14.7 Exercise 17

A large body of lava from a volcano has stopped flowing and is slowly cooling. The interior of the lava is at $\text{1200}º\text{C}$, its surface is at $\text{450}º\text{C}$, and the surroundings are at $\text{27} . \text{0}º\text{C}$. (a) Calculate the rate at which energy is transferred by radiation from $1 . \text{00 } \textrm{ }\text{m}^{2}$ of surface lava into the surroundings, assuming the emissivity is 1.00. (b) Suppose heat conduction to the surface occurs at the same rate. What is the thickness of the lava between the $\text{450}º\text{C}$ surface and the $\text{1200}º\text{C}$ interior, assuming that the lava’s conductivity is the same as that of brick?