Two part question, student has to rearrange the heat flow formula (stated in the question) to make T_1 or T_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.
\nNote that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "The amount of heat flowing along a metal rod is given by the formula \\[ Q=CA \\left( \\frac{T_2-T_1}{l} \\right) \\]where \\(C\\) is the thermal conductivity of the metal, \\(A\\) is the cross sectional area of the rod, \\(l\\) is the rod's length and \\(T_1\\) and \\(T_2\\) are the temperatures of the two ends of the rod.
", "advice": "We have \\begin{align}Q&=CA \\left( \\frac{T_2-T_1}{l} \\right)\\quad\\text{divide both sides by }CA\\\\\\frac{Q}{CA}&=\\left( \\frac{T_2-T_1}{l} \\right)\\quad\\text{multiply both sides by }l\\\\\\frac{Ql}{CA}&=\\left( T_2-T_1 \\right)\\quad\\text{add }T_1\\text{ to both sides}\\\\\\frac{Ql}{CA}+T_1&=T_2\\\\T_2&=\\frac{Ql}{CA}+T_1\\end{align}
\n\\begin{align}Q&=CA \\left( \\frac{T_2-T_1}{l} \\right)\\quad\\text{divide both sides by }CA\\\\\\frac{Q}{CA}&=\\left( \\frac{T_2-T_1}{l} \\right)\\quad\\text{multiply both sides by }l\\\\\\frac{Ql}{CA}&=\\left( T_2-T_1 \\right)\\quad\\text{add }T_1\\text{ to both sides}\\\\\\frac{Ql}{CA}+T_1&=T_2\\quad\\text{subtract }\\frac{Ql}{CA}\\text{ from both sides}\\\\T_1&=T_2-\\frac{Ql}{CA}\\end{align}
\nGiven \\(A=\\var{A}\\) m\\(^2\\), \\(l=\\var{l}\\) m, \\(C=50\\) W/mK, \\(Q=\\var{Q}\\) and \\(\\var{other_var}=\\var{L1}^\\circ\\) C we have
\n\\begin{align}T_2&=\\frac{\\var{Q}\\times\\var{l}}{50\\times\\var{A}}+\\var{L1}\\\\&\\approx\\var{precround(value,2)}^\\circ C\\end{align}
\n\\begin{align}T_1&=\\var{L1}-\\frac{\\var{Q}\\times\\var{l}}{50\\times\\var{A}}\\\\&\\approx\\var{precround(value,2)}^\\circ C\\end{align}
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", "templateType": "anything", "can_override": false}, "L1": {"name": "L1", "group": "Ungrouped variables", "definition": "random(50..90 #10)", "description": "Value of \"other_var\" for substitution part of question, random 50 to 90 in steps of 10
", "templateType": "anything", "can_override": false}, "variable": {"name": "variable", "group": "Ungrouped variables", "definition": "[latex('T_1'),latex('T_2')]", "description": "Variables which can be used for rearrangement part of question. Student will be asked to rearrange the heat flow formula with one of these variables as the subject.
", "templateType": "anything", "can_override": false}, "select": {"name": "select", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "selector to determine which variable of the heat flow formula is to be the subject - 0 = T_1, 1 = T_2.
", "templateType": "anything", "can_override": false}, "sel_var": {"name": "sel_var", "group": "Ungrouped variables", "definition": "variable[select]", "description": "Variable selected by select
", "templateType": "anything", "can_override": false}, "answers": {"name": "answers", "group": "Ungrouped variables", "definition": "[expression('T_2-(Q*l)/(C*A)'),expression('(Q*l)/(C*A)+T_1')]", "description": "rearrangements of heat flow formula for each possible variable
", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "answers[select]", "description": "correct formula for the variable selected by select
", "templateType": "anything", "can_override": false}, "other_var": {"name": "other_var", "group": "Ungrouped variables", "definition": "if(sel_var=\"T_1\",latex('T_2'),latex('T_1'))", "description": "unselected variable from \"variable\"
", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "Value of l for substitution part of question, random integer between 2 and 9
", "templateType": "anything", "can_override": false}, "Q": {"name": "Q", "group": "Ungrouped variables", "definition": "random(10..30)", "description": "Value of Q for substitution part of question, random integer between 10 and 30
", "templateType": "anything", "can_override": false}, "values": {"name": "values", "group": "Ungrouped variables", "definition": "[L1-Q*l/(50*A),Q*l/(50*A)+L1]", "description": "values for each form of rearranged equation with given variable values
", "templateType": "anything", "can_override": false}, "value": {"name": "value", "group": "Ungrouped variables", "definition": "values[select]", "description": "correct answer for selected variable after substitution
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\\(\\var{sel_var}=\\)[[0]] (You must show full working on your ahndwriten working for this part to get full marks)
\nIf \\(A=\\var{A}\\) m\\(^2\\), \\(l=\\var{l}\\) m, \\(C=50\\) W/mK, \\(Q=\\var{Q}\\) and \\(\\var{other_var}=\\var{L1}^\\circ\\) C, what is the value of \\(\\var{sel_var}\\)?
\n\\(\\var{sel_var}=\\)[[1]] degrees C (answer to 2 decimal places)
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