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Using a unified approach we study the entropy of extremal black holes throughthe entropy of an electrically charged thin shell. We encounter three cases inwhich a shell can be taken to its own gravitational or horizon radius andbecome an extremal spacetime. In case 1, we use a non extremal shell, calculateall the thermodynamics quantities including the entropy, take it to the horizonradius, and then take the extremal limit. In case 2, we take the extremal limitand the horizon radius limit simultaneously, i.e., as the shell approaches itshorizon radius it also approaches extremality. In case 3, we build first anextremal shell, and then take its horizon radius. We find that thethermodynamic quantities in general have different expressions in the threedifferent cases. The entropy is the Bekenstein-Hawking entropy $ S=A_+/4$(where $A_+$ is the horizon area) in cases 1 and 2, and in case 3 it can be anywell-behaved function of $A_+$. The contributions from the variousthermodynamic quantities for the entropy in all three cases are distinct.Indeed, in cases 1 and 2 the limits agree in what concerns the entropy but theydisagree in the behavior of all other thermodynamic quantities. Cases 2 and 3disagree in what concerns the entropy but agree in the behavior of the localtemperature and electric potential. Case 2 is in a sense intermediate betweencases 1 and 3. Our approach sheds light on the extremal black hole entropyissue.

Entropy of extremal black holes: horizon limits through charged thin shells, a unified approach