Amagnetic field b such that the energy of 2. consider a spin ½ magnet with n spins in the spin up state e↑ ε heat bath at temperature t whereas e. +ε . suppose the magnet is in contact with a (a) calculate the internal energy, entropy and free energy as a function of x -n/n where n = n-n, . you may assume n, and n, are both large numbers so you can apply stirling's approximation. hint: keep only the first two terms in stirling's approximation but do not assume x < < 1 . (b) what value of x minimizes the free energy and call it x? (c) make a plot of x. q versus t and explain the low temperature and high temperature limits.