Question

Consider two paramagnetic systems A and B, each with N spins, under the influence of an external magnetic field B0​. The energy associated with one spin is ϵ=−μ0​sB0​, where s is the spin variable and can take two possible values, s={−1,1} (spin down or spin up). The total magnetization of each system is given by MA​=0.2M0​ ,MB​=0.4M0​, where M0​ is the maximum magnetization each system could take (all spins are aligned to the external field). Initially, the two systems are isolated from each other.

1. Compute the temperatures of each system TA​ and TB​ in isolation.

Answer 1

The temperature of each system can be calculated using the magnetization values and the Curie's law equation. the temperatures of each system TA​ and TB​ in isolation comes to 5 and 2.5 respectively.

Step-by-step explanation:

The temperature of a paramagnetic system is related to its magnetization through the Curie's law which states that the magnetization is directly proportional to the temperature. The equation is given by:

M = C/T

Where M is the magnetization and T is the temperature. In this question, system A has a magnetization MA = 0.2M0 and system B has a magnetization MB = 0.4M0. Assuming that M0 is the maximum magnetization, the temperature of each system can be calculated using the given values of M and M0.

TA = M0/MA

TB = M0/MB

Substituting the values, we get:

TA = M0/0.2M0 = 1/0.2 = 5

TB = M0/0.4M0 = 1/0.4 = 2.5