Radiant heat makes it impossible to stand close to a hot lava flow. Calculate the rate of heat loss by radiation from 1.00 m^2 of 1190°C fresh lava into 30.0°C surroundings, assuming lava's emissivity is 1.

259.274 kW

Explanation:

Given:

Area of the lava, A = 1.00 m²

Temperature of the surrounding, T₁ = 30.0° C = 303 k

Temperature of the lava, T₂ = 1190° C = 1463 K

emissivity, e = 1

Now,

from the Stefan-Boltzmann law of radiation the rate of heat loss is given as,

u = σeA (T₂⁴ - T₁⁴)

where,

u = rate of heat loss

σ = Stefan-Boltzmann constant = 5.67 * 10⁻⁸ W/m²∙K⁴

on substituting the respective values, we get

u = 5.67 * 10⁻⁸ * 1 * 1 * (1463⁴ - 303⁴)

or

u = 259274.957 W

or

u = 259.274 kW