$-267 \textrm{ kW}$

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This is College Physics Answers with Shaun Dychko. We're going to calculate the rate of heat transfer due to radiation from one square meter of lava into its surroundings. And so, the emissivity of lava, we're told, is one. The temperature of the lava is 1200 degrees Celsius, which we have to convert into Kelvin by adding 273.15. And then, the temperature of the surroundings is 30 degrees Celsius, which converts to 303.15 Kelvin. So, we plug in to this formula to find the rate of heat transfer due to radiation. So, that's Stefan Boltzmann's constant times emissivity times area times the temperature of the surroundings to the power of four minus temperature of the lava to the power of four. So, that's 5.67 times ten to the minus eight times one times one square meter times this temperature of the surroundings to the power of four minus temperature of the lava to the power of four, which is negative 267 Kilowatts. And, we expected this negative sign here because this formula tells us the rate at which an object is gaining energy from its surroundings. And so, it's not gaining, it's losing, and that's indicated by this negative sign. And, there we go.