Worked solutions for example 2 Workshop 2 - Basic Algebra OES Contextual problems

1. 2a What is the thermal diffusivity for a 100m wide granite
intrusion which takes 240 years to cool via conduction?

2. 2a • Convert years to seconds:

3. 2a • Convert years to seconds:
240 years = 240 x 365 x 24 x 60 x 60 seconds = 7.57 x 109s

4. 2a • Convert years to seconds:
240 years = 240 x 365 x 24 x 60 x 60 seconds = 7.57 x 109s
• Rearrange the first equation for κ and substitute in the values
you know:

5. 2a • Convert years to seconds:
240 years = 240 x 365 x 24 x 60 x 60 seconds = 7.57 x 109s
• Rearrange the first equation for κ and substitute in the values
you know:
κ =
x2
tCHAR
=
1002m2
7.57 x 109s
= ퟏ. ퟑퟐ 퐱 ퟏퟎ−ퟔ퐦ퟐ퐬−ퟏ

6. 2b Use this to calculate the specific heat of granite if it has
density 2.7 x 103kgm-3 and thermal conductivity 2.8Wm-
1K-1 and check that the units are balanced.

7. 2b • Rearrange the second equation for Cp and substitute in the values you
know:

8. 2b • Rearrange the second equation for Cp and substitute in the values you
know:
κ =
k
ρ. Cp

9. 2b • Rearrange the second equation for Cp and substitute in the values you
know:
κ =
k
ρ. Cp
κρCp = k

10. 2b • Rearrange the second equation for Cp and substitute in the values you
know:
κ =
k
ρ. Cp
κρCp = k
Cp =
k
κρ
=
2.8
1.32 x 10−6 x 2.7 x 103 = ퟕퟖퟓ. ퟔퟑ퐉퐤퐠−ퟏ퐊−ퟏ

11. 2b • Rearrange the second equation for Cp and substitute in the values you
know:
κ =
k
ρ. Cp
κρCp = k
Cp =
k
κρ
=
2.8
1.32 x 10−6 x 2.7 x 103 = ퟕퟖퟓ. ퟔퟑ퐉퐤퐠−ퟏ퐊−ퟏ
• Check the units, remembering 1J = 1Ws:

12. 2b • Rearrange the second equation for Cp and substitute in the values you
know:
κ =
k
ρ. Cp
κρCp = k
Cp =
k
κρ
=
2.8
1.32 x 10−6 x 2.7 x 103 = ퟕퟖퟓ. ퟔퟑ퐉퐤퐠−ퟏ퐊−ퟏ
• Check the units, remembering 1J = 1Ws:
Wm−1K−1
m2s−1kgm−3 =
Js−1m−1K−1
s−1m−1kg
= 퐉퐤퐠−ퟏ퐊−ퟏ