Introduction

Boiling water may seem straightforward, but the process involves several steps that require a specific amount of energy. This article explores the detailed calculation required to boil 1 liter of frozen water, breaking down each step and providing a comprehensive understanding of the energy involved. We will delve into the key concepts of melting ice, heating water, and vaporization, and provide an in-depth analysis of the mathematical calculations.

Understanding the Process

To boil 1 liter of frozen water, we need to follow three main steps: first, melting the ice, second, heating the water, and third, vaporizing the water.

Melting the Ice

When ice at -18°C is heated to 0°C, it undergoes a phase change from solid to liquid. The energy required for this process is known as the latent heat of fusion.

Calculation

The latent heat of fusion for ice is approximately 334 J/g. For 1 liter (1000 g) of ice:

[ Q_1 m cdot c_{text{ice}} cdot Delta T 1000 , text{g} cdot 2.09 , frac{text{J}}{text{g°C}} cdot (0 - (-18) , text{°C}) 1000 cdot 2.09 cdot 18 , text{J} 37620 , text{J} ]

Heating the Water

Once the ice has melted, we need to heat the resulting liquid water from 0°C to 100°C. The energy required for this is determined by the specific heat capacity of water, which is approximately 4.18 J/g°C.

Calculation

[ Q_2 m cdot c_{text{water}} cdot Delta T 1000 , text{g} cdot 4.18 , frac{text{J}}{text{g°C}} cdot (100 - 0) , text{°C} 1000 cdot 4.18 cdot 100 , text{J} 418000 , text{J} ]

Vaporizing the Water

The final step involves the transformation of liquid water at 100°C to steam. This is done by adding the latent heat of vaporization, which is approximately 2260 J/g.

Calculation

[ Q_3 m cdot L_{text{vaporization}} 1000 , text{g} cdot 2260 , frac{text{J}}{text{g}} 2260000 , text{J} ]

Total Energy Required

By summing up the energy required for each step, we get the total energy required to boil 1 liter of frozen water:

[ Q_{text{total}} Q_1 Q_2 Q_3 37620 , text{J} 418000 , text{J} 2260000 , text{J} 2832620 , text{J} ]

This equates to approximately 2.83 MJ (megajoules).

Conclusion

Boiling 1 liter of frozen water requires a significant amount of energy, approximately 2.83 MJ. This energy is distributed across three stages: melting the ice, heating the water, and vaporizing the water. Understanding these stages and their associated energies is crucial for various applications, including scientific experiments and daily life scenarios.

Related Keywords

Energy Required to Boil Water Latent Heat of Fusion Heat of Vaporization

Additional Information

It's worth noting that reducing the pressure can significantly reduce the energy needed to vaporize water, a process that is particularly relevant in scientific and industrial contexts. However, for the purpose of boiling 1 liter of frozen water at atmospheric pressure, the calculations provided form a comprehensive approach.