Interpretations of adiabatic demagnetization:

• Final temperature T_f ∞ T_i (initial temperature)
• First demagnetization produces a temperature half that at start
• Second demagnetization produces a temperature
• Third demagnetization produces a temperature 
• rth demagnetization produces a temperature 

Infinite number of adiabatic demagnetizations will be required to attain absolute zero temperature.

FOWLER-GUGGENHEIM STATEMENT OF THIRD LAW:

It is impossible by any procedure, no matter how idealized, to reduce any condensed system to the absolute zero of temperature in a finite number of operations.

Any isothermal magnetization from 0 to H (magnetic intensity) such as k - i₁, f₁ - i₂ etc. is associated with the release of heat, i.e., a decrease in entropy (Fig. 1.40).

Fig. 1.40 T-H and T-S diagrams of a paramagnetic substance to show the equivalence of three statements of the third law

The processes i₁ - f₁, i₂ - f₂, i₃ - f₃ etc. represent reversible adiabatic demagnetizations with temperatures getting lower and lower. Repeated cycles of isothermal magnetization and adiabatic demagnetization would bring about a very low temperature. It is seen that [S(T, H) - S(T,0)] decreases as the temperature decreases, i.e., ΔS_III < ΔS_II < ΔS_I. Thus entropy change associated with an isothermal reversible process of a condensed system approaches zero. It is called Nernst-Simon statement of third law of thermodynamics.