Question

Why does it take more energy to boil 10 g of liquid water than to melt an equivalent mass of ice?

Short answer

It takes more energy to boil 10 g of liquid water than to melt an equivalent mass of ice because the latent heat of vaporization for water is much higher than its latent heat of fusion. Additionally, water has a higher specific heat capacity compared to ice, meaning more energy is needed to raise its temperature. For 10g of ice, melting requires 3335 J of heat, while vaporizing 10g of liquid water requires 22600 J of heat, which is significantly more energy.

Step-by-step solution

Understand specific heat capacity

Specific heat capacity is the amount of heat needed to raise the temperature of a substance by 1 degree Celsius. For water, the specific heat capacity is 4.18 J/g°C, while for ice it is 2.1 J/g°C. This means that water requires more heat to raise its temperature compared to ice.

Calculate the heat required to melt ice

The heat required to melt a substance without changing its temperature can be calculated using the latent heat of fusion formula: Q_melting = m × Lf Where: - Q_melting is the heat required to melt the substance (Joules) - m is the mass of the substance (g) - Lf is the latent heat of fusion (J/g) For water, the latent heat of fusion Lf = 333.5 J/g. Now, to calculate the heat required to melt 10g of ice: Q_melting = (10 g) × (333.5 J/g) = 3335 J

Calculate the heat required to boil liquid water

The heat required to boil a substance without changing its temperature can be calculated using the latent heat of vaporization formula: Q_vaporization = m × Lv Where: - Q_vaporization is the heat required to boil the substance (Joules) - m is the mass of the substance (g) - Lv is the latent heat of vaporization (J/g) For water, the latent heat of vaporization Lv = 2260 J/g. Now, to calculate the heat required to boil 10g of liquid water: Q_vaporization = (10 g) × (2260 J/g) = 22600 J

Compare the heat required for melting and vaporization

Comparing the heat required to melt 10g of ice (Q_melting) and to boil 10g of liquid water (Q_vaporization): Q_melting = 3335 J Q_vaporization = 22600 J As we can see, it requires a much larger amount of heat (22600 J) to vaporize 10g of liquid water compared to melting 10g of ice (3335 J). This is because the latent heat of vaporization is much higher than the latent heat of fusion for water, and because water has a higher specific heat capacity compared to ice.

Key concepts

Specific Heat Capacity

When we talk about specific heat capacity, we are referring to the amount of heat energy needed to change the temperature of 1 gram of a substance by 1°C. Imagine you have two different substances, like water and ice. Each of these requires a different amount of energy to change their temperatures because their molecular structures differ. For water, the specific heat capacity is 4.18 J/g°C. This means it takes 4.18 joules to increase the temperature of 1 gram of water by 1°C.

Ice, on the other hand, has a specific heat capacity of 2.1 J/g°C. This suggests that ice requires less energy compared to water to experience the same temperature change of 1°C. This concept is essential in understanding how quickly different materials can heat up or cool down, depending on their specific heat capacities. The differences play a vital role when we transition substances between different states like ice (solid) to water (liquid) or boiling water (liquid) to steam (gas).

The specific heat capacity is crucial in calculations involving heat energy and temperature change, especially when determining the energy required for heating or cooling processes.

Latent Heat of Fusion

Latent heat of fusion is the energy required to change a substance from the solid state to the liquid state without changing its temperature. During this phase change, the energy goes into breaking the bonds that hold the solid structure together instead of raising the temperature. For water, the latent heat of fusion is 333.5 J/g.

If you were to melt 10 grams of ice, you would need 3335 joules of energy, calculated as \(Q_{melting} = m \times Lf = 10 \times 333.5 = 3335 \) Joules.

Understanding latent heat of fusion is critical because it explains why a considerable amount of heat is required just to convert ice into water, even though the process does not increase the temperature. This concept highlights how energy is used to change the state of a material without temperature change until all the material completes the phase transition.

Latent Heat of Vaporization

Latent heat of vaporization is a term that describes the heat energy needed to transform a liquid into a gas without changing its temperature. This phase change involves increasing the distance between molecules in the liquid, allowing them to escape into the air as steam or vapor. For water, the latent heat of vaporization is significantly higher than the latent heat of fusion, at 2260 J/g.

To convert 10 grams of liquid water into steam, 22600 Joules of energy is required. This amount is calculated as \(Q_{vaporization} = m \times Lv = 10 \times 2260 = 22600 \) Joules.

Latent heat of vaporization is a critical concept in understanding why boiling water requires so much more energy than melting the same mass of ice. Turning liquid water into vapor requires plenty of energy because the bonds holding the liquid molecules together are stronger, and more work is needed to separate these molecules far enough apart to form a gas. This high energy requirement is why boiling occurs at a much higher threshold compared to melting.