The Earth intercepts 1.27 * 1017 W of radiant energy from the sun. Suppose the Earth, of volume 1.08 * 1021 m3, was composed of water. How long would it take for the Earth at 0$\degree$C to reach 100$\degree$C, if none of the energy was radiated or reflected back out into space?

Question

Quizplus · Accepted Answer

First, we need to find the amount of energy required to raise the temperature of the Earth by 100°F (which is equivalent to 55.6°C). We can use the specific heat capacity of water, which is 4.18 J/g°C.

The mass of the Earth can be found using the density of water, which is 1000 kg/m³.

mass = density x volume 
mass = 1000 kg/m³ x 1.08 x 10²¹ m³ 
mass = 1.08 x 10²⁴ kg

The energy required can be found using the formula:

energy = mass x specific heat capacity x temperature change

energy = 1.08 x 10²⁴ kg x 4.18 J/g°C x 55.6°C 
energy = 3.96 x 10²⁷ J

Now we need to find the time it takes for the Earth to receive this amount of energy, which is equal to the radiant energy intercepted from the sun.

power = energy / time

time = energy / power

We can convert the intercepted power to watts by multiplying by 10¹⁷.

power = 1.27 x 10¹⁷ W

time = 3.96 x 10²⁷ J / (1.27 x 10¹⁷ W) 
time = 1.13 x 10⁵ seconds or 1.13 x 10⁵ / (60 x 60 x 24 x 365.25) years 
time = 1.13 x 10⁵ seconds or 113 years

Therefore, the best choice is D.

The Earth Intercepts 1 °\degree° C to Reach 100 °\degree° C, If None of the Energy Was Radiated or Reflected

The Earth Intercepts 1 $\degree$ C to Reach 100 $\degree$ C, If None of the Energy Was Radiated or Reflected