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?

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