Final answer:
The solid-liquid interface of a 15-mm-thick layer of water with top and bottom surface temperatures of -4°C and 2°C, respectively, will be located 5 mm below the top surface, where the temperature reaches 0°C.
Step-by-step explanation:
When considering a 15-mm-thick horizontal layer of water with a top surface temperature of -4°C and a bottom surface temperature of 2°C, you need to determine the position of the solid-liquid interface at steady state. This problem relates to the phase diagram of water and how temperature gradients across a water layer can result in a phase change. According to the phase diagram, water freezes at 0°C under standard atmospheric pressure.
Given the temperature gradient in this scenario, we can infer that the solid-liquid interface will be located somewhere within the 15-mm layer where the temperature reaches 0°C.
Using the understanding that the temperature changes linearly through the thickness of the water layer, we can calculate the position of the 0°C isotherm, which would represent the solid-liquid interface.
Since the total temperature difference across the layer (ΔT) is 6°C (from -4°C to 2°C), the interface where temperature reaches 0°C can be found by a simple proportion.
The distance from the bottom at 2°C to the 0°C interface is given by: (0°C - (-4°C)) / 6°C * 15 mm, resulting in 10 mm from the bottom surface. Thus, the interface is 5 mm below the top surface. At this interface, the water will be in a solid state (ice), as per the given temperature conditions.