What law of thermodynamics explains the fact that if you drop an egg, the shell will not spontaneously repair itself?

The second law

The law of thermodynamics that explains why the shell of a dropped egg will not spontaneously repair itself is the second law of thermodynamics. This law is also known as the law of entropy or the law of increased disorder.

To understand the second law of thermodynamics, we need to know that it deals with the concept of entropy. Entropy refers to the measure of the disorder or randomness in a system.

According to the second law, the entropy of an isolated system will always tend to increase over time. In simple terms, it means that spontaneous processes in nature tend to lead to an increase in disorder or randomness.

Applying this to the dropped egg example, when an egg is dropped, the impact shatters the shell into many pieces. The force of the impact causes an irreversible increase in disorder in the eggshell. The broken shell cannot spontaneously repair itself because the natural tendency is towards increased disorder, not towards organizing the shell back into its original state.

In order for the eggshell to repair itself, additional energy and intervention is required, such as gluing the shell pieces back together. Without external intervention, the second law of thermodynamics tells us that the broken eggshell will not revert back to its intact state.