Question

If the temperature of the sun is doubled, the rate of energy received on the earth will increase by a factor of:
A. 2
B. 4
C. 8
D. 16

Answer 1

Hint: The energy radiated per unit area by a black body is governed by Stefan’s law.

Complete step by step answer:
The energy radiated per unit area is governed by Stefan’s law, which states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time is directly proportional to the fourth power of the black body's thermodynamic temperature T.
$\text{E}\propto {{\text{T}}^{\text{4}}}$
So let ${{\text{E}}_{\text{1}}}$ be the energy at temperature T and be ${{\text{E}}_{2}}$the energy at temperature 2T. Then the ratio of ${{\text{E}}_{2}}$ to ${{\text{E}}_{\text{1}}}$is,
$\dfrac{{{\text{E}}_{\text{2}}}}{{{\text{E}}_{\text{1}}}}=\dfrac{{{\text{T}}_{\text{1}}}^{\text{4}}}{{{\text{T}}_{\text{1}}}^{\text{4}}}=\left( \dfrac{{{(2\text{T)}}^{\text{4}}}}{{{\text{T}}^{\text{4}}}} \right)$

${{\text{E}}_{\text{2}}}=16{{\text{E}}_{\text{1}}}$
So the rate of energy received increases by 16 times.
So the answer to the question is option (D) 16.

Additional Information:
Solar radiation is created by nuclear fusion reactions in the sun's core, which causes it to emit a large amount of electromagnetic radiation, mostly in the form of visible light. This radiation is the energy that heats the Earth. The sun's surface emits about 63 million watts of energy per square meter.
Some of the solar energy that arrives at the Earth bounces off the atmosphere and clouds and back into space. The surface of the Earth receives about half of the incoming solar radiation. The solar energy takes the form of heat and visible light as well as ultraviolet rays, the type of energy that causes sunburn.

Note: Thermal radiation is energy transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures, the radiation is in the infrared region of the electromagnetic spectrum.