Question

An ice cube at \(0^{\circ} \mathrm{C}\) melts to water by absorbing heat. If 10.5 kcal of heat are required to melt the ice, how much energy must be lost to freeze the water, at \(0^{\circ} \mathrm{C},\) to ice?

Short answer

To freeze the water, 10.5 kcal of energy must be released.

Step-by-step solution

Understanding the Problem

We need to determine how much energy is required to freeze water at \(0^{\circ} \mathrm{C}\) into ice if we know that 10.5 kcal were needed to melt an ice cube into water, also at \(0^{\circ} \mathrm{C}\).

Identifying Key Principles

Melting ice and freezing water are opposite processes. The heat absorbed by the ice cube to melt (10.5 kcal) is the same amount of energy that must be released to freeze the water into ice.

Calculating the Heat Released

Since the melting of an ice cube requires 10.5 kcal, freezing the same amount of water will also require 10.5 kcal to be released. This is due to the conservation of energy; the process of freezing is the reverse of melting.

Key concepts

Heat Transfer

Heat transfer is a fundamental concept in thermodynamics. It refers to the movement of thermal energy from one object or substance to another, driven by temperature differences. In the context of our exercise, heat is absorbed by the ice cube to change its state from solid to liquid. This absorption of heat allows the ice to melt at the constant temperature of \(0^{\circ} \mathrm{C}\), which is the melting point of ice.

When we talk about heat transfer in this scenario, we're dealing with a process called phase change. The energy does not raise the temperature, but rather facilitates the change of state. Here are a few things to keep in mind about heat transfer during phase changes:

• Heat flows naturally from warmer to cooler substances.
• During phase changes, heat energy is used to break the bonds between molecules.
• The energy input or output during a phase change at a fixed temperature is called "latent heat."

In the given exercise, 10.5 kcal of heat are absorbed by the ice for it to melt. This amount defines the latent heat associated with the melting process.

Phase Change

Phase change is when a substance transitions from one state of matter to another, such as solid to liquid or liquid to solid. In our exercise, the transition of interest is between the phases of solid ice and liquid water, both occurring at \(0^{\circ} \mathrm{C}\).

Both melting and freezing belong to this category of phase transitions, with melting involving the absorption of heat and freezing requiring the release of heat. During the phase change:

• Temperature remains constant.
• Energy is used to alter the intermolecular forces.
• The amount of energy exchanged in a phase change is "latent heat" specific to the material involved.

For water, the latent heat of fusion is 10.5 kcal for the amount discussed in the exercise. This is the energy each process (melting or freezing) would either consume or release at \(0^{\circ} \mathrm{C}\).

Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. This is a core concept in understanding thermodynamic processes like those involving phase changes.

In the exercise, the melting and freezing processes are direct applications of this principle. When the ice cube absorbs 10.5 kcal to become water, that energy is stored in the water. Conversely, freezing that same water back into ice releases the exact same amount of energy (10.5 kcal). Because energy is conserved:

• The energy absorbed to change from ice to water is equal to the energy required to reverse the change.
• No net energy gain or loss occurs during a complete cycle of freezing then melting of the same amount of water.

This concept helps us understand that these processes are reversible, and energy is always accounted in these transitions.