Chapter 4, Problem 179P

When water, as in a pond or lake, is heated by warm air above it, it remains stable, does not move, and forms a warm layer of water on top of a cold layer. Consider a deep lake $(k=0.6\text{W/m}\text{.K},c_p=4.179\text{ kJ/kg}\text{.K)}$ and that is initially at a uniform temperature of 2°C and has its surface temperature suddenly increased to 20°C by a spring weather front. The temperature of the water 1 in below the surface 400 h after this change is

(a) 2.1°C

(b) 4.2°C

(c) 6.3°C

(d) 8.4°C

(e) 10.2°C