How much energy is radiated each second by one square meter of a star whose temperature is 10,000 K? Note: σ in the Stefan-Boltzmann law is equal to . A) 5.67 × 10¹² J B) 5.67 × 10⁸ J C) 5.67 × 10⁴ J D) 300 nm E) 300,000,000 nm

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Quizplus · Accepted Answer

The energy radiated per unit time per unit area (i.e. power density) by a blackbody radiator is given by the Stefan-Boltzmann law as P = σT^4, where σ is the Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4) and T is the temperature in Kelvin. Plugging in the given temperature of 10,000 K, we get P = 5.67 × 10^-8 × (10,000)^4 = 5.67 × 10^15 W/m^2. This is approximately equal to 5.67 × 10^12 J/s/m^2 or 5.67 × 10^9 mW/m^2. The closest answer choice is B, 5.67 × 10^8 J/s/m^2 (which can also be written as 5.67 × 10^8 W/m^2 since 1 J/s equals 1 W).

How Much Energy Is Radiated Each Second by One Square