Why is the entropy of perfectly crystalline substances zero at absolute zero?

The entropy of perfectly crystalline substances is zero at absolute zero because there is only one possible microstate.

Entropy is a measure of the number of ways that the energy of a system can be distributed among its particles. In a perfectly crystalline substance at absolute zero, all the particles are in their lowest energy state and there is only one way to arrange the particles to achieve this state. This means there is only one possible microstate, or arrangement of particles, for the system. According to the Boltzmann's entropy formula, S = k ln W, where S is the entropy, k is the Boltzmann constant, and W is the number of microstates, if W equals to 1, the natural logarithm of 1 is zero, hence the entropy is zero.

This concept is known as the third law of thermodynamics, which states that the entropy of a perfect crystal at absolute zero is exactly equal to zero. Absolute zero, 0 Kelvin, is the lowest possible temperature, where all thermal motion stops. In a perfect crystal, the atoms are arranged in a repeating pattern that extends in all three spatial dimensions. At absolute zero, each atom in the crystal is perfectly at rest in its place in the pattern. There is no disorder or randomness in the system, so there are no other possible microstates.

However, it's important to note that this is an idealised situation. In reality, it's impossible to reach absolute zero, and no crystal is perfectly defect-free. Even at very low temperatures, there will always be some thermal motion and some defects in the crystal structure, leading to a greater number of possible microstates and a higher entropy. But the third law of thermodynamics gives us a useful reference point for calculating changes in entropy, by setting a baseline of zero entropy at absolute zero for perfect crystals.

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