Without doing any calculations, predict what temperature corresponds to equal populations of up and down spin states. (See Exercise 4.54.)

Exercise 4.54

The populations p of the up and down spin states of electrons in a magnetic field B are given by

where DE = 2μ_BB is the energy difference between the two spin states. (See Exercise 4.53.) Plot these two populations as a function of temperature for B = 1 T. 

Exercise 4.53

The molar entropy of electron spins in a magnetic field B is

where ΔE = 2μ_BB is the separation in energy of the two spin states in a magnetic field, and μ_B is the Bohr magneton, μ_B = 9.274 * 10^–24 J · T^–1. Plot this function against temperature for the following values of B: 0.1 T, 1 T, 10 T, and 100 T. 

Pdown = 1 + e 1 and Pup = - 1 + e