Building a refrigerator is a great way to teach a child about some laws of physics, and the project can be a great way to learn about design. However, do-it-yourself refrigerators are unlikely to compete with commercially built refrigerators.
Refrigerators exploit gas laws, which deal with the pressure, temperature and volume of gases. When a gas is compressed, it heats up. Hot, compressed refrigerant in a refrigerator is cooled to room temperature, generally with the help of a fan. When it's decompressed, the resulting gas is cool. This cool gas is sent through walls in the refrigerator, where it can absorb heat and make the system cooler.
Building a refrigerator is also a great way to show how common items can be used for multiple purposes. Fans designed to use in computers can be used to remove heat from the hot refrigerant and for promoting air flow within the refrigerator. Refrigerators are far more efficient when they're insulated well, which can lead to lessons about how material holds air within a system.
Homemade refrigerators are unlikely to be as efficient as models sold in stores, which have been refined over decades to operate using as little energy as possible. Those looking to teach their children about physics and spend some time together, however, might find building a refrigerator to be a worthwhile project.