Water flows through a duct of varying area. The difference in stagnation pressures between two sections is \(4.5 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}\).

(a) If the water remains at a constant temperature, how much heat will be transferred in this length of duct?

(b) If the system is perfectly insulated against heat transfer, compute the temperature change of water as it flows through the duct.