Answer
We can use the same equation as before:
Q = m·ΔHf
where Q is the heat required, m is the mass of ice, and ΔHf is the heat of fusion of ice.
ΔHf for ice is 333.55 J/g. Substituting this value and the given mass of ice, we get:
Q = (66 g)·(333.55 J/g) = 22,013.3 J
The heat gained by the water can be calculated using the specific heat capacity of water (4.184 J/g·K):
Q = m·c·ΔT
where c is the specific heat capacity of water, ΔT is the temperature change, and m is the mass of water.
We know that the final temperature of the water is 25°C, which is 25 + 273.15 = 298.15 K. The initial temperature of the water is 20°C, which is 20 + 273.15 = 293.15 K. Substituting these values, we get:
Q = (1000 g)·(4.184 J/g·K)·(298.15 K - 293.15 K) = 20,920 J
So the heat required to melt the ice is greater than the heat gained by the water, which means that not all of the ice will melt and some ice will remain in the water. The amount of ice that melts can be calculated by dividing the heat gained by the heat of fusion of ice:
m = Q/ΔHf = 20,920 J / 333.55 J/g ≈ 62.68 g
So approximately 62.68 g of ice will melt and mix with the water, while the remaining 3.32 g of ice will remain solid.
Work Step by Step
We can use the same equation as before:
Q = m·ΔHf
where Q is the heat required, m is the mass of ice, and ΔHf is the heat of fusion of ice.
ΔHf for ice is 333.55 J/g. Substituting this value and the given mass of ice, we get:
Q = (66 g)·(333.55 J/g) = 22,013.3 J
The heat gained by the water can be calculated using the specific heat capacity of water (4.184 J/g·K):
Q = m·c·ΔT
where c is the specific heat capacity of water, ΔT is the temperature change, and m is the mass of water.
We know that the final temperature of the water is 25°C, which is 25 + 273.15 = 298.15 K. The initial temperature of the water is 20°C, which is 20 + 273.15 = 293.15 K. Substituting these values, we get:
Q = (1000 g)·(4.184 J/g·K)·(298.15 K - 293.15 K) = 20,920 J
So the heat required to melt the ice is greater than the heat gained by the water, which means that not all of the ice will melt and some ice will remain in the water. The amount of ice that melts can be calculated by dividing the heat gained by the heat of fusion of ice:
m = Q/ΔHf = 20,920 J / 333.55 J/g ≈ 62.68 g
So approximately 62.68 g of ice will melt and mix with the water, while the remaining 3.32 g of ice will remain solid.
