Abstract: By applying the radiation spectrum obtained from tunnel effect, we obtain the normal canonical entropy of black hole by discussing the entropy of non-rotation black hole. The entropy satisfies the Bekenstein-Hawking area law, and contains the terms of correction whose main terms are proportional to the logarithm of the area, and the rest of the correction terms are related to the thermal capacity of black hole. With the help of the obtained normal canonical entropy, we studied the phase transition and showed that when the thermal capacity is emanative, there are no plural numbers at this point in the normal canonical entropy, which shows that the phase transition is of the second order.

Keywords: 
• canonical ensemble /
• quantum correction /
• phase transition of black hole