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Answer :
The final change in entropy of the system when the iceberg has completely melted is approximately 4.06 x [tex]10^{5}[/tex] J/K.
To calculate the change in entropy, we need to consider the heat transfer during the phase change from solid (iceberg) to liquid (water) and the change in temperature.
First, we need to calculate the heat transfer during the phase change. The heat required to melt the iceberg can be calculated using the equation: Q = m × ΔH, where Q is the heat transfer, m is the mass of the iceberg, and ΔH is the heat of fusion for ice.
The heat of fusion for ice is the amount of heat required to change a substance from a solid to a liquid phase at its melting point. For water, it is 334,000 J/kg.
Calculating the heat transfer during the phase change: Q = 128000 kg × 334000 J/kg = 4.27 x [tex]10^{10}[/tex]J.
Next, we calculate the heat transfer due to the change in temperature. The equation for heat transfer is Q = m × c × ΔT, where c is the specific heat capacity of the substance and ΔT is the change in temperature.
The specific heat capacity of ice is 2010 J/kg °C. We need to consider the temperature change from -4°C to 2.38°C.
Calculating the heat transfer due to the change in temperature: Q = 128000 kg × 2010 J/kg °C × (2.38°C - (-4°C)) = 4.81 x [tex]10^{8}[/tex] J.
The total heat transfer is the sum of the heat transfer during the phase change and the heat transfer due to the change in temperature: Q_total = Q_phase change + Q_temperature change = 4.27 x [tex]10^{10}[/tex] J + 4.81 x [tex]10^{8}[/tex]J = 4.31 x [tex]10^{10}[/tex] J.
The change in entropy (ΔS) is given by ΔS = Q_total / T, where T is the temperature in Kelvin.
Converting the temperature from Celsius to Kelvin: T = 2.38°C + 273.15 = 275.53 K.
Calculating the change in entropy: ΔS = (4.31 x [tex]10^{10}[/tex] J) / (275.53 K) ≈ 4.06 x [tex]10^{5}[/tex] J/K.
Therefore, the final change in entropy of the system when the iceberg has completely melted is approximately 4.06 x [tex]10^{5}[/tex] J/K.
Learn more about heat transfer here:
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