Temperature Variation of Paramagnetism

In our discussion of the kinetic theory of gases we have already shown that a statistical argument gives Boltzmann s distribution law for the probability of a definite energy state, according to which a definite state with energy E has the probability 

The form in which the temperature T appears in this expression is deduced from thermodynamical considerations h is Boltzmann s constant. In our case, thercvfore, the probability that the magnetic moment will set itself at a definite angle 0 to the direction of the field is given by 

In the limiting case C 1, i.e. for weak fields or high temperatures, we obtain the expression 

In this limiting case, however, we could have obtained the rnanlt more easily by introducing a power series in into the formula d( Iiuiiig M cos 6. We then have 

The first term in the numerator vanishes on integration, while tho second gives 2 S/3. Even the first term in the denominator dilTers from zero, its value being 2. The quotient gives the expression stated above. 

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