A 66000 kg iceberg at −6.7◦C breaks away

from the polar ice shelf and floats away into
the ocean at 6.36◦C.
What is the final change in the entropy
of the system, when the iceberg has completely melted? The specific heat of ice is
2010 J/kg ·◦C.

To find the final change in entropy of the system when the iceberg has completely melted, we need to calculate the change in entropy for each phase of the process and then sum them up.

1. Change in entropy during the warming from -6.7°C to 0°C (ice phase):
Since the temperature range is relatively small, we can assume the specific heat capacity (C) of ice to be constant. The change in entropy (ΔS) is given by the formula:

ΔS = ∫ (C/T) dT

Where C is the specific heat capacity and T is the temperature in Kelvin.

Converting temperatures to Kelvin:
T1 = -6.7 + 273.15 = 266.45 K
T2 = 0 + 273.15 = 273.15 K

Calculating the change in entropy:
ΔS1 = ∫ (C/T) dT
= C ln(T2/T1)
= 2010 J/kg · °C * ln(273.15/266.45)

2. Change in entropy during phase change from ice to water:
During this phase change, the entropy change is given by:

ΔS2 = Q/T

Where Q is the heat added to melt the ice and T is the absolute temperature at which the heat is added.

We need to calculate the heat (Q) required to melt the ice. The heat required (Q) is given by:

Q = m * L

Where m is the mass of the iceberg and L is the latent heat of fusion.

Mass of iceberg (m) = 66000 kg
Latent heat of fusion (L) = 334000 J/kg (latent heat of ice)

Calculating the change in entropy:
ΔS2 = Q/T
= (66000 kg * 334000 J/kg) / 273.15 K

3. Change in entropy during the warming from 0°C to 6.36°C (water phase):
The change in entropy is calculated using the same formula as in step 1:

T1 = 0 + 273.15 = 273.15 K
T2 = 6.36 + 273.15 = 279.51 K

Calculating the change in entropy:
ΔS3 = ∫ (C/T) dT
= C ln(T2/T1)
= 2010 J/kg · °C * ln(279.51/273.15)

Now we can sum up the individual entropy changes to find the total change in entropy:

Total change in entropy (ΔS_total) = ΔS1 + ΔS2 + ΔS3

Calculating the final result will give you the answer to the question.