Question

Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation, in kW, from 1.02 m2 of 1000ºC fresh lava into 25.3ºC surroundings, assuming lava’semissivity is 0.97.

Answer 1

1.5 x 10⁵ W

Step-by-step explanation:

A = Area of the fresh lava = 1.02 m²

T = Temperature of fresh lava = 1000 °C = 1000 + 273 = 1273 K

T₀ = Temperature of surrounding = 25.3 °C = 25.3 + 273 = 298.3 K

ε = emissivity of the lava = 0.97

σ = stefan's constant = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴

Rate of transfer is given as

E = σ ε A (T⁴ - T₀⁴)

E = (5.67 x 10⁻⁸) (0.97) (1.02) ((1273)⁴ - (298.3)⁴)

E = 1.5 x 10⁵ W