// Numbas version: exam_results_page_options {"name": "Balancing heating in materials + wavelength", "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": "Assuming the {Mat_string} is a perfect blackbody, what was the peak wavelength of emission for the {Mat_string} when it was fully heated in the flame, in microns (μm), to three significant figures. Assume Wien's displacement constant k<sub>W</sub> = {kw} μmK.
", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "type": "numberentry", "maxValue": "siground(wavelength,3)+siground(abs(wavelength/100),3)", "marks": "2", "scripts": {}, "minValue": "siground(wavelength,3)-siground(abs(wavelength/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"}, "wavelength": {"description": "", "group": "Q values", "definition": "kw/temp2", "templateType": "anything", "name": "wavelength"}, "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"}, "temp1": {"description": "", "group": "Random variables", "definition": "temp0+random(1.0..10.0#0.1)", "templateType": "anything", "name": "temp1"}, "mass2": {"description": "", "group": "Random variables", "definition": "random(2.0..9.9#0.1)", "templateType": "anything", "name": "mass2"}, "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"}, "material_list": {"description": "", "group": "Lists of values", "definition": "['Silver','Aluminium','Iron','Copper','Gold']", "templateType": "anything", "name": "material_list"}, "d_temp2": {"description": "", "group": "Q values", "definition": "Q_water_kj*(-1000)/(mass*solid_heatcap)", "templateType": "anything", "name": "d_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"}, "temp2": {"description": "", "group": "Q values", "definition": "temp1+273.15-d_temp2", "templateType": "anything", "name": "temp2"}, "kw": {"description": "", "group": "Q values", "definition": "2898", "templateType": "anything", "name": "kw"}, "fusion_temp_list": {"description": "", "group": "Lists of values", "definition": "[1235,933,1811,1357,1337]", "templateType": "anything", "name": "fusion_temp_list"}, "Q_water": {"description": "", "group": "Q values", "definition": "mass2*water_heatcap*(temp1-temp0)", "templateType": "anything", "name": "Q_water"}, "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)
\nFirstly, calculate the initial temperature of the {Mat_string} in K:
\nT = {siground(d_temp2*(-1),3)} + {temp0} + 273.15 = {siground(temp2,3)} K
\nThen calculate the wavelength:
\nWavelength = K<sub>W</sub> / T = {kw} /{siground(temp2,3)}
\nSo the {mat_string} was glowing with a peak at {siground(wavelength,3)} μm.
", "name": "Balancing heating in materials + wavelength", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "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.
"}, "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/"}]}