A metallic bar at 37°C is placed inside an oven whose interior is maintained at a temperature of 1100 K. The absorptivity of the bar (at 37°C) is a function of the temperature of incident radiation and a few representative value are given below: Temp (K) 310 700 1100 α 0.8 0.68 0.52   The rate of emission by the metallic bar is (in kW/m2)

A metallic bar at 37°C is placed inside an oven whose interior is maintained at a temperature of 1100 K. The absorptivity of the bar (at 37°C) is a function of the temperature of incident radiation and a few representative value are given below: Temp (K) 310 700 1100 α 0.8 0.68 0.52   The rate of emission by the metallic bar is (in kW/m2) Correct Answer 0.42

CONCEPT:

Stefan's Law: 

• According to Stefan’s law, the radiant energy emitted by a black body is directly proportional to the fourth power of its absolute temperature.

⇒ E = є σ T4A

Where E = Radiate energy, σ = Stefan-Boltzmann Constant, T = absolute temperature in Kelvin, є = Emissivity of the material, and A = Area of the emitting body.

• The value of Stefan's constant is 5.67 × 10-8 W/m2K4.

• Stefan's Law is used to accurately find the temperature Sun, Stars, and the earth.
• A black body is an ideal body that absorbs or emits all types of electromagnetic radiation.

EXPLANATION:

Rate of emission (E) = ϵσT⁴

• According to Kirchhoff’s Law of radiation,

⇒ σ = ϵ

⇒ At T = 37°C = 310 K,

⇒ α = ϵ = 0.8

• The rate of emission by the metallic bar is (in kW/m2) is 

⇒ E = 0.8 × 5.67 × 10 ^{- 8} × (310)⁴ × 10 ^{- 3}

⇒ E = 0.4189 kW/m² ≈  0.42 kW/m2