Final answer:
Stirling's approximation can be used to find an approximate formula for the multiplicity of a two-state paramagnet, which represents the number of microstates associated with a macrostate. The formula is β ≈ 2^N, where N is the number of particles in the paramagnet.
Step-by-step explanation:
Stirling's approximation can be used to find an approximate formula for the multiplicity of a two-state paramagnet. The multiplicity, denoted as β, represents the number of microstates associated with a macrostate. Stirling's approximation states that for large values of n, n! can be approximated as √(2πn)(n/e)^n. In the case of a two-state paramagnet, there are two possible microstates: spin up and spin down. Therefore, the multiplicity can be approximated as β ≈ 2^N, where N is the number of particles in the paramagnet. This formula gives an estimate of the number of microstates for a given macroscopic state of the system.