Radiation cooling of the water will occur ____________ than the ground.

• A. faster
• B. slower
• C. the same
• D. not at all

Answer: (B)

Radiation cooling translates into how fast the surface temperature drops, and that rate depends on how much energy must be removed to change the temperature. The temperature change over time is roughly dT/dt = -P/(m c), where P is the radiative power leaving the surface, m is mass, and c is specific heat. Even if the radiative power is similar for water and the ground, water has a much higher heat capacity (larger m and/or larger c). That means more energy must be shed to produce the same temperature drop, so the temperature of water falls more slowly for the same radiative loss. Consequently, the water’s radiation cooling occurs more slowly than the ground’s.