rubecuber said:
how do i find out how much energy a 20 solar Mass Black Hole would radiate given that it consumes 20 Kilograms worth of matter a second (or any reasonable amount)
Thanks,
Rubecuber!
Hi Nereid, hi Rubecuber!
Rubecuber, Nereid is understandably puzzled by your two questions. first a 20 solar mass black hole wouldn't radiate hardly any watts cause it would be so cold, so the question comes across as naive!
But then you are 15 years old and learning physics on your own, obviously outside the school context.
You also seem pretty smart, so might be fun to talk to.
now you want to MAKE the black hole radiate some energy by dropping stuff into it.
the answer clearly depends on how the matter goes in!
when matter spirals into a BH it is not the BH itself that is radiating
(it doesn't contribute significantly more Hawking radiation)
the most inefficient conversion would be if you just dropped blocks of matter straight in, kerplunk. Like you have a bunch of used television sets each 20 kilogram, and you dropped them straight in one at a time, one per second.
this would radiate almost nothing because the television sets would not get hot and glow and ionize----they would just stay cold and electrically neutral and fall in and never be seen again. the hole would eat them without even a burp.
the most efficient conversion would be if the hole was surrounded by an ACCRETION DISK of matter spiraling in. and as it spirals in it collides with itself and rubs on itself and gets very hot and glows with X-ray light and goes faster and faster, circling millions of times before it gets close enough to be eaten up.
So you could have, I suppose, millions of tons of matter whizzing around the BH and glowing hot and gradually spiralling in, so that only 20 kilogram gets consumed per second.
Energywise what is happening is that the GRAVITATION POTENTIAL ENERGY of the matter in the accretion disk is being given up, as the matter gets closer and closer in. And a large percentage of the graviational potential energy is being converted to Xray and other electromagnetic glow------because the ionized particles bump each other as they get more and more crowded, as they spiral in tighter and tighter.
So the answer to your question depends a lot on your ASSUMPTIONS of how you are letting the matter fall in.
It could be that almost none of the gravitational energy gets converted
It could be that a large percent of the gravitational energy gets converted.
How do you want to imagine it?
If this were a textbook or homework problem, I think they would TELL you what assumptions to assume. But you seem to be doing something more interesting, you are posing yourself problems that you make up. And they so far lack some definition. you need to make them more definite.
Are you trying to learn what is a TYPICAL energy conversion rate of a TYPICAL accretion disk of a kind of usual-size black hole? I'll bet someone here has that information.
Also I agree with Nereid that this question is related to the one you asked earlier, although it is a different question. And of course if there is any concern or issue about it you should clarify is a homework question or not.
If you are trying to learn about typical accretion disk energy conversion efficiency, let us know. Nereid or others may have some good links about that.