A random heating question, that randomly picks a material, and then heats it through either one or two phase changes, provides an example graph of the heating with scaled temperature ranges (though not with scaled latent and specific heats), and a table with the suitable constants.
", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Josh's copy of Heating/phase change", "preamble": {"js": "", "css": ""}, "ungrouped_variables": [], "variable_groups": [{"variables": ["switcharoo_comment", "switcharoo_type", "phase_temp", "phase_latentheat"], "name": "switcharoo (phase type) values"}, {"variables": ["mass_string"], "name": "kg or g"}, {"variables": ["mat_string", "phase1_temp", "phase2_temp", "gas_heatcap", "phase1_latentheat", "liquid_heatcap", "phase2_latentheat", "solid_heatcap"], "name": "Material values"}, {"variables": ["solidheat", "fusionheat", "liquidheat", "vapourheat", "gasheat", "totalheat", "totalheat_m"], "name": "Energy"}, {"variables": ["st_string", "et_string"], "name": "K or C"}, {"variables": ["material_list", "solid_hc_list", "liquid_hc_list", "gas_hc_list", "fusion_lh_list", "vapour_lh_list", "fusion_temp_list", "vapour_temp_list"], "name": "Lists of values"}, {"variables": ["switcharoo", "wat_mat", "start_temp", "end_temp", "k_c_switch", "mass"], "name": "Random variables"}, {"variables": ["advice1", "advice2", "advice3", "advice4", "advice5"], "name": "advice"}], "extensions": ["jsxgraph"], "functions": {"onestep": {"parameters": [], "language": "javascript", "type": "html", "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=\"oC\";\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": {"parameters": [], "language": "javascript", "type": "html", "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=\"oC\";\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;"}}, "rulesets": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "type": "question", "variables": {"vapourheat": {"description": "", "name": "vapourheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo>0,mass*phase2_latentheat,0),6)"}, "switcharoo": {"description": "", "name": "switcharoo", "group": "Random variables", "templateType": "anything", "definition": "random(0..2)"}, "mass_string": {"description": "", "name": "mass_string", "group": "kg or g", "templateType": "anything", "definition": "if(mass<1,dpformat(mass*1000,0)+' g',dpformat(mass,2)+' kg')"}, "phase1_latentheat": {"description": "", "name": "phase1_latentheat", "group": "Material values", "templateType": "anything", "definition": "fusion_lh_list[wat_mat]"}, "start_temp": {"description": "", "name": "start_temp", "group": "Random variables", "templateType": "anything", "definition": "if(switcharoo<2,random(100..phase1_temp-10),random(phase1_temp+10..phase2_temp-10))"}, "advice3": {"description": "", "name": "advice3", "group": "advice", "templateType": "anything", "definition": "\"Heating the liquid: $Q = m \\\\times C_L \\\\times \\\\Delta T = \"+\nswitch(\n switcharoo=0,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+end_temp+\" - \"+phase1_temp+\")\",\n switcharoo=1,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+phase2_temp+\" - \"+phase1_temp+\")\",\n switcharoo=2,mass+' \\\\times '+liquid_heatcap+\" \\\\times (\"+phase2_temp+\" - \"+start_temp+\")\"\n)\n+\"= {liquidheat} J$\""}, "end_temp": {"description": "", "name": "end_temp", "group": "Random variables", "templateType": "anything", "definition": "if(switcharoo>0,random(phase2_temp+10..phase2_temp+100),random(phase1_temp+10..phase2_temp-10))"}, "vapour_temp_list": {"description": "", "name": "vapour_temp_list", "group": "Lists of values", "templateType": "anything", "definition": "[373,630,2835,3243]"}, "switcharoo_comment": {"description": "", "name": "switcharoo_comment", "group": "switcharoo (phase type) values", "templateType": "list of strings", "definition": "[ \"solid_to_liquid\", \"solid_to_gas\", \"liquid_to_gas\" ]"}, "et_string": {"description": "", "name": "et_string", "group": "K or C", "templateType": "anything", "definition": "if(k_c_switch,end_temp+' K',(end_temp-273)+' \u00b0C') "}, "liquid_hc_list": {"description": "", "name": "liquid_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[4200,140,490,150]"}, "solid_hc_list": {"description": "", "name": "solid_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[2100,110,390,130]"}, "switcharoo_type": {"description": "", "name": "switcharoo_type", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switcharoo_comment[switcharoo]"}, "phase2_temp": {"description": "", "name": "phase2_temp", "group": "Material values", "templateType": "anything", "definition": "vapour_temp_list[wat_mat]"}, "st_string": {"description": "", "name": "st_string", "group": "K or C", "templateType": "anything", "definition": "if(k_c_switch,start_temp+' K',(start_temp-273)+' \u00b0C') "}, "solidheat": {"description": "", "name": "solidheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo<2,mass*solid_heatcap*(phase1_temp-start_temp),0),6)"}, "advice4": {"description": "", "name": "advice4", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=0,\" \",\"Vaporising the \"+Mat_string+\": $Q = m \\\\times L_H = \"+mass+\" \\\\times \"+phase2_latentheat+\" = \"+vapourheat+\" J$\")"}, "fusionheat": {"description": "", "name": "fusionheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo<2,mass*phase1_latentheat,0),6)"}, "wat_mat": {"description": "", "name": "wat_mat", "group": "Random variables", "templateType": "anything", "definition": "random(0..3)"}, "phase2_latentheat": {"description": "", "name": "phase2_latentheat", "group": "Material values", "templateType": "anything", "definition": "vapour_lh_list[wat_mat]"}, "advice1": {"description": "", "name": "advice1", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=2,\" \",\"Heating the solid: $Q = m \\\\times C_S \\\\times \\\\Delta T = \"+mass+\" \\\\times \"+solid_heatcap+\" \\\\times (\"+phase1_temp+\"-\"+start_temp+\") = \"+solidheat+\" J $\")"}, "advice5": {"description": "", "name": "advice5", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=0,\" \",\"Heating the gas: $Q = m \\\\times C_G \\\\times \\\\Delta T = \"+mass+\" \\\\times \"+gas_heatcap+\" (\"+end_temp+\"-\"+phase2_temp+\") = \"+gasheat+\" J$\")"}, "advice2": {"description": "", "name": "advice2", "group": "advice", "templateType": "anything", "definition": "if(switcharoo=2,\" \",\"Melting the \"+Mat_string+\": $Q = m \\\\times L_H = \"+mass+\" \\\\times \"+phase1_latentheat+\" = \"+fusionheat+\" J$\")"}, "mass": {"description": "", "name": "mass", "group": "Random variables", "templateType": "anything", "definition": "siground(if(random(0,1)=0,random(0.01..0.99#0.01),random(1.00..10.00#0.01)),3)"}, "phase_latentheat": {"description": "", "name": "phase_latentheat", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switch(switcharoo=0,phase1_latentheat,switcharoo=2,phase2_latentheat,0)"}, "totalheat": {"description": "", "name": "totalheat", "group": "Energy", "templateType": "anything", "definition": "solidheat+fusionheat+liquidheat+vapourheat+gasheat"}, "liquid_heatcap": {"description": "", "name": "liquid_heatcap", "group": "Material values", "templateType": "anything", "definition": "liquid_hc_list[wat_mat]"}, "phase_temp": {"description": "", "name": "phase_temp", "group": "switcharoo (phase type) values", "templateType": "anything", "definition": "switch(switcharoo=0,phase1_temp,switcharoo=2,phase2_temp,0)"}, "fusion_lh_list": {"description": "", "name": "fusion_lh_list", "group": "Lists of values", "templateType": "anything", "definition": "[336000,11300,207000,63000]"}, "k_c_switch": {"description": "", "name": "k_c_switch", "group": "Random variables", "templateType": "anything", "definition": "random(0,1)"}, "gas_heatcap": {"description": "", "name": "gas_heatcap", "group": "Material values", "templateType": "anything", "definition": "gas_hc_list[wat_mat]"}, "material_list": {"description": "", "name": "material_list", "group": "Lists of values", "templateType": "anything", "definition": "['H2O','Mercury','Copper','Gold']"}, "fusion_temp_list": {"description": "", "name": "fusion_temp_list", "group": "Lists of values", "templateType": "anything", "definition": "[273,234,1357,1337]"}, "liquidheat": {"description": "", "name": "liquidheat", "group": "Energy", "templateType": "anything", "definition": "siground(switch(switcharoo=0,mass*liquid_heatcap*(end_temp-phase1_temp),switcharoo=1,mass*liquid_heatcap*(phase2_temp-phase1_temp),switcharoo=2,mass*liquid_heatcap*(phase2_temp-start_temp),0),6)"}, "solid_heatcap": {"description": "", "name": "solid_heatcap", "group": "Material values", "templateType": "anything", "definition": "solid_hc_list[wat_mat]"}, "gasheat": {"description": "", "name": "gasheat", "group": "Energy", "templateType": "anything", "definition": "siground(if(switcharoo>0,mass*gas_heatcap*(end_temp-phase2_temp),0),6)"}, "totalheat_m": {"description": "", "name": "totalheat_m", "group": "Energy", "templateType": "anything", "definition": "totalheat/10^6"}, "gas_hc_list": {"description": "", "name": "gas_hc_list", "group": "Lists of values", "templateType": "anything", "definition": "[2000,135,350,110]"}, "phase1_temp": {"description": "", "name": "phase1_temp", "group": "Material values", "templateType": "anything", "definition": "fusion_temp_list[wat_mat]"}, "vapour_lh_list": {"description": "", "name": "vapour_lh_list", "group": "Lists of values", "templateType": "anything", "definition": "[2260000,293000,4730000,1580000]"}, "mat_string": {"description": "", "name": "mat_string", "group": "Material values", "templateType": "anything", "definition": "material_list[wat_mat]"}}, "parts": [{"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["Solid, Liquid
", "Solid, Liquid, Gas
", "Liquid, Gas
"], "type": "1_n_2", "displayType": "radiogroup", "prompt": "What phases does the {mat_string} go through.
", "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacements": [], "distractors": ["", "", ""], "minMarks": 0, "matrix": ["if(switcharoo=0,1,0)", "if(switcharoo=1,1,0)", "if(switcharoo=2,1,0)"], "scripts": {}, "customMarkingAlgorithm": "", "displayColumns": 0}, {"showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "choices": ["Melting
", "Melting,Vaporisation
", "Vaporisation
"], "type": "1_n_2", "displayType": "radiogroup", "prompt": "What phase changes does the {mat_string} go through.
", "showCellAnswerState": true, "marks": 0, "showCorrectAnswer": true, "maxMarks": 0, "extendBaseMarkingAlgorithm": true, "shuffleChoices": false, "variableReplacements": [], "distractors": ["", "", ""], "minMarks": 0, "matrix": ["if(switcharoo=0,1,0)", "if(switcharoo=1,1,0)", "if(switcharoo=2,1,0)"], "scripts": {}, "customMarkingAlgorithm": "", "displayColumns": 0}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "maxValue": "siground(totalheat_m,3)+siground(abs(totalheat_m/100),3)", "minValue": "siground(totalheat_m,3)-siground(abs(totalheat_m/100),3)", "marks": "1", "allowFractions": false, "type": "numberentry", "mustBeReduced": false, "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "prompt": "Calculate the total heat absorbed by the {Mat_string} through this process in MJ to three significant figures.
", "showCorrectAnswer": false, "strictPrecision": true, "precision": "3", "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "precisionType": "sigfig"}], "statement": "{mass_string} of {Mat_string} is heated from {st_string} to {et_string}, changing in temperature and phase.
\n\n{if(switcharoo=1,twostep(),onestep())}
\n| \n | Solid specific heat | \nLatent Heat of fusion | \nLiquid specific heat | \nLatent Heat of vapourisation | \nGaseous specific heat | \nFusion Temperature | \nVaporisation Temperature | \n
| {Mat_string} | \n{solid_heatcap} JK<sup>-1</sup>kg<sup>-1</sup> | \n{phase1_latentheat} Jkg<sup>-1</sup> | \n{liquid_heatcap} JK<sup>-1</sup>kg<sup>-1</sup> | \n{phase2_latentheat} Jkg<sup>-1</sup> | \n{gas_heatcap} JK<sup>-1</sup>kg<sup>-1</sup> | \n{phase1_temp} K | \n{phase2_temp} K | \n
{advice1}
\n{advice2}
\n{advice3}
\n{advice4}
\n{advice5}
\n\nTotal Heat:
\n{totalheat} J = {sigformat(totalheat/1000000,3)} MJ
", "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}]}]}], "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}, {"name": "Josh Lim", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2990/"}]}