To calculate the distance at which the gage should be positioned to receive irradiation of 1000 W/m², we can use the inverse square law for radiation. The formula is:
Irradiation = Emissive Power / (4 * π * distance^2)
where Irradiation is in W/m², Emissive Power is in W, and distance is in meters.
(a) Let's solve for the distance:
1000 W/m² = 3.72 × 10^5 W/m / (4 * π * distance^2)
Rearranging the equation to solve for distance:
distance^2 = (3.72 × 10^5 W/m) / (4 * π * 1000 W/m²)
distance^2 = 296.94 m²
distance ≈ √(296.94) ≈ 17.23 meters
Therefore, the gage should be positioned at a distance of approximately 17.23 meters from the furnace aperture to receive irradiation of 1000 W/m².
(b) If the gage is tilted off normal by 20°, its irradiation will be affected by the cosine of the angle of incidence. The formula is:
Irradiation = Irradiation_normal * cos(angle)
where Irradiation_normal is the irradiation when the gage is normal to the radiation, and angle is the angle of incidence.
Given that the irradiation_normal is 1000 W/m², and the angle of incidence is 20°, we can calculate:
Irradiation = 1000 W/m² * cos(20°)
Irradiation ≈ 1000 W/m² * 0.9397 ≈ 939.7 W/m²
Therefore, if the gage is tilted off normal by 20°, its irradiation will be approximately 939.7 W/m².