Compute the energy released in kilojoules when the sun converts 1.00 metric ton into energy. NOTE: 1 metric ton = 1000 kg.
To compute the energy released when the sun converts 1.00 metric ton (1000 kg) into energy, we can use Einstein's famous equation, E = mc², where E represents energy, m represents mass, and c represents the speed of light.
First, we need to calculate the mass of 1.00 metric ton in kilograms. Given that 1 metric ton is equal to 1000 kg, the mass (m) is:
m = 1000 kg
Next, we need to find the speed of light (c). The speed of light is a constant value, approximately equal to 3.00 x 10^8 meters per second (m/s).
c = 3.00 x 10^8 m/s
Now we can plug the values into the equation E = mc² to calculate the energy released:
E = (1000 kg) * (3.00 x 10^8 m/s)²
First, let's square the speed of light:
(3.00 x 10^8 m/s)² = (9.00 x 10^16 m²/s²)
Now, multiply the mass and the squared speed of light:
E = (1000 kg) * (9.00 x 10^16 m²/s²)
To simplify this expression, we can convert the units from square meters per second squared (m²/s²) to kilojoules (kJ).
To do that, we can use the conversion factor: 1 J = 1 kg * m²/s².
Since 1 kilojoule (kJ) is equal to 1000 joules (J), we can write the conversion factor as 1 kJ = 1000 J.
E = (1000 kg) * (9.00 x 10^16 m²/s²) * (1 kJ / 1000 J)
By simplifying the units, we have:
E = (1000 kg) * (9.00 x 10^16 m²/s²) * (1/1000) kJ
Simplifying further:
E = 9.00 x 10^13 kg * m²/s² * kJ
E = 9.00 x 10^13 kJ
Therefore, the energy released in kilojoules when the sun converts 1.00 metric ton into energy is approximately 9.00 x 10^13 kilojoules.