Chapter 13, Problem 13.43P

A flat-bottomed hole 6 mm in diameter is bored to a depth of 24 mm in a diffuse, gray material having an emissivity of 0.8 and a uniform temperature of 1000 K.
(a) Determine the radiant power leaving the opening of the cavity.
(b) The effective emissivity ${\epsilon }_e$ of a cavity is defined as the ratio of the radiant power leaving the cavity to that from a blackbody having the area of the cavity opening and a temperature of the inner surfaces of the cavity. Calculate the effective emissivity of the cavity described above.
(c) If the depth of the hole were increased, would ${\epsilon }_e$ increase or decrease? What is the limit of ${\epsilon }_e$ as the depth increases?