// Numbas version: exam_results_page_options {"name": "Assignment 2", "metadata": {"description": "

MECE3930U: Heat Transfer Assignment 2

\n

Please follow the Numbas guidance first if you did not attend the Numbas session.

", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", ""], "questions": [{"name": "A2Q1 v2", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "

The student enters a quantity with units.

", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "

The scalar part of the student's quantity

", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "

The units of the student's quantity, before converting.

", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "

The units of the student's quantity.

\n

If the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.

", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "

The student's answer, interpreted as a quantity.

\n

Marking fails if the student does not enter a valid quantity.

", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "

Are the units of the student's quantity compatible with the units of the expected quantity?

", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "

/Are the student's quantity and the expected quantity in exactly the same units?

", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "

Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.

", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "

Is the student's quantity within the allowed tolerance of the expected answer?

", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "

Is the scalar part of the student's answer a valid number?

", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:
\n", "input_type": "dropdown", "default_value": "incorrect", "choices": [{"value": "incorrect", "label": "Mark as incorrect"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "convert", "label": "Mark as if correct units used"}]}, {"name": "different_units_action", "label": "What to do if different units used", "help_url": "", "hint": "If the student's answer is given in different units to the expected answer:
\n", "input_type": "dropdown", "default_value": "convert", "choices": [{"value": "convert", "label": "Convert"}, {"value": "warn", "label": "Warn and convert"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "incorrect", "label": "Mark incorrect"}]}, {"name": "different_units_penalty", "label": "Penalty if different units used", "help_url": "", "hint": "This penalty is applied if the student gives their answer in different units to the expected answer. The selected percentage of the student's score is taken away.", "input_type": "percent", "default_value": "100"}, {"name": "wiggle", "label": "Margin of error", "help_url": "", "hint": "The student's answer is marked correct if the difference between it and the correct answer is at most this value, measured in the same units as the correct answer.", "input_type": "mathematical_expression", "default_value": "10^-12", "subvars": true}], "public_availability": "always", "published": true, "extensions": ["quantities"]}, {"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "

The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

", "help_url": "", "input_widget": "radios", "input_options": {"correctAnswer": "if(eval(settings[\"correct_answer_expr\"]), 0, 1)", "hint": {"static": true, "value": ""}, "choices": {"static": true, "value": ["Yes", "No"]}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\nif(studentanswer=correct_answer,\n correct(),\n incorrect()\n)\n\ninterpreted_answer:\nstudentAnswer=0\n\ncorrect_answer:\nif(eval(settings[\"correct_answer_expr\"]),0,1)", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "if(studentanswer=correct_answer,\n correct(),\n incorrect()\n)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "studentAnswer=0"}, {"name": "correct_answer", "description": "", "definition": "if(eval(settings[\"correct_answer_expr\"]),0,1)"}], "settings": [{"name": "correct_answer_expr", "label": "Is the answer \"Yes\"?", "help_url": "", "hint": "An expression which evaluates to true or false.", "input_type": "mathematical_expression", "default_value": "true", "subvars": false}], "public_availability": "always", "published": true, "extensions": []}], "resources": [["question-resources/Capture_uT4SIJA.PNG", "/srv/numbas/media/question-resources/Capture_uT4SIJA.PNG"], ["question-resources/A2Q1_v2.png", "/srv/numbas/media/question-resources/A2Q1_v2.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Seama Koohi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4775/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

\n

A thin tube has a diameter of $\\var{d1}$ mm. Inside the tube, there is a cold fluid flow at $\\var{Tf}$K. Outside the tube, air flows at $\\var{To1}$K with convection coefficient of $\\var{h}$ W/m2K.

", "advice": "", "rulesets": {}, "variables": {"To1": {"name": "To1", "group": "Ungrouped variables", "definition": "random(260 .. 280#1)", "description": "

Temperature of the flowing air at the outside.

", "templateType": "randrange"}, "Tf": {"name": "Tf", "group": "Ungrouped variables", "definition": "random(245 .. 258#1)", "description": "

Cold fluid temperature, inside the tube (K).

", "templateType": "randrange"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(80 .. 120#1)", "description": "

Convection coefficient (W/m^2K).

", "templateType": "randrange"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(8 .. 16#2)", "description": "

Thin tube diameter (mm).

", "templateType": "randrange"}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "d1/2", "description": "", "templateType": "anything"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "h*2*pi*(r1/1000)*(To1-Tf)", "description": "", "templateType": "anything"}, "r2": {"name": "r2", "group": "Ungrouped variables", "definition": "random(2 .. 5#0.5)", "description": "

Frost layer thickness (mm).

", "templateType": "randrange"}, "r3": {"name": "r3", "group": "Ungrouped variables", "definition": "random(5 .. 10#1)", "description": "

Frost layer thickness, grown case (mm). 

", "templateType": "randrange"}, "q2": {"name": "q2", "group": "Ungrouped variables", "definition": "(To1-Tf)/((1/(h*2*pi*((r1+r2)/1000)))+ln((r2+r1)/r1)/(2*pi*k))", "description": "", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(0.2 .. 0.8#0.1)", "description": "", "templateType": "randrange"}, "Re3": {"name": "Re3", "group": "Ungrouped variables", "definition": "(1/(h*2*pi*((r1+r3)/1000)))", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["To1", "Tf", "h", "d1", "r1", "r3", "r2", "k", "q", "q2", "Re3"], "variable_groups": [{"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": true, "customName": "Part 1.a", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the direction of the heat flow?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["From the cold fluid to the air, in radial direction.", "From the cold fluid to the air, in radial direction and from cold fluid to the tube, in axial direction", "From the air to the cold fluid, in radial direction.", "From the air to the cold fluid, in radial direction and from air to the tube, in axial direction"], "matrix": [0, 0, "0.3", 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.b", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What mode of heat transfer is dominant between the tube and the air?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Conduction", "Convection", "Radiation", "All"], "matrix": [0, "0.3", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.c", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What mode of heat transfer is dominant between the tube and the cold fluid?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Conduction", "Convection", "Radiation", "All"], "matrix": [0, "0.2", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.d", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What mode of heat transfer is dominant in the tube layer?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Conduction", "Convection", "Radiation", "All"], "matrix": ["0.3", "0", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.e", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

If the tube is thin, how would its temperature vary in the radial direction?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Does not vary much", "

Varies significantly

", "

Cannot comment

"], "matrix": ["0.3", 0, 0], "distractors": ["", "", ""]}, {"type": "yes-no", "useCustomName": true, "customName": "Part 1.e", "marks": "0.3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

If the tube is thin, can we assume the negligible temperature change between its inner and outter sides?

", "settings": {"correct_answer_expr": "true"}}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.f", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

If the convection heat transfer coefficient of the cold fluid is very very large, what is the temperature of the tube wall at the inner surface of the tube?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["Larger than the cold fluid", "Same as the cold fluid", "Smaller than the cold fluid", "All of the choices are possible"], "matrix": [0, "0.3", 0, 0], "distractors": ["", "", "", ""]}, {"type": "quantity", "useCustomName": true, "customName": "Part 2", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the heat flow rate per unit length of the tube? 

\n

q'=? (W/m)

", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Hint: Use the information above to find the temperature of the tube outer surface first and calculate the heat flow rate per unit length then.

"}], "settings": {"correctAnswer": "qty(q,\"W/m\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "quantity", "useCustomName": true, "customName": "Part 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

In more humid conditions, the water vapor in the air creates a $\\var{r2}$ mm thick frost layer on the outer side of the tube. What is the heat flow rate per unit length with the frost layer assuming the frost conductivity is $\\var{k}$ W/mK? (ignore heat transfer due to frost formation)

\n

q2'=? (W/m)

", "stepsPenalty": 0, "steps": [{"type": "1_n_2", "useCustomName": true, "customName": "MC", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

How is the frost layer changing thermal resistance between the fluid and the air?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

Does not change it

", "Makes it larger", "

Makes it smaller

", "

All of the choices are possible

"], "matrix": [0, "0.25", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "MC", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

How is the frost layer changing heat transfer rate between the fluid and the air?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

Does not change it

", "Makes it larger", "

Makes it smaller

", "

All of the choices are possible

"], "matrix": [0, "0", "0.25", 0], "distractors": ["", "", "", ""]}, {"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Hint: Do exactly as before, but this time include the frost layer in your analysis. Thermal circuit analysis might help too, although it is not the only way you can solve this.

"}], "settings": {"correctAnswer": "qty(q2,\"W/m\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "quantity", "useCustomName": true, "customName": "Part 4", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

If the frost layer thickness grows to $\\var{r3}$ mm, how does thermal resistance for convection heat transfer per unit length vary?

\n

Provide the new thermal resistance for convection heat transfer.

\n

Please provide your answer in the following example format: 5.26 m*kelvin/W

\n

", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Hint: Do exactly as before, but this time with an increased frost layer thickness.

"}], "settings": {"correctAnswer": "qty(Re3,\"m*kelvin/W\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "prevent", "different_units_penalty": "0", "wiggle": "1"}}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "A2Q2 v2", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "

The student enters a quantity with units.

", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "

The scalar part of the student's quantity

", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "

The units of the student's quantity, before converting.

", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "

The units of the student's quantity.

\n

If the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.

", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "

The student's answer, interpreted as a quantity.

\n

Marking fails if the student does not enter a valid quantity.

", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "

Are the units of the student's quantity compatible with the units of the expected quantity?

", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "

/Are the student's quantity and the expected quantity in exactly the same units?

", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "

Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.

", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "

Is the student's quantity within the allowed tolerance of the expected answer?

", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "

Is the scalar part of the student's answer a valid number?

", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:
\n", "input_type": "dropdown", "default_value": "incorrect", "choices": [{"value": "incorrect", "label": "Mark as incorrect"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "convert", "label": "Mark as if correct units used"}]}, {"name": "different_units_action", "label": "What to do if different units used", "help_url": "", "hint": "If the student's answer is given in different units to the expected answer:
\n", "input_type": "dropdown", "default_value": "convert", "choices": [{"value": "convert", "label": "Convert"}, {"value": "warn", "label": "Warn and convert"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "incorrect", "label": "Mark incorrect"}]}, {"name": "different_units_penalty", "label": "Penalty if different units used", "help_url": "", "hint": "This penalty is applied if the student gives their answer in different units to the expected answer. The selected percentage of the student's score is taken away.", "input_type": "percent", "default_value": "100"}, {"name": "wiggle", "label": "Margin of error", "help_url": "", "hint": "The student's answer is marked correct if the difference between it and the correct answer is at most this value, measured in the same units as the correct answer.", "input_type": "mathematical_expression", "default_value": "10^-12", "subvars": true}], "public_availability": "always", "published": true, "extensions": ["quantities"]}], "resources": [["question-resources/1_KUd3zOP.PNG", "/srv/numbas/media/question-resources/1_KUd3zOP.PNG"], ["question-resources/1_RkA5lTG.PNG", "/srv/numbas/media/question-resources/1_RkA5lTG.PNG"], ["question-resources/1_Bpt4XTH.PNG", "/srv/numbas/media/question-resources/1_Bpt4XTH.PNG"], ["question-resources/2_64U8S7t.PNG", "/srv/numbas/media/question-resources/2_64U8S7t.PNG"], ["question-resources/3_y8gDUnF.PNG", "/srv/numbas/media/question-resources/3_y8gDUnF.PNG"], ["question-resources/Capture_zMDQefW.PNG", "/srv/numbas/media/question-resources/Capture_zMDQefW.PNG"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Seama Koohi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4775/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "

\n

\n

A brass rod $\\var{L}$ mm long and $\\var{d}$ mm in diameter extends horizontally from a casting at $\\var{Tc}$°C. The rod is in an air environment with $\\var{Ta}$°C and h=$\\var{h}$ W/m2K

\n

\n

If the tip of the rod is insulated,

\n

", "advice": "", "rulesets": {}, "variables": {"L": {"name": "L", "group": "Ungrouped variables", "definition": "random(80 .. 150#1)", "description": "", "templateType": "randrange"}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "random(2 .. 7#1)", "description": "

D

", "templateType": "randrange"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "((4*h)/(k*(0.001*D)))^(1/2)", "description": "

Area

", "templateType": "anything"}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(110 .. 150#1)", "description": "

k

", "templateType": "randrange"}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "qf*tanh(m*l0)", "description": "", "templateType": "anything"}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(20 .. 40#1)", "description": "

h

", "templateType": "randrange"}, "Tc": {"name": "Tc", "group": "Ungrouped variables", "definition": "random(170 .. 230#1)", "description": "", "templateType": "randrange"}, "Ta": {"name": "Ta", "group": "Ungrouped variables", "definition": "random(20 .. 26#0.5)", "description": "", "templateType": "randrange"}, "l0": {"name": "l0", "group": "Ungrouped variables", "definition": "0.001*L", "description": "", "templateType": "anything"}, "at": {"name": "at", "group": "Ungrouped variables", "definition": "random(20 .. 79#1)", "description": "", "templateType": "randrange"}, "Tx": {"name": "Tx", "group": "Ungrouped variables", "definition": "Tc+(((Tc-Ta)/cosh(m*l0))*cosh(m*(l0-0.001*at)))", "description": "", "templateType": "anything"}, "qf": {"name": "qf", "group": "Ungrouped variables", "definition": "sqrt(h*pi*0.001*D*k*pi*(((0.001*D)^2)/4))*(Tc-Ta)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "100*(q/pc)", "description": "", "templateType": "anything"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "(Tc-Ta)/cosh(m*l0)", "description": "", "templateType": "anything"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "m*l0", "description": "", "templateType": "anything"}, "pc": {"name": "pc", "group": "Ungrouped variables", "definition": "h*pi*0.001*D*l0*(Tc-Ta)", "description": "", "templateType": "anything"}, "pd": {"name": "pd", "group": "Ungrouped variables", "definition": "h*pi*(0.25*(0.001*D)^2)*(Tc-Ta)", "description": "", "templateType": "anything"}, "ef": {"name": "ef", "group": "Ungrouped variables", "definition": "q/pd", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["L", "D", "m", "k", "q", "h", "Tc", "Ta", "l0", "at", "Tx", "qf", "n", "b", "c", "pc", "pd", "ef"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": true, "customName": "Part 1.a", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Consider a slice of the rod. What is (are) the mode(s) of heat transfer involved with this cut?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Conduction", "Convection", "

Radiation

"], "matrix": ["0.15", "0.15", 0], "distractors": ["", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.b", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the temperature of the rod where it connects to the casting (x = 0)?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{Ta}$°C", "$\\var{Tc}$°C", "$\\var{Tc-Ta}$°C", "We do not know based on current information."], "matrix": [0, "0.25", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": true, "customName": "Part 1.c", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the temperature of the rod at its tip?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{Ta}$°C", "$\\var{Tc}$°C", "$\\var{Tc-Ta}$°C", "We do not know based on current information."], "matrix": [0, "0", 0, "0.25"], "distractors": ["", "", "", ""]}, {"type": "gapfill", "useCustomName": true, "customName": "Part 1.d", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Please fill in the blanks with numbers for the temperature distribution along the rod for constant k (k=$\\var{k}$ W/m K.)

\n

\n

T (x) =  [[0]]  +  [[1]]  cos h ([[2]] – [[3]]*x)

", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Evaluate first the fin paramater.

"}, {"type": "1_n_2", "useCustomName": true, "customName": "Step", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What does the temperature distribution along the rod look like?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["T(x) = a + b x", "T (x) = a + b x + c x^2", "T (x) = a + b e^{cx}", "T (x) = a + b cosh(cdx)"], "matrix": [0, 0, 0, "0.2"], "distractors": ["", "", "", ""]}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "Tc-1", "maxValue": "Tc+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b-1", "maxValue": "b+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c-0.2", "maxValue": "c+0.2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "m-0.5", "maxValue": "m+0.5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "quantity", "useCustomName": true, "customName": "Part 2", "marks": "0.7", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the temperature of the rod at $\\var{at}$ mm from the casting?

\n

\n

please provide celsius instead of °C as the unit of your answer.

", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Use the temperature distribution in the previous part to find this.

"}], "settings": {"correctAnswer": "qty(Tx,\"celsius\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "prevent", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "quantity", "useCustomName": true, "customName": "Part 3", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the rate of heat loss from the rod?

", "settings": {"correctAnswer": "qty(q,\"W\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "prevent", "different_units_penalty": "0", "wiggle": "0.05"}}, {"type": "quantity", "useCustomName": true, "customName": "Part 4", "marks": "0.85", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the efficiency of the rod?

\n

(Please put % symbol as unit)

", "stepsPenalty": 0, "steps": [{"type": "quantity", "useCustomName": true, "customName": "Step a", "marks": "0.4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the rate of heat loss from the rod if it was a perfect rod?

", "settings": {"correctAnswer": "qty(pc,\"W\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Hint: Use the rate of heat loss from the rod if it was a perfect rod, and the rate of heat loss from your actual rod to calculate this.

"}], "settings": {"correctAnswer": "qty(n,\"%\")", "hint": "show units", "allow_unitless": false, "incompatible_units_action": "prevent", "different_units_action": "prevent", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "numberentry", "useCustomName": true, "customName": "Part 5", "marks": "0.85", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the effectiveness of the rod?

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What would have been the heat transfer rate if there was no rod extending from the casting surface?

", "settings": {"correctAnswer": "qty(pd,\"W\")", "hint": "show units", "allow_unitless": true, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "0.003"}}, {"type": "information", "useCustomName": true, "customName": "Hint", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Hint: Use the rate of heat loss from the rod if there was no rod extending from the casting surface, and the rate of heat loss from your actual rod to calculate this.

"}], "minValue": "ef-1", "maxValue": "ef+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "warnifunattempted", "message": "

You did not complete all the questions. Are you sure you want to leave?

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Time is up.

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5 minutes left!

"}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "contributors": [{"name": "Seama Koohi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4775/"}], "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "

The student enters a quantity with units.

", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "

The scalar part of the student's quantity

", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "

The units of the student's quantity, before converting.

", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "

The units of the student's quantity.

\n

If the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.

", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "

The student's answer, interpreted as a quantity.

\n

Marking fails if the student does not enter a valid quantity.

", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "

Are the units of the student's quantity compatible with the units of the expected quantity?

", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "

/Are the student's quantity and the expected quantity in exactly the same units?

", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "

Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.

", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "

Is the student's quantity within the allowed tolerance of the expected answer?

", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "

Is the scalar part of the student's answer a valid number?

", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:
\n", "input_type": "dropdown", "default_value": "incorrect", "choices": [{"value": "incorrect", "label": "Mark as incorrect"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "convert", "label": "Mark as if correct units used"}]}, {"name": "different_units_action", "label": "What to do if different units used", "help_url": "", "hint": "If the student's answer is given in different units to the expected answer:
\n", "input_type": "dropdown", "default_value": "convert", "choices": [{"value": "convert", "label": "Convert"}, {"value": "warn", "label": "Warn and convert"}, {"value": "prevent", "label": "Prevent submission"}, {"value": "incorrect", "label": "Mark incorrect"}]}, {"name": "different_units_penalty", "label": "Penalty if different units used", "help_url": "", "hint": "This penalty is applied if the student gives their answer in different units to the expected answer. The selected percentage of the student's score is taken away.", "input_type": "percent", "default_value": "100"}, {"name": "wiggle", "label": "Margin of error", "help_url": "", "hint": "The student's answer is marked correct if the difference between it and the correct answer is at most this value, measured in the same units as the correct answer.", "input_type": "mathematical_expression", "default_value": "10^-12", "subvars": true}], "public_availability": "always", "published": true, "extensions": ["quantities"]}, {"source": {"pk": 1, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/1/edit"}, "name": "Yes/no", "short_name": "yes-no", "description": "

The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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