Problem 100 - Chemistry: The Central Science in SI Units, Global Edition

Question

An aluminum can of a soft drink is placed in a freezer. Later, you find that the can is split open and its contents have frozen. Work was done on the can in splitting it open. Where did the energy for this work come from?

Step-by-Step Solution

Answer

The energy for the work done on the aluminum can in splitting it open comes from the latent heat released during the phase change of the soft drink from liquid to solid. As the soft drink freezes and expands, it loses energy to the freezer environment, which is then converted into mechanical work that causes pressure on the can's walls and splits it open.

Step 1: Understand the freezing process

When the can of soft drink is placed in the freezer, the temperature of the liquid inside decreases. As the liquid cools, it reaches its freezing point, at which it transforms from liquid to solid. This phase change is accompanied by expansion, as the molecules of the substance rearrange themselves into a more rigid structure. This expansion puts pressure on the walls of the can, eventually causing it to split open. The work done in splitting open the can comes from the energy involved in the phase change of the liquid.

Step 2: Phase change and energy transfer

During a phase change, energy transfer occurs between the system (here, the contents of the can) and the surroundings (the freezer). For the liquid to freeze, it must lose energy, specifically as latent heat. Latent heat is the energy required to change the phase of a substance without a change in temperature. As the liquid loses energy to the freezer environment, this energy is removed from the system, allowing it to freeze and expand.

Step 3: Energy conversion in the system

As the soft drink freezes and expands, the stored energy within the can transforms into a different form. The latent heat energy, which was previously tied up in the soft drink's liquid state, is now released and converted into the mechanical work required to cause pressure on the can's walls and split it open. This energy conversion, from latent heat to mechanical work, represents the transfer of energy required to do work on the aluminum can.

Step 4: Identify the energy source

In conclusion, the energy for the work done on the can in splitting it open comes from the latent heat released during the phase change of the soft drink from liquid to solid. The liquid loses energy to its surroundings, allowing it to freeze and expand, and this energy is then converted into mechanical work that causes pressure on the can's walls, ultimately leading to the can splitting open.

Key Concepts

Latent Heat

Latent heat is an essential concept when discussing phase changes, such as the transition from liquid to solid. It refers to the energy absorbed or released by a substance during a phase change while maintaining a constant temperature. In the case of a soft drink can placed in a freezer, as the liquid inside reaches its freezing point, it undergoes a phase change from liquid to solid. This process involves the release of latent heat, as the substance lets go of the energy it previously stored in its liquid form.

When a substance changes phase, such as from liquid to solid, it organizes its molecular structure. This rearrangement requires energy, known as latent heat of fusion in the context of freezing. The latent heat released during this process is crucial because it's what allows the liquid to solidify into a more rigid state without changing temperature. Understanding latent heat helps clarify where the energy involved in phase changes comes from, making it an important topic in thermodynamics.

Phase Change

A phase change is when a substance transitions from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. In our example of a soft drink in a can inside a freezer, the key phase change is from liquid to solid. This transformation is driven by the removal of energy, particularly through losing latent heat to the surrounding environment.

During a phase change, the temperature remains constant even though energy is being transferred. The energy removed or added goes into changing the state of the material, rather than altering its temperature. For the soft drink, as it loses heat, its molecular motion decreases, allowing the molecules to lock into a structured pattern, resulting in a solidified form.

In addition to the regular cooling effects of the freezer, the phase change amplifies stress inside the can, often leading to expansion and pressure against the can’s walls—potentially causing it to split open. This connection between phase change and mechanical work is a fascinating display of energy dynamics, which is a core concept in physics.

Mechanical Work

Mechanical work in physics refers to the energy required to move an object over a distance or to cause some form of physical change. In the scenario concerning the aluminum soft drink can, the concept of mechanical work is illustrated through the movement and force applied on the can's walls, resulting in them splitting open.

When the soft drink inside the can freezes and expands during its phase change from liquid to solid, it doesn't just stay the same size. The molecular structure changes lead to an expansion which exerts pressure onto the can's aluminum walls. The mechanical work done here is the physical force applied to split open the can due to this expansion. The origin of this mechanical work is rooted in the energy transfer involved in the phase change—specifically, the energy released as latent heat.

This process exemplifies how energy can be transformed from one type to another. In this case, it transitions from internal energy (latent heat) due to the phase change into mechanical work required to deform the can’s structure. Understanding mechanical work in this context helps to better grasp how energy transformations facilitate everyday phenomena, like a can splitting open due to freezing.