At what temperature between 136 and 165 K the glass transition of water occurs is still controversial, while the crystallization of water prevents the determination. To confine water in nanopores stabilizes its liquid state down to low temperatures. Heat capacities and enthalpy relaxation effects of the water confined within MCM-41 nanopores with diameters in the range 1.5-5.0 nm were measured in this work by using adiabatic calorimetry. No fusion of the confined water was detected up to 2.0 nm, part of the water exhibited fusion in 2.1 nm pores, and the whole internal water which excludes excludes the molecules interacting with the pore-wall atoms crystallized within pores with diameter of 2.3 nm and above. A glass transition of the internal water occurred at a temperature T(g) = 160-165 K for pore diameters in the range 1.5-2.0 nm and at 205-210 K for diameters of 2.0 and 2.1 rim; thus, the T(g) jumped from 165 to 205 K at 2.0 nm. The jump is connected to the development of hydrogen-bond network to a more complete one as the diameter is increased, and is conjectured as caused by the increase in the number, from three to four, of hydrogen bonds formed by each molecule. These imply that the glass transition of bulk water occurs at 210 K, which is much higher than 136 or 165 K debated so far.