Final answer:
If the Sun fell into a black hole, the energy radiated would be enormous due to heat generated, potentially millions of degrees, as matter is pulled into the black hole's gravitational field. This process could result in energy emissions comparable to a thousand galaxies as seen in quasars. This vast amount of energy is attributed to the mass-energy conversion described by Einstein's equation E = mc².
Step-by-step explanation:
The question of how much energy would be released if the Sun fell into a black hole pertains to the immense energy release associated with mass moving into a black hole's intense gravitational pull. According to Albert Einstein's mass-energy equivalence formula, E = mc², a massive amount of energy could be liberated. If the Sun were to fall into a black hole, the matter from the Sun would heat up to incredibly high temperatures, potentially reaching millions of degrees, and radiate a significant amount of energy in the process. This energy is not from mass loss in atoms, but due to the gravitational energy conversion as matter falls closer to the black hole.
For a stellar mass black hole like one with 10 times the mass of the Sun (10 Msun), the energies released can be enormous. If a supermassive black hole, like those found at the centers of galaxies, with a billion solar masses (10⁹ Msun) were to accrete additional mass at a rate of about 10 Msun per year, it could release as much energy as a thousand galaxies, similar to the energies observed in quasars. Kelvin and Helmholtz's rate of the Sun's contraction gives us insight into the vast energy generation by the Sun, but the energy generated if the Sun were to collapse into a black hole would be on a much grander scale.