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 frozen. Work was done on the can in splitting it open. Where did the energy for this work come from?

Short answer

In conclusion, the energy for splitting the can came from the energy removed by the freezer when it cooled down the soft drink and caused it to freeze. This energy was stored in the soft drink's increased volume when changing from a liquid to a solid state, and is then released as it expands, causing the aluminum can to split open.

Step-by-step solution

Identify changes of state and potential sources of energy

First, let's list the potential sources of energy in this scenario: - The energy contained in the soft drink (internal energy in the molecules) - The energy provided by the freezer (which removes heat from substances) - The work done by the expanding soft drink (in splitting the can) Since the problem states that the can was split open and the soft drink contents were frozen, we should focus our analysis on the change in state from liquid to solid.

Understand the process of freezing and how expanding volume is related to energy

When a substance undergoes a phase change from liquid to solid (i.e., freezing), energy is taken away from the substance. Conceptually, as a substance loses energy, its molecules move slower, and the attractive forces between them become stronger. As a result, the molecules become arranged in a more ordered, solid structure. In the case of water and most soft drinks, the solid structure takes up more volume than the liquid structure, leading to expansion. To understand where the energy for this work comes from, we need to know how energy is being exchanged during the freezing process and focus on the energy transfer that goes into splitting the can.

Analyzing energy input and output in the freezing process

The energy involved in this problem can be classified into two main categories: 1. Add energy to the system: Molten can 2. Remove energy from the system: Solid can plus escaped energy. The can splits when in the solid state, so we know that the energy involved in the expansion (and consequently splitting the can) has been removed from the system and must be accounted for by the freezer.

Accounting for the energy used to split the can

Since the energy input to the system is not enough to cause the can to split when it's in a molten state, we can conclude that the energy used to split the can comes from the energy removed by the freezer during the freezing process. In essence, when the freezer extracts energy from the soft drink, the expansion of the soft drink as it freezes causes an increase in volume, corresponding to the work done in splitting the can. In conclusion, the energy for splitting the can came from the energy removed by the freezer when it cooled down the soft drink and caused it to freeze. This energy was stored in the soft drink's increased volume when changing from a liquid to a solid state, and is then released as it expands, causing the aluminum can to split open.