The total U.S. consumption of electricity in a particular year was 5.0 x 10^12 kilowatt-hours. What is the mass equivalence of this amount of energy? Show all calculations leading to an answer.
How would I solve it?
E = m c^2
c^2 = (3*10^8)^2 = 9 * 10^16
E = 5 * 10^15 watts * 3600 seconds
= 18 * 10^18 Joules
m = 18*10^18/9*10^16
= 2 * 10^2
= 200 Kg
about two big people mass :)
could you explain how you got your answer..step by step
I thought I did :)
surely you can google E = m c^2
(Albert Einstein)
there
E is in Joules which is watt seconds
c is speed of light, about 3*10^8 meters/second
an hour is 3600 seconds
a kilowatt is 1000 watts which is 1000 Joules/second
thank you so much! :)
To solve this problem, you need to use Einstein's famous equation E=mc^2, which relates energy (E) to mass (m) and the speed of light (c). First, let's convert the given energy from kilowatt-hours to joules, since the SI unit of energy is joules.
1 kilowatt-hour (kWh) = 3.6 x 10^6 joules
So, 5.0 x 10^12 kilowatt-hours = (5.0 x 10^12) x (3.6 x 10^6) joules
Multiply these numbers to get the result:
5.0 x 10^12 kilowatt-hours = 1.8 x 10^19 joules
Now, we can use the equation E=mc^2 to find the mass equivalence. Rearranging the equation, we have:
m = E / c^2
where c is the speed of light, approximately equal to 3.0 x 10^8 meters per second.
Substituting the given energy value and the speed of light into the equation, we have:
m = (1.8 x 10^19 joules) / (3.0 x 10^8 m/s)^2
Simplifying further:
m = (1.8 x 10^19 joules) / (9.0 x 10^16 m^2/s^2)
m = 2.0 x 10^2 kilograms
Therefore, the mass equivalence of the given amount of energy (5.0 x 10^12 kilowatt-hours) is approximately 2.0 x 10^2 kilograms.