Specific Latent Heat Of Fusion Of Ice Calculation And Explanation

In the realm of thermodynamics, understanding the energy required to change the state of a substance is crucial. One key concept in this area is latent heat, which refers to the heat absorbed or released during a phase transition, such as melting or freezing, without changing the temperature. Specifically, the specific latent heat of fusion is the amount of heat energy required to change 1 kilogram of a substance from a solid to a liquid state at its melting point. This article aims to delve into the calculation of the specific latent heat of fusion of ice, using a practical example and providing a comprehensive explanation of the underlying principles. This exploration is essential for anyone studying physics, engineering, or related fields, as it demonstrates the application of fundamental thermodynamic concepts to real-world scenarios. Understanding the specific latent heat of fusion is not only academically important but also practically relevant in various applications, such as designing cooling systems, understanding weather patterns, and developing efficient energy storage methods.

The central question we aim to address is: What is the specific latent heat of fusion of ice if it takes 863 kJ (kilojoules) of heat energy to convert 4.6 kg (kilograms) of ice into water at 0°C (degrees Celsius)? This problem provides a clear and concise scenario that allows us to apply the concept of specific latent heat of fusion. To solve this, we will use the fundamental formula that relates heat energy, mass, and specific latent heat. The given parameters—863 kJ of heat and 4.6 kg of ice—provide the necessary data to calculate the specific latent heat of fusion. By working through this problem, we will not only arrive at a numerical answer but also reinforce our understanding of the physical principles involved. The problem's simplicity makes it an excellent example for illustrating the concept, while the practical nature of ice melting makes it relatable and easy to visualize. This combination of simplicity and relevance is crucial for effective learning and retention of the material. In addition to the direct calculation, we will also discuss the implications of the result and how it fits within the broader context of thermodynamics and phase transitions.

To determine the specific latent heat of fusion of ice, we employ a straightforward yet powerful formula rooted in the principles of thermodynamics. The formula is expressed as:

$$L_f = \frac{Q}{m}$$

Where:

• $L_f$ represents the specific latent heat of fusion, which is the quantity we aim to calculate. It is measured in joules per kilogram (J/kg).
• $Q$ denotes the amount of heat energy required to change the phase of the substance, in this case, to melt the ice. It is given in joules (J) or kilojoules (kJ).
• $m$ stands for the mass of the substance undergoing the phase change, measured in kilograms (kg).

This formula is derived from the fundamental concept that the heat energy required for a phase change is directly proportional to the mass of the substance. The specific latent heat of fusion serves as the proportionality constant, quantifying the amount of energy needed per unit mass. In our specific problem, we are given the values for $Q$ (863 kJ) and $m$ (4.6 kg). Before we can plug these values into the formula, we need to ensure that the units are consistent. Since the formula requires energy to be in joules (J), we will convert the given kilojoules (kJ) into joules by multiplying by 1000, as 1 kJ is equal to 1000 J. This conversion is a crucial step in ensuring the accuracy of our calculation. Once we have the values in the correct units, we can substitute them into the formula and perform the division to find the specific latent heat of fusion ($L_f$). This methodical approach, starting with the fundamental formula and carefully handling unit conversions, is essential for solving physics problems accurately and efficiently. The simplicity of the formula belies its power, as it encapsulates the core relationship between heat, mass, and phase transitions, making it a cornerstone of thermodynamics.

To accurately calculate the specific latent heat of fusion of ice, we need to follow a step-by-step process, ensuring that we handle units correctly and apply the formula precisely. First, we begin with the given information: the heat energy required ($Q$) is 863 kJ, and the mass of the ice ($m$) is 4.6 kg. As we discussed in the methodology section, the formula for specific latent heat of fusion is:

$$L_f = \frac{Q}{m}$$

However, before we can substitute the values into the formula, we must convert the heat energy from kilojoules (kJ) to joules (J). This is because the specific latent heat of fusion is typically expressed in joules per kilogram (J/kg). The conversion factor is 1 kJ = 1000 J. Therefore, we multiply the given heat energy by 1000:

$$Q = 863 \text{ kJ} imes 1000 \frac{\text{J}}{\text{kJ}} = 863,000 \text{ J}$$

Now that we have the heat energy in joules, we can substitute the values into the formula:

$$L_f = \frac{863,000 \text{ J}}{4.6 \text{ kg}}$$

Performing the division, we get:

$$L_f = 187,608.7 \frac{\text{J}}{\text{kg}}$$

This result indicates that the specific latent heat of fusion of ice is approximately 187,608.7 J/kg. In scientific notation, this can be expressed as $1.876087 imes 10^5$ J/kg. For practical purposes, we can round this value to $1.88 imes 10^5$ J/kg. This calculated value represents the amount of energy required to convert 1 kilogram of ice at 0°C into water at 0°C. The precision of our calculation highlights the importance of accurate measurements and unit conversions in scientific problem-solving. Furthermore, this result provides a quantitative understanding of the energy involved in phase transitions, which is crucial for various applications, from climate modeling to industrial processes. The meticulous approach we have taken, from unit conversion to final calculation, ensures the reliability of our result and enhances our understanding of the underlying physics.

Based on our calculations, the specific latent heat of fusion of ice is approximately 187,608.7 J/kg, which can be expressed as 1.876087 × 10^5 J/kg in scientific notation, and rounded to 1.88 × 10^5 J/kg for practical purposes. This result corresponds most closely with option B in the given choices, which is $1.87 imes 10^5 J kg^{-1}$. This value signifies the amount of energy required to transform one kilogram of ice at 0°C into water at the same temperature. The significance of this value lies in its practical and theoretical implications. On a practical level, understanding the specific latent heat of fusion is crucial in various applications, including refrigeration, air conditioning, and food preservation. For instance, the large amount of energy required to melt ice explains why ice is an effective cooling agent. It can absorb a significant amount of heat from its surroundings while undergoing a phase change, thus maintaining a lower temperature. In the realm of climate science, the specific latent heat of fusion plays a vital role in regulating global temperatures. The melting and freezing of ice at the polar ice caps and glaciers involve substantial energy exchange, influencing ocean currents and weather patterns. The high latent heat of fusion of ice means that a considerable amount of energy is either absorbed from the environment during melting or released into the environment during freezing. This energy exchange has a moderating effect on temperature fluctuations, preventing extreme temperature variations in certain regions. Theoretically, the specific latent heat of fusion is a key concept in thermodynamics, illustrating the energy dynamics of phase transitions. It highlights that energy is required to overcome the intermolecular forces holding a substance in its solid state, allowing it to transition into a liquid state. This energy does not raise the temperature of the substance but is instead used to change its physical state. The precise calculation and understanding of this value are essential for accurate modeling and prediction in various scientific and engineering contexts. The congruence of our calculated result with option B underscores the validity of our methodology and the accuracy of our calculations, reinforcing the fundamental principles of thermodynamics.

In summary, we have successfully calculated the specific latent heat of fusion of ice, determining it to be approximately 1.88 × 10^5 J/kg. This calculation involved applying the fundamental formula $L_f = \frac{Q}{m}$, where $L_f$ is the specific latent heat of fusion, $Q$ is the heat energy required for the phase transition, and $m$ is the mass of the substance. We carefully converted the given heat energy from kilojoules to joules to ensure consistency in units, and then substituted the values into the formula to arrive at our result. This exercise underscores the importance of understanding and applying basic thermodynamic principles. The specific latent heat of fusion is a critical property of substances, dictating the amount of energy required for phase transitions. For ice, this value is particularly significant due to its widespread presence and role in various natural and industrial processes. From a practical standpoint, the high specific latent heat of fusion of ice makes it an effective cooling agent, widely used in refrigeration and air conditioning systems. It also plays a crucial role in climate regulation, as the melting and freezing of ice absorb and release substantial amounts of energy, influencing global temperatures and weather patterns. Theoretically, this calculation reinforces the concept that phase transitions involve energy exchange without temperature change. The energy is used to overcome intermolecular forces rather than increasing the kinetic energy of the molecules. This understanding is fundamental to thermodynamics and is applied in various scientific and engineering disciplines. The process of solving this problem highlights the importance of meticulous calculations and unit conversions in scientific problem-solving. It also demonstrates how a simple formula can provide valuable insights into complex phenomena. By accurately determining the specific latent heat of fusion of ice, we have not only answered the posed question but also reinforced our understanding of the underlying physics and its practical implications. This comprehensive approach, combining theoretical knowledge with practical application, is essential for mastering scientific concepts and applying them effectively in real-world scenarios.