14.7 Exercise 1

Conversely, dark space is very cold, about $\text{3K} (− \text{454}º \text{F})$, so that the Earth radiates energy into the dark sky. Owing to the fact that clouds have lower emissivity than either oceans or land masses, they reflect some of the radiation back to the surface, greatly reducing heat transfer into dark space, just as they greatly reduce heat transfer into the atmosphere during the day. The rate of heat transfer from soil and grasses can be so rapid that frost may occur on clear summer evenings, even in warm latitudes.

What is the change in the rate of the radiated heat by a body at the temperature $T_{1} = \text{20}º \text{C}$ compared to when the body is at the temperature $T_{2} = \text{40}º \text{C}$?