Question

A thin, square metal plate measures 15 cm on each side and has emissivity of 0.80. The plate is heated to a temperature of 605°C. What is the rate at which the plate radiates energy ? The Stefan-Boltzmann constant is 5.67 × 10-8 W/(m2 ∙ K4). Remember that the plate will radiate energy from both its top and bottom surfaces.

Answer 1

Answer:

1213 Watt

Explanation:

A = 15 x 15 = 225 cm^2 = 0.0225 m^2

e = 0.80

T = 605 C = 605 + 273 = 878 K

σ = 5.67 x 10^-8 W / (m2 . K^4)

Energy per unit time = σ A e T^4

Energy per unit time = 5.67 x 10^-8 x 0.80 x 0.0225 x (878)^4

Energy per unit time = 606.5 Watt

Rate of energy radiated from both the surfaces = 2 x 606.5 = 1213 Watt

Answer 2

L = 15cm = 0.15m
A = 0.15 × 0.15 = 0.0225
Sradiation is transfered from bottom
σ = 5.67 × 10⁻⁸ W/m²k
T = 605 c = 878k
Rate of energy transfer
Q = σ × A × E × T⁴
5.67 × 10⁻⁸ × 0.0225 × 2 × 0.8 × 878⁴
1792.17 W