Question 868: Thermodynamics & KTG

Question

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

Accepted Answer

To determine the factor by which the rate of energy received by the Earth will increase if the temperature of the Sun is doubled, we should consider the Stefan-Boltzmann law. The Stefan-Boltzmann law states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature. Mathematically, it is expressed as:
$$E \propto T^4$$
where $ E $ is the energy radiated per unit area and $ T $ is the absolute temperature.
If the original temperature of the Sun is $ T $ and the temperature is doubled to $ 2T $, then the new rate of energy radiated ( $ E' $ ) can be calculated as follows:
$$E' \propto (2T)^4$$
Expanding this, we get:
$$E' \propto 2^4 \cdot T^4$$
Since $ 2^4 = 16 $, we have:
$$E' \propto 16 \cdot T^4$$
This means the new rate of energy radiated by the Sun is 16 times the original rate of energy. Therefore, the rate of energy received by the Earth will be increased by a factor of 16.
The correct option is:
Option D: 16

Answer

8

Answer

2

Answer

4

Answer

16

Thermodynamics & KTG

If the temperature of the sun is doubled, the rate of energy received by the earth will be increased by a factor

Choose the correct answer: