A radiometer views a small target (1) that is being heated by a ring-shaped disk heater (2). The target has an area of A₁ = 0.0004 m², a temperature of T₁ = 500 K, and a diffuse, gray emissivity of ?₁ = 0.8. The heater operates at T₂ = 1000 K and has a black surface. The radiometer views the entire sample area with a solid angle of w = 0.0008 sr.

(a) Write an expression for the radiant power leaving the target, which is collected by the radiometer, in terms of the target radiosity J₁ and relevant geometric parameters. Leave in symbolic form.

(b) Write an expression for the target radiosity J₁ in terms of its irradiation, emissive power and appropriate radiative properties. Leave in symbolic form.

(c) Write an expression for the irradiation on the target, G₁, due to emission from the heater in terms of the heater emissive power, the heater area, and an appropriate view factor. Use this expression to numerically evaluate G₁.

(d) Use the foregoing expressions and results to determine the radiant power collected by the radiometer.

Radiometer + D,= 05 m D, = 0.25 m Heater, A T; = 1000 K, e 1 L= 0 25 m Sample, A, = 0.0004 m? T= 500 K. E, = 0.8