// Numbas version: exam_results_page_options {"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": "
Calculate the total heat absorbed by the water through this process, in kJ, to three significant figures.
", "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": "Calculate the change in temperature of the {Mat_string} in the water, to three significant figures.
", "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": "Calculate the starting temperature of the {mat_string}.
", "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": "\nA room is in complete thermal equilibrium at {temp0} °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} °C.
\n\n\n | Solid {Mat_string} | \nLiquid water | \n
Specific heat capacity | \n{solid_heatcap} JK<sup>-1</sup>kg<sup>-1</sup> | \n{water_heatcap} JK<sup>-1</sup>kg<sup>-1</sup> | \n
a)
\nQ = m * C<sub>{'S'}</sub> * ΔT
Q = {mass2} * {water_heatcap} * ({temp1}-{temp0})
\nQ = {siground(q_water,6)} J
\nSo the heat added to the water is {siground(q_water_kj,3)} kJ.
\nb)
\nThe heat added to the water was taken from the {Mat_string}, so that
\nQ<sub>{Mat_string}</sub> = -{siground(q_water_kj,3)} kJ.
\nQ<sub>{Mat_string}</sub> = m * C<sub>{Mat_string}</sub> * ΔT
\nso
\nΔT = Q<sub>{Mat_string}</sub>/(m * C<sub>{Mat_string}</sub>)
\nΔT = -{siground(q_water,3)}/({mass} * {solid_heatcap})
\nΔT ={siground(d_temp2,3)} K
\nc)
\nCalculate the initial temperature of the {Mat_string} in K:
\nT = {siground(d_temp2*(-1),3)} + {temp0} + 273.15 = {siground(temp2,3)} K
", "name": "Balancing heating in materials", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "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.
"}, "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/"}]}]}], "contributors": [{"name": "Tom Stallard", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/841/"}]}