Question

The earth receives 1.8 ✕ 1014 kj/s of solar energy. what mass of solar material is converted to energy over a 24-h period to provide the daily amount of solar energy to the earth?

Answer 1

Before starting, we will convert all the givens into standard units as follows:
1.8 * 10^14 KJ/sec = 1.8 * 10^14 * 1000 = 1.8 * 10^17 J/sec
24 hours = 24 * 60 * 60 = 86400 second

Now, we are given that:
The earth receives 1.8 * 10^17 J/sec. We will begin by calculating the total energy received by the earth in 24-hours
Total energy = 1.8 * 10^17 * 86400 = 1.5552 * 10^22 Joules

Then we will get the mass from the following rule:
E = m * c^2 where:
E is the total energy = 1.5552 * 10^22 Joules
m is the mass we need to find
c is the speed of light = 3 * 10^8 m/sec

Substitute with the givens to get the mass as follows:
1.5552 * 10^22 = m * (3*10^8)^2
m = 172800 kg