Heat and temperature [temp] - graph - Numbas at mathcentre.ac.uk

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Tom Stallard

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Tom Stallard 8 years, 9 months ago

Created this as a copy of Heating/phase change - core.

Name	Status	Author	Last Modified
Heating/phase change - core	draft	Tom Stallard	19/06/2016 01:44
Heat and temperature [temp] - graph	draft	Tom Stallard	03/02/2021 13:59
Heating/phase change	Ready to use	Tom Stallard	08/02/2018 18:18
Balancing heating in materials + wavelength	draft	Tom Stallard	12/02/2017 15:03
Balancing heating in materials	draft	Tom Stallard	12/02/2017 15:02
Solid phase change + power	Needs to be tested	Tom Stallard	16/11/2020 15:07
Christian's copy of Heating/phase change	draft	Christian Lawson-Perfect	13/04/2017 15:26
Heating/phase change - 3 tier	draft	Tom Stallard	12/01/2019 15:17
Solid phase change, radiation, entropy	draft	Tom Stallard	12/01/2019 13:56
Simple heating/phase change	draft	Tom Stallard	12/01/2019 14:00
Josh's copy of Heating/phase change	draft	Josh Lim	01/07/2019 11:58
Josh's copy of Solid phase change, radiation, entropy	draft	Josh Lim	01/07/2019 11:59
David's copy of Balancing heating in materials + wavelength	draft	David Rickard	03/12/2018 20:15
B: Solid phase change, radiation, entropy	draft	Tom Stallard	12/01/2019 14:27
B: Simple heating/phase change	draft	Tom Stallard	13/02/2019 11:44
A3: Heating/phase change - 3 tier	draft	Tom Stallard	12/01/2019 15:32
Heating/Phase Change	draft	Melissa D'Ascenzio	15/08/2019 12:35

There are 25 other versions that do you not have access to.

Question statement

{onestep(a,b,x2,y2)}

The above graph shows a line which has an equation of the form $y=ax+b$ , where $a$ and $b$ are integers.

You are given two points on the line, $(0,\var{b})$ and $(\var{x2},\var{y2})$ , as indicated on the diagram.

Give any introductory information the student needs.

			Name	Type	Generated Value

switcharoo_comment	list	List of 3 items
switcharoo_type	string	solid_to_gas
phase_temp	integer	273
phase_latentheat	integer	334000

			Name	Type	Generated Value

g_or_kg	integer	0
g_or_kg_string	string	kg
mass_string	number	1.61

			Name	Type	Generated Value

phase2_temp	integer	373
phase1_temp	integer	273
phase2_latentheat	integer	2264760
phase1_latentheat	integer	334000

			Name	Type	Generated Value

Unnamed
end_temp	integer	469
mass	number	1.61
start_temp	integer	262
switcharoo	integer	1
asfdasd	integer	2
a		Definition of variable `a` is empty.
b		Definition of variable `b` is empty.
x2		Definition of variable `x2` is empty.
y2		Definition of variable `y2` is empty.

Automatically regenerate variables?

Name

Data type

Value

(text strings)

Description

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

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Generated value: `list`

[ "solid_to_liquid", "solid_to_gas", "liquid_to_gas" ]

→ Used by:

switcharoo_type

Parts

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

Write the equation of the line in the diagram. The line described by your equation will also be drawn on the diagram.

Advice

First Method.

You are given that the line goes through $(0,\var{b})$ and $(-1,\var{b-a})$ and the equation of the line is of the form $y=ax+b$

Hence:

1) At $x=0$ we have $y=\var{b}$, and this gives $\var{b}=a \times 0 +b =b$ on putting $x=0$ into $y=ax+b$.

So $b=\var{b}$.

2) At $x=-1$ we have $y=\var{b-a}$, and this gives $\var{b-a}=a \times (-1) +b =\simplify[all,!collectNumbers]{-a+{b}}$ on putting $x=-1$ into $y=ax+b$.

On rearranging we obtain $a=\simplify[all,!collectNumbers]{{b}-{b-a}}=\var{a}$.

So $a=\var{a}$.

So the equation of the line is $\simplify{y={a}*x+{b}}$.

Second Method.

The equation $y=ax+b$ tells us that the graph crosses the $y$-axis (when $x=0$) at $y=b$.

So looking at the graph we immediately see that $b=\var{b}$.

$a$ is the gradient of the line and is given by the change from $(-1,\var{b-a})$ to $(0,\var{b})$:

\[a=\frac{\text{Change in y}}{\text{Change in x}}=\frac{\simplify[all,!collectNumbers]{({b-a}-{b})}}{-1-0}=\var{a}\]

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This question is used in the following exam:

Heat by Jim Kelly in Jim's workspace.

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Heat and temperature [temp] - graph

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Tom Stallard 8 years, 9 months ago

Error in variable testing condition

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Generated value: `list`

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Heat and temperature [temp] - graph

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Tom Stallard 8 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Information only

Generated value: `list`