Final answer:
Given equal heat transfer and specific heat capacities, the smaller mass flow rate of 3 kg/s of cold water will undergo a larger temperature change in a counter-flow heat exchanger compared to the larger mass flow rate of 12 kg/s of hot water.
Step-by-step explanation:
In a counter-flow heat exchanger, when we compare temperature changes between the hot water and the cold water flowing in the system, we have to consider the mass flow rates and the heat capacity of each fluid. The amount of heat transferred (Q) by a substance is proportional to the mass (m), specific heat capacity (c), and the change in temperature (ΔT), and is expressed as Q = mcΔT. For water, assuming the specific heat capacity is constant and similar for hot and cold water, the temperature change is directly proportional to the heat transferred and inversely proportional to the mass flow rate.
Given the mass flow rates of the hot water (12 kg/s) and cold water (3 kg/s) respectively, and assuming equal and opposite amounts of heat are transferred between them, the smaller mass flow rate (cold water) will undergo a larger temperature change. This is because the same amount of heat is being divided by a smaller mass for the cold water, resulting in a higher temperature change ΔT. Thus, the correct answer is:
A. cold water