How much energy is radiated each second by one square meter of a star whose temperature is 10,000 K? s in the Stefan-Boltzmann law is equal to ,

Question

How much energy is radiated each second by one square meter of a star whose temperature is 10,000 K? s in the Stefan-Boltzmann law is equal to  ,

Quizplus · Accepted Answer

The Stefan-Boltzmann law states that the energy radiated per second per unit area of a black body is proportional to the fourth power of its temperature. The constant of proportionality is given by s = 5.67 x 10^-8 W/m^2K^4. Thus, the energy radiated per second per unit area (or emissivity) of a star with a temperature of 10,000 K can be calculated as:

E = s x T^4
E = 5.67 x 10^-8 x (10,000)^4
E = 5.67 x 10^-8 x 10^16
E = 5.67 x 10^8 J/m^2s

Therefore, one square meter of a star with a temperature of 10,000 K radiates 5.67 x 10^8 J of energy per second, which corresponds to answer choice B. The Stefan-Boltzmann law states that the energy radiated per unit area per unit time (also known as the emissive power or flux density) is proportional to the fourth power of the temperature (in Kelvin) of the object. This relationship is given by the equation E = σT^4, where E is the emissive power, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), and T is the temperature of the object in Kelvin. Plugging in the given temperature of 10,000 K, we find that the energy radiated per second per square meter is:

E = σT^4 = (5.67 x 10^-8 W/m^2K^4)(10,000 K)^4 = 5.67 x 10^8 W/m^2

Therefore, the answer is B) 5.67 x 10^8 J/s (or W).

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