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We study low temperature expansion of the first law of thermodynamics for near extremal black holes. We show that for extremal black holes with non-vanishing entropy, the leading order contribution {yields an expression for their extremal entropy in agreement with the entropy function result} and the Cardy formula for the entropy of a two dimensional chiral conformal field theory (CFT). When their entropy vanishes due to the vanishing of a {one-cycle} on the horizon, such leading contribution is always compatible with the first law satisfied by a BTZ black hole. These results are universal and consistent both with the presence of local AdS${}_2$ and AdS${}_3$ near horizon throats for extremal black holes and the suggested quantum microscopic descriptions (AdS${}_2$/CFT${}_1$, Kerr/CFT and EVH/CFT).
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