Final answer:
The rate of heat transfer by radiation from 1.00 m² of 1200ºC fresh lava into 30.0ºC surroundings, assuming lava's emissivity is 1.00, is approximately 1,236,000 W.
Step-by-step explanation:
The rate of heat transfer by radiation can be calculated using the Stefan-Boltzmann law:
Q = εσA(T1⁴ - T2⁴)
Where Q is the rate of heat transfer, ε is the emissivity, σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴), A is the surface area, T1 is the temperature of the hot object, and T2 is the temperature of the surroundings.
In this case, we have:
A = 1.00 m², T1 = 1200ºC = 1473K, T2 = 30ºC = 303K, and ε = 1.00.
Plugging in the values:
Q = (1.00)(5.67 x 10⁻⁸ W/m²K⁴)(1.00 m²)((1473K)⁴ - (303K)⁴)
Q ≈ 1,236,000 W
The correct answer is option d) 1,236,000 W.