Page 187 - Physical Principles of Sedimentary Basin Analysis

6.16 Solidification and latent heat of fusion 169

10

8 f(x)

6

4

2 g(x)

0
0.0 0.5 1.0 1.5
x
Figure 6.32. f (x) = e −x 2 /(x erf(x)) and g(x) = e −x 2 /(x(1 + erf(x))).

0.0
1 day
0.5 3 days

1.0 7 days
depth [m] 1.5 15 days

2.0 31 days

2.5

3.0
0 200 400 600 800 1000
temperature [°C]
Figure 6.33. The temperature in solidified magma at ˆ t = 1, 3, 7, 15 and 31 days.

Exercise 6.30 How thick is the layer of solidified magma after 1 day, 10 days and
100 days? Assume that magma has L = 400 kJ kg −1 , c = 1kJ kg −1 K −1 and a tem-
perature difference T m − T 0 = 1000 K, where T m is the melting temperature and T 0 is
initial temperature of the surrounding rock.

Exercise 6.31 How much time is needed for the ice on a lake to become 1 m thick when
the surface temperature is −10 C? Use that L = 320 kJ kg −1 and c = 4kJ kg −1 K −1 for
◦
water.