;\npt2 = Numbas.jme.unwrapValue(scope.variables.phase2_temp)+k_c_corr;\n\n\n// The function provided by the JSXGraph extension wraps the board up in\n// a div tag so that it's easier to embed in the page.\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','300px',\n    {boundingBox: [-5,et+(et-st)/10.,28,st-(et-st)/10.],\n     axis: false,\n     showNavigation: false,\n     grid: false\n    });\n\n// div.board is the object created by JSXGraph, which you use to\n// manipulate elements\nvar board = div.board;\n\n\n\n// create the x-axis.\n//var xaxis = board.create('line',[[0,0],[1,0]], {strokeColor: 'black', fixed: true});\n//var xticks = board.create('ticks',[xaxis,20],{\n//  drawLabels: true,\n//  minorTicks: 0\n//});\n\n// create the y-axis\n\nvar yaxis = board.create('line',[[0,0],[0,1]], { strokeColor: 'black', fixed: true });\nvar yticks = board.create('ticks',[yaxis,parseInt((et-st)/50.)*10],{\ndrawZero:true,\ndrawLabels: true,\nlabel: {offset: [20, 0]},\nminorTicks: 0\n});\n\n\n// full size of the five slopes\nvar allslope=(et-st);\nvar s1sz=(8*(pt1-st)/allslope);\nvar s3sz=(8*(pt2-pt1)/allslope);\nvar s5sz=(8*(et-pt2)/allslope);\n\n\n//\n//slope 1\nvar slope1 = board.create('line',[[4,st],[s1sz+4,pt1]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope2 = board.create('line',[[s1sz+4,pt1],[s1sz+8,pt1]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope3 = board.create('line',[[s1sz+8,pt1],[s1sz+s3sz+8,pt2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope4 = board.create('line',[[s1sz+s3sz+8,pt2],[s1sz+s3sz+12,pt2]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar slope5 = board.create('line',[[s1sz+s3sz+12,pt2],[s1sz+s3sz+s5sz+12,et]], {straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n//var slope6 = board.create('line',[[4,pt1],[20,pt2]], {dash:2,straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\nvar dash1 = board.create('line',[[s1sz+4,st-10],[s1sz+4,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash2 = board.create('line',[[s1sz+8,st-10],[s1sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash3 = board.create('line',[[s1sz+s3sz+8,st-10],[s1sz+s3sz+8,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\nvar dash4 = board.create('line',[[s1sz+s3sz+12,st-10],[s1sz+s3sz+12,et+10]], {dash:2, strokewidth:1, straightFirst:false, straightLast:false, strokeColor: 'black', fixed: true });\n\n\n//label the y-axis\n  var label = board.create('text',[-2,(et+st)/2,k_c_str]);\n\n\n// and return the container div\nreturn div;"}}, "advice": "<p><strong>a)</strong></p>\n<p>Q = m * C&lt;sub&gt;{'S'}&lt;/sub&gt;&nbsp; * <span class=\"st\" data-hveid=\"41\">&Delta;</span>T<strong><br/></strong></p>\n<p>Q = {mass2} * {water_heatcap} * ({temp1}-{temp0})</p>\n<p>Q = {siground(q_water,6)} J</p>\n<p>So the heat added to the water is {siground(q_water_kj,3)} kJ.</p>\n<p><strong>b)</strong></p>\n<p>The heat added to the water was taken from the {Mat_string}, so that</p>\n<p>Q&lt;sub&gt;{Mat_string}&lt;/sub&gt; = -{siground(q_water_kj,3)} kJ.</p>\n<p>Q&lt;sub&gt;{Mat_string}&lt;/sub&gt; = m * C&lt;sub&gt;{Mat_string}&lt;/sub&gt; * <span class=\"st\" data-hveid=\"41\">&Delta;</span>T</p>\n<p>so</p>\n<p><span class=\"st\" data-hveid=\"41\">&Delta;</span>T = Q&lt;sub&gt;{Mat_string}&lt;/sub&gt;/(m * C&lt;sub&gt;{Mat_string}&lt;/sub&gt;)</p>\n<p><span class=\"st\" data-hveid=\"41\">&Delta;</span>T = -{siground(q_water,3)}/({mass} * {solid_heatcap})</p>\n<p><span class=\"st\" data-hveid=\"41\">&Delta;</span>T ={siground(d_temp2,3)} K</p>\n<p><strong>c)</strong></p>\n<p>Calculate the initial temperature of the {Mat_string} in K:</p>\n<p>T = {siground(d_temp2*(-1),3)} + {temp0} + 273.15 = {siground(temp2,3)} K</p>", "name": "Balancing heating in materials", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A random heating question, that randomly picks a material, and then heats it, then plunges it into water. The student must calculate the energy change in the water, and use this to calculate the original temperature of the material.&nbsp; </p>"}, "tags": [], "variable_groups": [{"variables": ["mass_string", "mass2_string"], "name": "kg or g"}, {"variables": ["mat_string", "phase1_temp", "solid_heatcap", "water_heatcap"], "name": "Material values"}, {"variables": ["material_list", "solid_hc_list", "fusion_temp_list"], "name": "Lists of values"}, {"variables": ["wat_mat", "temp0", "temp1", "mass", "mass2"], "name": "Random variables"}, {"variables": ["Q_water", "Q_water_kj", "d_temp2", "temp2", "wavelength", "kw"], "name": "Q values"}], "type": "question", "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}], "resources": []}]}], "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}]}