Which state has higher entropy? Explain in terms of probability. (a) A perfectly ordered crystal of solid nitrous oxide
or a disordered crystal in which the molecules are oriented randomly (b) Quartz glass (an amorphous solid) or a quartz crystal

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1. Entropy is a measure of the disorder or randomness in a system. A perfectly ordered crystal has low entropy because the molecules are arranged in a highly ordered state.
2. In a disordered crystal, the molecules are oriented randomly, leading to a higher number of possible microstates and thus higher entropy.
3. For part (a), compare the perfectly ordered crystal of nitrous oxide with the disordered crystal. The disordered crystal has higher entropy due to the increased randomness and number of possible arrangements.
4. Quartz glass is an amorphous solid, meaning it lacks a long-range ordered structure, leading to higher entropy compared to a quartz crystal, which has a well-defined, ordered lattice structure.
5. For part (b), the quartz glass, being amorphous, has higher entropy than the quartz crystal due to its lack of long-range order and greater number of possible microstates.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates a greater degree of disorder and a higher number of possible arrangements of particles.

Probability and Microstates

In statistical mechanics, the concept of microstates refers to the specific detailed configurations of a system at the molecular level. The probability of a system being in a particular macrostate is related to the number of microstates associated with that macrostate. A state with more microstates has a higher probability of being realized, leading to higher entropy.

Order vs. Disorder in Solids

The arrangement of particles in solids can significantly affect their entropy. A perfectly ordered solid, like a crystal, has fewer microstates compared to a disordered solid, where particles are arranged randomly. This difference in arrangement leads to the disordered solid having higher entropy due to its greater number of possible configurations.