Josh's copy of Solid phase change, radiation, entropy

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Josh Lim 6 years, 4 months ago

Created this as a copy of Solid phase change, radiation, entropy.

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

A {mass_string} cube of solid {Mat_string} measures {x} cm along each side. It has a temperature of {phase1_temp} K, the fusion temperature of {mat_string}. The cube sits in an oven with a temperature of {oven_temp} K and is heated only by radiation (no conduction or convection) until it entirely melts.

Assume Stefan's constant $\sigma = \var{ksb2}\times10^{-8}$ $W m^{-2}K^{-4}$ and Wien's displacement constant $k_W = \var{kw}$ $\mu mK$ .

	Latent Heat of fusion	emissivity
{Mat_string}	{phase1_latentheat} Jkg<sup>-1</sup>	{emissivity}

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

mass_string

string

242 g

			Name	Type	Generated Value

mat_string	string	Copper
container_string	string	crucible
phase1_temp	integer	1357
phase1_latentheat	integer	207000
emissivity	number	0.22
density	number	8.97

			Name	Type	Generated Value

fusionheat	number	50094
fh_kj	number	50.094
p_kw	number	0.5074138203
time	number	98.7241537265
power	number	507.4138203177
tt	number	0.027423376
pp	number	0.1409482834
x	integer	3
xx	rational	3/100
xxx	number	27
area	rational	27/5000
ksb	number	0.0000000567
ksb2	number	5.67
kw	integer	2898
wave	rational	126/59

			Name	Type	Generated Value

material_list	list	List of 7 items
fusion_lh_list	list	List of 7 items
fusion_temp_list	list	List of 7 items
material_emissivity	list	List of 7 items
material_density	list	List of 7 items

			Name	Type	Generated Value

wat_mat	integer	2
start_temp	number	1083.85
oven_start_temp	number	1544.85
mass	number	0.242
oven_temp	number	1818

			Name	Type	Generated Value

switcharoo	integer	1
answer	number	0.027423376
question_string	string	with a power of 507.413820317

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(mass<1,dpformat(mass*1000,0)+' g',dpformat(mass,2)+' kg')

JME function reference

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

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Generated value: `string`

242 g

← Depends on:

mass

→ Used by:

Statement

Advice

$Q = m L_H$

$Q = \var{mass} \times \var{phase1_latentheat} = \var{fusionheat}$

So the energy needed to melt the cube is {sigformat(fh_kj,3)} kJ.

$P_{net} = e \sigma A \Delta T^4$

$P_{net} = e \sigma A (T_1^4 - T_2^4)$

where A is the surface area of the cube: $A = 6x^2 = 6 \times (\var{xx}^2) = 6*\var{xx^2} = \var{area}$

$P_{net} = \var{emissivity} \times \var{ksb2}\times10^{-8} \times \var{area} \times (\var{phase1_temp}^4 - \var{oven_temp}^4) = \var{-power}$

So the net power emitted by the cube is {sigformat(-p_kw,3)} W , and the net power absorbed by the block is {sigformat(p_kw,3)} W.

$t = \frac{E}{P}$

$t = \frac{\var{fusionheat}}{\var{sigformat(power,5)}} = \var{time} $

So the time the cube takes to melt is {sigformat(time,3)} seconds.

$\lambda_{max} = \frac{K_W}{T}$

$\lambda_{max} = \frac{\var{kw}}{\var{phase1_temp}} = \var{wave}$

So the wavelength at which the cube's radiation is at a maximum is {sigformat(wave,3)} microns.

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This question is used in the following exam:

Interesting NUMBAS examples by Josh Lim in NUMBAS workshop demo.

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Josh's copy of Solid phase change, radiation, entropy

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Taxonomy: mathcentre

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Josh Lim 6 years, 4 months ago

Error in variable testing condition

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Generated value: `string`

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Josh's copy of Solid phase change, radiation, entropy

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Josh Lim 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Number entry

Advanced settings

Generated value: `string`