Heat flow formula

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From users who are members of MfEP Progress Quizzes :

Hanh Vo

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Ready to use

3 years, 2 months ago

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Don Shearman 11 months, 4 weeks ago

Published this.

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Hanh Vo 3 years, 2 months ago

Gave some feedback: Ready to use

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Don Shearman 3 years, 5 months ago

Created this as a copy of Parallel inductors formula.

Name	Status	Author	Last Modified
Voltage drop formula	Ready to use	Don Shearman	14/05/2024 05:36
Parallel inductors formula	Ready to use	Don Shearman	06/05/2024 05:49
Parallel resistors formula	Ready to use	Don Shearman	06/05/2024 05:53
Heat flow formula	Ready to use	Don Shearman	06/05/2024 05:47

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Question 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.

Give any introductory information the student needs.

			Name	Type	Generated Value

A	number	0.2
L1	integer	90
variable	list	[ latex("T_1"), latex("T_2") ]
select	integer	1
sel_var	string	T_2
answers	list	List of 2 items
ans	expression	Ql/(CA) + T_1
other_var	string	T_1
l	integer	7
Q	integer	24
values	list	[ 73.2, 106.8 ]
value	number	106.8

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(0.2..0.9 #0.1)

JME function reference

Description

value of A for substitution part of question, random 0.2 to 0.9 in steps of 0.1

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

0.2

→ Used by:

values

Advice
"Unnamed part" - prompt

Parts

Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Rearrange the formula to make $\var{sel_var}$ the subject. (Note: to type a variable such as $T_1$ , type T_1, to enter a fraction such as $\frac{a}{b}$ , type a/b.)

$\var{sel_var}=$ Gap 0. (You must show full working on your ahndwriten working for this part to get full marks)

If $A=\var{A}$ 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 $\var{sel_var}$ ?

$\var{sel_var}=$ Gap 1. degrees C (answer to 2 decimal places)

Advice

We have

$\begin{align}Q&=CA \left( \frac{T_2-T_1}{l} \right)\quad\text{divide both sides by }CA\\\frac{Q}{CA}&=\left( \frac{T_2-T_1}{l} \right)\quad\text{multiply both sides by }l\\\frac{Ql}{CA}&=\left( T_2-T_1 \right)\quad\text{add }T_1\text{ to both sides}\\\frac{Ql}{CA}+T_1&=T_2\\T_2&=\frac{Ql}{CA}+T_1\end{align}$

Given $A=\var{A}$ m $^2$ , $l=\var{l}$ m, $C=50$ W/mK, $Q=\var{Q}$ and $\var{other_var}=\var{L1}^\circ$ C we have

$\begin{align}T_2&=\frac{\var{Q}\times\var{l}}{50\times\var{A}}+\var{L1}\\&\approx\var{precround(value,2)}^\circ C\end{align}$

$\begin{align}T_1&=\var{L1}-\frac{\var{Q}\times\var{l}}{50\times\var{A}}\\&\approx\var{precround(value,2)}^\circ C\end{align}$

Give a worked solution to the whole question.

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This question is used in the following exam:

SCC Final Exam by Hanh Vo in SCC PrelimMaths.

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Checkpoint description

Don Shearman 11 months, 4 weeks ago

Hanh Vo 3 years, 2 months ago

Don Shearman 3 years, 5 months ago

Error in variable testing condition

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Heat flow formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Don Shearman 11 months, 4 weeks ago

Hanh Vo 3 years, 2 months ago

Don Shearman 3 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`