Final answer:
With similar specific heat capacities assumed, the hot water with the lower mass flow rate of 2 kg/s will likely experience a greater temperature change than the cold water in a counter-flow heat exchanger.
Step-by-step explanation:
In a counter-flow heat exchanger, the water flow experiencing the largest temperature change is typically the one with the smallest mass flow rate and the highest specific heat capacity. Limited information is provided regarding the specific heat capacities or initial and final temperatures of the fluids, so we must rely on mass flow rate and the principle that, for the same heat exchange, the fluid with the lower mass flow rate will undergo a greater temperature change, assuming the specific heat capacities are similar.
Given the mass flow rates of 2 kg/s for hot water and 8 kg/s for cold water, under the assumption of similar specific heat capacities, the hot water with the smaller mass flow rate would experience a larger temperature change compared to the cold water. This is because the lower mass flow rate of the hot water means each kilogram of water has to absorb or release more heat to achieve the same amount of total heat transfer as the mass of cold water, hence leading to a larger temperature change.