A flat-bottomed hole \(8 \mathrm{~mm}\) in diameter is bored to a depth of \(24 \mathrm{~mm}\) in a diffuse, gray material having an emissivity of 0.8 and a uniform temperature of \(1000 \mathrm{~K}\).

(a) Determine the radiant power leaving the opening of the cavity.

(b) The effective emissivity \(\varepsilon_{e}\) 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 \(\varepsilon_{e}\) increase or decrease? What is the limit of \(\varepsilon_{e}\) as the depth increases?