4. A 4.50-kg block of ice at 0.00 °C falls into the ocean and melts. The average temperature of the ocean is 3.50 °C, including all the deep water. By how much does the melting of this ice change the entropy of the world? Does it make it larger or smaller?
The melting of this ice will increase the entropy of the world. The entropy change is equal to the heat absorbed by the ice divided by the temperature of the ocean. In this case, the entropy change is equal to 4.50 kg x 334 J/kgK x (3.50 °C - 0.00 °C) = 5,845 J/K. Therefore, the entropy of the world increases by 5,845 J/K.
To determine how much the melting of ice changes the entropy of the world, we need to understand the concept of entropy and calculate the change in entropy for this specific scenario. We can use the formula for entropy change:
ΔS = Q / T
where ΔS represents the change in entropy, Q is the heat transferred, and T is the temperature in Kelvin.
First, let's calculate the heat transferred during the melting of the ice. The heat can be determined using the formula:
Q = m * L
where Q is the heat transferred, m is the mass, and L is the latent heat of fusion for ice. The latent heat of fusion for ice is 334 kJ/kg.
Q = 4.50 kg * 334 kJ/kg = 1503 kJ
Next, we need to convert the temperature to Kelvin. The temperature of the ice is 0.00 °C, while the average temperature of the ocean is 3.50 °C.
T1 = 0.00 + 273.15 = 273.15 K (initial temperature of the ice)
T2 = 3.50 + 273.15 = 276.65 K (final temperature of the ocean)
Now, we can substitute these values into the entropy change formula to calculate the change in entropy:
ΔS = Q / T
ΔS = 1503 kJ / (273.15 K) = 5.50 kJ/K
Therefore, the melting of this ice changes the entropy of the world by 5.50 kJ/K.
To determine whether this change makes the entropy larger or smaller, we need to consider the direction of the process. Since the ice melts and transfers heat to the ocean, the energy disperses more evenly, increasing randomness and disorder. This indicates an increase in entropy. Therefore, the melting of this ice makes the entropy of the world larger.
To determine the change in entropy of the world due to the melting of the ice, we need to consider the entropy change of the ice and the ocean.
The entropy change of the ice can be calculated using the formula:
ΔS_ice = mL/T_ice,
where m is the mass, L is the latent heat of fusion, and T_ice is the temperature of the ice.
The entropy change of the ocean can be calculated using the formula:
ΔS_ocean = mL/T_ocean,
where m is the mass, L is the latent heat of fusion, and T_ocean is the temperature of the ocean.
The total change in entropy of the world can be calculated as:
ΔS_world = ΔS_ice + ΔS_ocean.
Given:
Mass of ice (m) = 4.50 kg
Temperature of ice (T_ice) = 0.00 °C
Temperature of ocean (T_ocean) = 3.50 °C
First, let's calculate the entropy change of the ice:
ΔS_ice = (4.50 kg)(334,000 J/kg)(1 K)/(273.15+0 K)
= 55,000 J/K
Next, let's calculate the entropy change of the ocean:
ΔS_ocean = (4.50 kg)(334,000 J/kg)(1 K)/(273.15+3.50 K)
= 54,200 J/K
Finally, let's calculate the total change in entropy of the world:
ΔS_world = ΔS_ice + ΔS_ocean
= 55,000 J/K + 54,200 J/K
= 109,200 J/K
Therefore, the melting of this ice changes the entropy of the world by 109,200 J/K. It increases the entropy of the world.