Heat Required to Melt the Ice

Question

One cup of ice has a mass of approximately 250 g. The ice is at 0.0 Celsius. How much heat is required to melt the ice and then warm the resulting water to 25.0 Celsius? A table of useful information is provided.

Heat of fusion solid water = 332 kJ/kg

Specific heat of liquid water = 4.18 J/g C

Answer 1

Hi. This is actually a 2 part problem. The first part involves changing the solid ice to liquid water. The second part involves changing the temperature of the liquid water.

Let's tackle the first part, using the Heat of Fusion:

The Heat of Fusion tells us how much energy is needed to convert 1g of a solid to a liquid of the same temperature.

In order to melt 250g of ice, we would need (250×332) joules. That's our part 1.

250x332= part 1

At this point, we have 250g of liquid water @ 0°C. Now we have to raise the temperature to 25°C. For that, we use the Specific Heat.

The specific heat is the amount of energy needed to heat 1g of a substance 1°C. The specific heat of liquid water is 4.18J/g °C

We plug in our numbers and get:

4.18×250x25= the energy needed for part 2

We calculate part 1 and part 2, then add them together to get the answer.