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# Heat of Fusion: How Much Heat is Needed to Melt Greenland

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Source:
Author: Jerry Silver

### The Idea

Ice anywhere requires a certain specific amount of heat to melt. Ice melts at 0° C. Once at that temperature, the amount of heat needed depends only on how much ice you have. Heat can either change the temperature of something or cause it to change from one state to another. In this experiment, that change is from solid to liquid. You will determine how much heat is needed to melt a given mass of ice by carefully keeping track of temperature changes and heat flows.

### What You Need

• Styrofoam cup
• cube of ice
• water
• thermometer
• stirring rod
• scale

### Method

1. Fill the beaker with exactly 150 mL of water at a temperature of at least 25 degrees centigrade. This results in a mass of the water, mw, of 150 g.
2. Remove an ice cube from the freezer and let it sit out until it just begins to melt. This establishes its temperature at (very close to) 0 degrees centigrade.
3. Measure the mass of the ice cube, mice, in grams. If significant melting has occurred, you can use a paper towel to absorb any excess liquid water before measuring the mass.
4. Measure the initial temperature of the water, Ti, before the ice cube is added.
5. Drop in the ice cube. Stir gently. Measure the final temperature, Tf, as soon as the ice cube has completely melted.
6. Calculate how much heat was needed to melt the ice through the following steps (see Figure 89-1):

• Heat extracted from the water
• Given by Qw = mw Cw (Tf – Ti) where Cw is the specific heat of water = 4.18J/g° C. This means that 4.18 joules of energy (which is how energy is measured) are needed to raise each gram of water every 1 degree centigrade.

• Heat needed to bring the melted ice from 0° C to the final liquid temperature
• Given by Qmelted ice = mice Cw (Tf – 0)

• Heat needed to melt 1 gram of ice
• Hf = (Qw – Qmelted ice) / mice

### Expected Results

The expected result is Hf = 334 J/g. This means 334 joules of heat energy are needed to melt 1 gram of ice.

### Why It Works

When a cube of ice is placed in a beaker of water, some heat is taken from the water. This loss of heat results in the water being brought to a lower equilibrium temperature, which is lower than the starting temperature. The heat lost by the water accomplishes two things: 1) it melts the ice, and 2) it brings the liquid resulting from the melting ice up to the equilibrium temperature. This gives the overall equation:

Qw = Qmelted ice + miceHf

Solving for Hf gives the equation used to find the heat of fusion for ice.

### Other Things to Try

Determine the temperature of a freezer. As before, place an ice cube (this time immediately removed from the freezer) in a Styrofoam cup filled with water of a known temperature. Do this by using the known value for the heat of fusion of ice and the heat transfer equation used previously.

Determine the temperature of a hot object (such as a red-hot nail) by measuring the temperature before and the equilibrium temperature after immersion of the object. Then solve the heat equations for the initial temperature of the object.

Calculate the amount of heat needed to melt the Greenland ice caps: Greenland contains 2.85 million cubic kilometers of ice or 1.4 × 1014 ice cubes each with a mass of 20 g. Based on the heat of fusion for ice (0 degrees C) determined in this experiment, the Greenland ice caps would require 9.5 × 1023 Joules of heat energy to melt.

### The Point

When objects at different temperatures are mixed, they result in an equilibrium temperature that is between the highest and lowest temperatures in the mixture. The amount of heat needed to cause a certain temperature change for a given mass of material is characterized by the specific heat for that material. In addition to causing temperature change in a material, some heat (called latent heat) results in a change of phase from solid to liquid.