High School

A body in a room at [tex]300 \, \text{K}[/tex] is heated to [tex]3000 \, \text{K}[/tex]. By what factor does the amount of energy emitted each second by the body increase?

Answer :

The amount of energy emitted each second by the body increases by a factor of approximately 16.

According to the Stefan-Boltzmann law, the energy emitted by a black body per unit surface area is directly proportional to the fourth power of its temperature. In this case, the initial temperature is 300 K, and when heated to 3000 K, the temperature increases by a factor of 10.

According to the Stefan-Boltzmann law, the energy emitted is proportional to the temperature raised to the power of 4. Therefore, the increase in temperature by a factor of 10 results in an increase in energy emitted by a factor of 10^4, which is equal to 10,000.

Hence, the amount of energy emitted each second by the body increases by a factor of approximately 16 (10,000/625).

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