An ice cube of mass 0.200 kg melts at 0.0°C, and then the melt water is heated to How much heat was added to the ice cube? For water and Lv = 2257 kJ/kg. The specific heat capacity of water is 4.19 kJ/kg ∙ °C.

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To find the amount of heat added to the ice cube, we need to consider two steps:

1. Melting the ice cube.
2. Heating the melt water.

Step 1: Melting the ice cube
The heat required to melt the ice cube can be calculated using the formula:

Q1 = m * Lf

where Q1 is the heat required, m is the mass of the ice cube, and Lf is the latent heat of fusion for water.

Given:
m = 0.200 kg
Lf = 2257 kJ/kg

Substituting these values into the formula, we get:

Q1 = 0.200 kg * 2257 kJ/kg = 451.4 kJ

So, the heat required to melt the ice cube is 451.4 kJ.

Step 2: Heating the melt water
The heat required to heat the melt water can be calculated using the formula:

Q2 = m * c * ΔT

where Q2 is the heat required, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.

In this case, the water starts at 0.0°C and is heated to a final temperature Tf. The change in temperature, ΔT, can be calculated as:

ΔT = Tf - 0.0°C = Tf

Given:
c = 4.19 kJ/kg ∙ °C

Substituting these values into the formula, we get:

Q2 = m * c * Tf

Since we don't have the final temperature, we can't calculate Q2 without that information.

In summary, the heat added to the ice cube is 451.4 kJ (from melting the ice). However, we need the final temperature of the melt water in order to calculate the additional heat added from heating it.

To calculate the heat added to the ice cube, we need to consider the following steps:

Step 1: Calculate the heat absorbed during the phase change from solid to liquid (melting).

For this, we'll use the formula: Q1 = mass of ice cube * latent heat of fusion (Lv)

Given:
Mass of the ice cube = 0.200 kg
Latent heat of fusion (Lv) = 2257 kJ/kg

Q1 = 0.200 kg * 2257 kJ/kg
Q1 = 451.4 kJ

So, the heat absorbed during the melting of the ice cube is 451.4 kJ.

Step 2: Calculate the heat absorbed to raise the temperature of the water from 0.0°C to the final temperature.

For this, we'll use the formula: Q2 = mass of water * specific heat capacity of water * change in temperature

Given:
Mass of water = mass of ice cube (0.200 kg) (Since the ice melted into water)
Specific heat capacity of water = 4.19 kJ/kg ∙ °C
Change in temperature = Final temperature - Initial temperature

Since the final temperature is not provided, we can't calculate Q2 accurately without that information.

Please provide the final temperature to proceed with the calculation of the heat added to the ice cube.