A 200 kg block of ice at 0.0c is placed in a large lake the temperature of the lake is just slightly higher than 0 C and the ice melts very slowly.

i) what is the entropy change of ice
ii) What is the entropy change of the lake
iii) What is the entropy change of the universe

To calculate the entropy change of the ice, lake, and the universe, we can use the formula:

ΔS = q/T

where ΔS represents the entropy change, q is the heat transfer, and T is the temperature.

i) To find the entropy change of the ice, we need to calculate the heat transferred during the melting process. The heat transferred (q) is given by the equation:

q = m * L

where m is the mass of the ice and L is the latent heat of fusion for ice.

Given:
Mass of ice (m) = 200 kg
Latent heat of fusion for ice (L) = 334,000 J/kg (at 0°C)

Therefore, q = 200 kg * 334,000 J/kg = 66,800,000 J

Since the temperature remains constant during melting, T = 0°C.

ΔS (ice) = q / T = 66,800,000 J / (273.15 K) ≈ 245,451.10 J/K

ii) The entropy change of the lake can be calculated using the same formula. Since we know that the ice is melting very slowly and the temperature of the lake is just slightly higher than 0°C, we can assume that the lake absorbs the heat from the melting ice without changing its temperature significantly.

Therefore, the heat transferred (q) is the same as the heat gained by the ice, which is 66,800,000 J.

Since the temperature of the lake is slightly higher than the melting point of ice (0°C), we can take T = 0°C + ε (a small positive value close to zero).

ΔS (lake) = q / T = 66,800,000 J / (0°C + ε) ≈ infinity

The entropy change of the lake would be very large (virtually infinite) because the temperature difference is small, and the lake absorbs a large amount of heat.

iii) The entropy change of the universe is the sum of the entropy changes of the ice and the lake.

ΔS (universe) = ΔS (ice) + ΔS (lake) ≈ 245,451.10 J/K + infinity ≈ infinity

The entropy change of the universe would also be very large (virtually infinite) due to the significant entropy change of the lake and the positive entropy change of the ice.