  In this paper, we study the thermodynamics of black holes using a generalized
uncertainty principle (GUP) with a correction term linear order in the momentum
uncertainty. The mass-temperature relation and heat capacity are calculated
from which critical and remnant masses are obtained. The results are exact and
are found to be identical. The entropy expression gives the famous area theorem
upto leading order corrections from GUP. In particular, the linear order term
in GUP leads to a $\sqrt{A}$ correction to the area theorem. Finally, the area
theorem can be expressed in terms of a new variable termed as reduced horizon
area only when the calculation is done to the next higher order correction from
GUP.

General Relativity and Quantum Cosmology;High Energy Physics - Theory;Quantum Physics