#### marcus

Gold Member
Dearly Missed
to keep things simple the units are c=G=hbar=k=1 and
all black holes are non-rotating uncharged.

I think everybody here probably has a qualitative notion of how the Hawking radiation arises from the event horizon of a black hole---there has been tons of pop-sci journalism about this. What may be lacking is a corresponding quantitative feel---an ability to estimate magnitudes.

If a black hole surface area is on the order of a square angstrom, for instance, what is the temperature compared with things you know about----a hot sidewalk, the surface of the sun, the core of the sun, the big bang, etc?

Again, if the surface area is a square angstrom or so, what is the wattage roughly speaking? One should have a rough quantitative grasp to fill out the intuitive picture.

History: in 1974 Bekenstein said the entropy S is given by
S = A/4, where A is the area

And according to Hawking (1975) the temperature T is given by
1/sqrt(4piA)

We should do an example to get a feel for that----say area is 1050 planck, which is about a square angstrom.
then 4piA is 12.6E50 and sqrt(4piA) is 3.5E25 and the temperature (one over that) is 0.28E-25

This is about one quarter of the temperature at the core of the sun----suncore temp is 10-25, roughly 1200 eevee.
Being a quarter of that one can think of it as soft xray or hard UV or whatever. So it isnt big bang temperature which would be just one, or even suncore, but about a quarter of that.

What is the luminosity or wattage of this thing? Well the Boltzmann law says take the fourth power of the temp and multiply by pi2/60. That gives the radiant power per unit area and then you have to multiply by A to get the overall power.

The Hawking temperature, remember, is 1/sqrt(4piA). And so
the fourth power is 1/(4piA)2

And multiplying by the Stefan-Boltzmann const pi2/60
gives us (1/960)(1/A2) which is power per unit area

And then multiplying by A to get the total power gives

(1/960)(1/A) which if you want you can write 1/(960A)

*****THAT'S ALL, the tutorial is over*****

But there is one more little thing having to do with SI units.
Suppose you love metric units and want to put back in all the hbar and cees and stuff and do a purely metric calculation of the same thing. Here is how to get the metric formula back:

Planck power is c5/G
Planck area is Ghbar/c3

That is all you need to know! You just take the 1/(960A) formula and instead of A you put in (A'/planckarea) where A' is the area in metric. Then the formula becomes

1/(960 A') x (planckarea in metric) x (planckpower in metric),

in other words (1/960A') x hbar c2.

This hbar ceesquared is just what is needed to
make the units agree, if you choose to work in SI metric.

Related Astronomy and Astrophysics News on Phys.org

#### kyle_soule

I appreciate the time you put into this It is an excellent tutorial and much needed, it's not often described in any further detail as how the event occurs with no or very little mathematical accompaniment.

Thanks for enlightening me on the realistic approach to Hawking Radiation

#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
I appreciate the time you put into this It is an excellent tutorial and much needed, it's not often described in any further detail as how the event occurs with no or very little mathematical accompaniment.

Thanks for enlightening me on the realistic approach to Hawking Radiation
You are most welcome Kyle and I thank you for the kind words. Actually your response helps me in what I am doing.

I am looking for potential textbook examples of interesting things that natural units (c=G=hbar=k) are good for calculating.
I figure there could be a dynamite kickass physics textbook either online or hardcopy that would show things that are neat to do with natural units.

The relation between a black hole area and brightness is one
possible example-----simply 1/960A

Another is the Chandrasekhar limit (the threshhold mass for having a supernova explode) it is incredibly easy to calculate
the Chandra limit just from knowing one thing: the mass of a proton. Would this interest you?

BTW in planck the proton's mass is 1/(13E18)

actually instead of 13 one can say 12.99 some. But 13 is
plenty close for back of envelope calculation. A lot of neat stuff
can be calculated just from the mass of a proton.

Anyway, I want to find stuff that grabs people's interest and which also is extremely simple to calculate in planck and is
tedious and involved to calculate in metric.

The chandrasekhar limit is a good example---it is a pain in the butt to calculate in metric.

Another example is the light-bending formula of GR. By how much is a ray of light bent that passes a million miles from the sun (from the sun's center). Yucky to calculate in metric but a snap in planck.

I want to see if a textbook-like thing can be put together of such things. Also it has to be fun. Your reactions help guide me in this.

#### kyle_soule

Originally posted by marcus
You are most welcome Kyle and I thank you for the kind words. Actually your response helps me in what I am doing.

I am looking for potential textbook examples of interesting things that natural units (c=G=hbar=k) are good for calculating.
I figure there could be a dynamite kickass physics textbook either online or hardcopy that would show things that are neat to do with natural units.

The relation between a black hole area and brightness is one
possible example-----simply 1/960A

Another is the Chandrasekhar limit (the threshhold mass for having a supernova explode) it is incredibly easy to calculate
the Chandra limit just from knowing one thing: the mass of a proton. Would this interest you?

BTW in planck the proton's mass is 1/(13E18)

actually instead of 13 one can say 12.99 some. But 13 is
plenty close for back of envelope calculation. A lot of neat stuff
can be calculated just from the mass of a proton.

Anyway, I want to find stuff that grabs people's interest and which also is extremely simple to calculate in planck and is
tedious and involved to calculate in metric.

The chandrasekhar limit is a good example---it is a pain in the butt to calculate in metric.

Another example is the light-bending formula of GR. By how much is a ray of light bent that passes a million miles from the sun (from the sun's center). Yucky to calculate in metric but a snap in planck.

I want to see if a textbook-like thing can be put together of such things. Also it has to be fun. Your reactions help guide me in this.
This would interest me very much indeed! Epecially the SNe threshold. You don't come across many (none in my experience) of down to earth, real life (meaning common experience) examples in a not-so-mathematical explantion.

#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
This would interest me very much indeed! Epecially the SNe threshold. You don't come across many (none in my experience) of down to earth, real life (meaning common experience) examples in a not-so-mathematical explantion.
It's 11:30 PM and I'm getting sleepy so shd probably start on that tomorrow. You in Illinois---must be 1:30AM, nightowl.

Thing about Ch. limit. Everybody says it is 1.4 solar masses
but nobody says why.

Well it happens that in natural units solar mass is 0.93E38
so 1.4 solar is 1.3E38

So here we have this unexplained number. Why does a no-longer-fusing ball explode if its mass is 1.3E38
and not explode if its mass is less, say 1.2E38?

Where does this number come from.

Turns out it comes from the mass of the proton which is
one over 13E18.

the chandra limit is (pi/4)(13E18)2

really not all that hard to calculate in the c=hbar=G=1 system
but gets messy if you have to include a whole lot of G's and hbar's and cees in it.
Here you just have to square 13E18---the proton compton wavelength actually, reciprocal of its mass----and then multiply by pi/4.

Should get to bed, dream of exploding stars.

#### kyle_soule

Originally posted by marcus
It's 11:30 PM and I'm getting sleepy so shd probably start on that tomorrow. You in Illinois---must be 1:30AM, nightowl.

Thing about Ch. limit. Everybody says it is 1.4 solar masses
but nobody says why.

Well it happens that in natural units solar mass is 0.93E38
so 1.4 solar is 1.3E38

So here we have this unexplained number. Why does a no-longer-fusing ball explode if its mass is 1.3E38
and not explode if its mass is less, say 1.2E38?

Where does this number come from.

Turns out it comes from the mass of the proton which is
one over 13E18.

the chandra limit is (pi/4)(13E18)2

really not all that hard to calculate in the c=hbar=G=1 system
but gets messy if you have to include a whole lot of G's and hbar's and cees in it.
Here you just have to square 13E18---the proton compton wavelength actually, reciprocal of its mass----and then multiply by pi/4.

Should get to bed, dream of exploding stars.
Yep, approaching 2 am...where exactly, please excuse my foolishness, does pi/4 come from? And is there something that actually makes 1.3E38 special, a reason for the explosion?

#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
Yep, approaching 2 am...where exactly, please excuse my foolishness, does pi/4 come from? And is there something that actually makes 1.3E38 special, a reason for the explosion?
foolishness! (false modesty) it is one of the more astute questions I have heard on PF

I can only share with you where I am on this.
Frank Shu (UC Berkeley) has a remarkable textbook called
"The Physical Universe---An Introduction to Astronomy"
(expensive, so use interlibrary loan and get it free) and on page 128 it gives a formula for the Chandrasekhar mass as a certain number times the mass of the proton.

Even tho it's messy I will copy out this number.
It has a term (Z/A)^2 which is where the 1/4 comes from.
After the star stops fusing it has some chemical composition
with an average atomic number Z and average atomic weight A.

Like Carbon12 has Z=6 and A=12, so its (Z/A)=1/2 and the square is 1/4.

What this is talking about is the "proton fraction"
the mass is made up of protons and neutrons and if it is already neutrony it is easier to crush into neutronmatter, so the threshhold for collapse is a little lower
but if it is very protony( high Z/A, like carbon) then the threshhold is higher. Maybe I should not be so informal but that is the intuitive content of the 1/4 in the formula. It is really (Z/A)^2 but that is approximately 1/4.

The most extreme case of a star that has finished fusing is iron---the whole core is iron---and that has Z/A = 26/56, which is not quite 1/2 but still close enough for rough estimates.

So rather than get into the Z/A detail I just say 1/4.

Here is Frank Shu verbatim

0.20 (Z/A)2 (hc/Gmprot2)3/2

That is a pure dimensionless number and the mass threshhold is what you get by multiplying that number by the mass of the proton.

This is hard. My guess is that unless you are as smart as Chandrasekhar it will take a few days to assimilate this.
You might want to tinker with it algebraically.

It conceals the planck mass = sqrt(hbar c/G), or rather, it
conceals the square of the planck mass = hbar c/G

It conceals, if you scramble around algebraically a bit,
the RATIO of the proton mass, mprot to the
planck mass.

What would happen if you rewrote the formula to be in terms of
the planck mass instead of (as Frank Shu has it) in terms of the proton mass?----after all that's just a changes of units.

Anyway mess with it a bit if you have time and we will talk later.

#### marcus

Gold Member
Dearly Missed
Why 1.3E38 is special

Oh yes, you asked why that mass is special.

It is the strength limit of ordinary matter.

Ordinary matter (nuclei made of protons and neutrons, plus a sea of electrons) will crush itself by its own weight and turn into
neutron matter (roughly a thousandth the diameter) if there is too much of it.

this mass 1.3E38 is how much it takes for this to happen

Imagine a ball of iron with that mass. The pressure is so
great that it causes the protons to eat the electrons and become neutrons
then the neutrons clump together into neutron matter which occupies only a billionth as much space (very roughly speaking).

So the whole ball of iron is suddenly in free fall towards its own center. A jillion loaded freight elevators have suddenly all at the same moment busted their cables. Gravitational potential energy is being released on a mammoth scale and being converted into
kinetic energy.

The nerd's term for forcing the neutrons to eat the electrons is
"reverse beta decay" and it incidentally releases a neutrino.
So suddenly a jillion neutrinos blow out of the center of this ball of iron.

Various other things take place and everybody has a great time.

They say we are made of the material blown out into space by these explosions---because without them most of the carbon nitrogen oxygen etc that is cooked by fusion in starcores would be trapped in dead cores and not get out into space where it can condense into planets and stuff. So these explosions are a necessary part of life as well as being beautiful.

#### kyle_soule

Let's see if I understand this...if instead of Carbon or any other close to 1/2 element, you use Radon instead and get (86/222)2 and come much closer to 2/13 or for rough estimate purposes, 1/7. This would change &pi;/4 into &pi;/7?

Basically, a fourth isn't a set number, but simply a rough estimate of what (Z/A)2 comes out to?

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#### Labguy

By Marcus:
Another is the Chandrasekhar limit (the threshhold mass for having a supernova explode) it is incredibly easy to calculate
The Chandrasekhar limit is not a limit above which a star will explode. Very few supernovae have anything at all to do with the "Chandra limit" of 1.44 Sm for He cores, and 1.79 sm for Fe cores.

The rest of your math post didn't catch my eye...

(Edited to correct to the 1.79 figure above)

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#### marcus

Gold Member
Dearly Missed
Originally posted by Labguy
By Marcus: The Chandrasekhar limit is not a limit above which a star will explode. Very few supernovae have anything at all to do with the "Chandra limit" of 1.44 Sm for He cores, and 1.39 sm for Fe cores.

The rest of your math post didn't catch my eye...
What I thought I said was that it was a mass limit for no-longer-fusing stars. Perhaps you did not see that condition.

At the end of fusion, when the core is (say) iron which cant fuse anymore, then the star has no source of heat to fight against gravity. Then, if it exceeds the limit, it can collapse.

I have been over this so many times I may occasionally skip details but don't believe I said anything misleading.

Of course by the time a star has finished fusing it will in many cases have already blown off most of its mass (in red giant etc) and be essentially a core of its former self.

There are a lot of scenarios----like the type Ia binary star mass transfer onto a white dwarf etc----but the Chandra limit is
the important triggering mass threshhold that always comes in somewhere in the story.

#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
Let's see if I understand this...if instead of Carbon or any other close to 1/2 element, you use Radon instead and get (86/222)2 and come much closer to 2/13 or for rough estimate purposes, 1/7. This would change &pi;/4 into &pi;/7?

Basically, a fourth isn't a set number, but simply a rough estimate of what (Z/A)2 comes out to?
Yes! You got it! (unless Labguy wants to contradict)

Here is something interesting you can check if you just have a periodic table of the elements. The highest a star can fuse to is IRON. It cannot go to Radon!!!! So there is a limit on how low Z/A can get. For rough and ready I just take it to be 1/2 because it is around that or a little less, for iron.

Here is how to check it. It is called "the curve of binding energy" and you calculate it say for iron-56 by dividing the atomic weight
55.935 by the nucleon number 56. this gives the mass-energy per nucleon (per proton or neutron).

It is at a minimum for iron. So nuclear fusion reactions can be exothermic (yielding energy) up to iron. But it actually COSTS energy to squash iron nucleuses together to get still heavier things.

The elements higher than iron are actually synthesized in the violent explosion of a supernova when there is a lot of extra energy around to waste on side-reactions.

the heavier-than-irons are not made in normal slow thermonsuclear burning that goes on throughout the stars life.

My attitude is very back-of-envelope about this. I say 1/4 instead of (Z/A)^2. But I am glad your impulse is to be more careful. By being deliberate and analytical you have uncovered this thing about iron being the minimum of the curve of energy. Or maximum depending on how you draw the curve.

#### Labguy

Originally posted by marcus
What I thought I said was that it was a mass limit for no-longer-fusing stars. Perhaps you did not see that condition.

At the end of fusion, when the core is (say) iron which cant fuse anymore, then the star has no source of heat to fight against gravity. Then, if it exceeds the limit, it can collapse.

I have been over this so many times I may occasionally skip details but don't believe I said anything misleading.

Of course by the time a star has finished fusing it will in many cases have already blown off most of its mass (in red giant etc) and be essentially a core of its former self.

There are a lot of scenarios----like the type Ia binary star mass transfer onto a white dwarf etc----but the Chandra limit is
the important triggering mass threshhold that always comes in somewhere in the story.

No critical error, it is just that the Chandar limit(s) are masses above where the mass must collapse to a different state. Stars explode or not based on many other criteria, and only then does the Chandra limit(s) come into play. In some stars, usually Type II supernovae, the iron core can cause the implosion/rebound/explosion if the core exceeds the limit. In smaller stars a white dwarf may be the end result and do nothing but cool over many years. In most binaries, an accretting white dwarf will not explode even if the white dwarf exceeds the limit. No explosion; just a collapse to a neutron star. Type Ia supernovae are extremely rare cases, regardless of most oversimplified texts and websites.

#### marcus

Gold Member
Dearly Missed
Originally posted by Labguy
By Marcus: The Chandrasekhar limit is not a limit above which a star will explode. Very few supernovae have anything at all to do with the "Chandra limit" of 1.44 Sm for He cores, and 1.79 sm for Fe cores.

The rest of your math post didn't catch my eye...

(Edited to correct to the 1.79 figure above)
Hello Labguy it interests me very much that you edited your
post just now to change from 1.39 solar (for a core of iron)
to 1.79 solar (for a core of iron). Do you have a web resource
giving chandra mass for various chemical makeups that you would like to share with us?

#### marcus

Gold Member
Dearly Missed
Originally posted by Labguy
No critical error, it is just that the Chandar limit(s) are masses above where the mass must collapse to a different state. Stars explode or not based on many other criteria, and only then does the Chandra limit(s) come into play. In some stars, usually Type II supernovae, the iron core can cause the implosion/rebound/explosion if the core exceeds the limit. In smaller stars a white dwarf may be the end result and do nothing but cool over many years. In most binaries, an accretting white dwarf will not explode even if the white dwarf exceeds the limit. No explosion; just a collapse to a neutron star. Type Ia supernovae are extremely rare cases, regardless of most oversimplified texts and websites.
Ah! I am reassured that there was no critical error you were pointing to! Your point is that sometimes there can be a collapse (say down to neutron matter) without an explosion.

I agree. the gravitational energy that is released can be carried off in various ways. I believe (correct me if I am mistaken) that some very bright gamma ray bursts are not so far thoroughly understood and there is theorizing that they may be due to
a star's sudden collapse----the model being in some ways similar to a supernova but in other essential ways different. If you have some websites to add to the discussion please contribute them. It is an interesting topic. Some collapses apparently two-stage---first down to neutron matter and then after a few days of cooling or something proceeding to black hole---or so I'm told. Like to know more about this.

#### Labguy

Hello Labguy it interests me very much that you edited your....
The edit was just because I typed the wrong number the first time, just a typo.

I have not yet found a website (haven't hunted either) with enough detail to go into the specifics of the two different "Chandra Limits". My source is SUPERNOVAE by Paul and lesley Murdin, as well as several other books by Wheeler, S.E. Woosley and others.

Chandra did calculate another, you may know, and this is the 3.2 solar masses beyond where any matter, usually neutron stars, would have to collapse further to a black hole. Lately, there is good evidence for "Strange Quark" stars also.

I only jumped in here because of the statement that "Another is the Chandrasekhar limit (the threshhold mass for having a supernova explode)..". I know, that you know, there are many other factors involved. Just got bugged--- -- by the general oversimplification. It is a bad habit of mine..

Damn, you can sure type long responses. I am a two-finger guy, very slow.

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#### kyle_soule

Yes! You got it! (unless Labguy wants to contradict)

Here is something interesting you can check if you just have a periodic table of the elements. The highest a star can fuse to is IRON. It cannot go to Radon!!!! So there is a limit on how low Z/A can get. For rough and ready I just take it to be 1/2 because it is around that or a little less, for iron.

Here is how to check it. It is called "the curve of binding energy" and you calculate it say for iron-56 by dividing the atomic weight
55.935 by the nucleon number 56. this gives the mass-energy per nucleon (per proton or neutron).

It is at a minimum for iron. So nuclear fusion reactions can be exothermic (yielding energy) up to iron. But it actually COSTS energy to squash iron nucleuses together to get still heavier things.

The elements higher than iron are actually synthesized in the violent explosion of a supernova when there is a lot of extra energy around to waste on side-reactions.

the heavier-than-irons are not made in normal slow thermonsuclear burning that goes on throughout the stars life.

My attitude is very back-of-envelope about this. I say 1/4 instead of (Z/A)^2. But I am glad your impulse is to be more careful. By being deliberate and analytical you have uncovered this thing about iron being the minimum of the curve of energy. Or maximum depending on how you draw the curve.
Let me see how this works, as I want to graph this curve:

56Fe
MMg=55.934942

A=56 Z=26

N=A-Z

MH=1.007825

Mn=1.008665

[del]MA=MMg-Z*MH-N*Mn
[del]MA=55.934942-26*1.007825-30*1.008665=-0.528458

-Sign Reversal-

EB=931.5*0.528458

EB=8.79033263 MeV (per A)

is all this work correct? Just want to make sure Of course I could just go rip off some binding energy curves that somebody else did, but where is the fun in this?

#### marcus

Gold Member
Dearly Missed
Hi Kyle, I just got back to the computer and saw your post. I have not checked the math but am responding impulsively impromptu.
I believe we should look at a few sample points on the curve first.
Like, be very empirical.
I have my fat CRC Handbook out and Im opening it to
the table of isotopes. Everybody should have the CRC Handbook of chemstry and physics----or is this stuff on the web?

It fell open to sodium-23----22.9898
Flip the page oxygen-16----15.9949
Have to have hydrogen-1---1.00797
And of course carbon-12----12.0000
Another at random silver-107---106.9051

I chose these more or less randomly but
they are common isotopes in each case---stable.
Now I could be wrong. What I expect is that if
in each case I divide the weight by the nucleon number
I will get a minimum at iron.

hydrogen-1----1.00797
carbon-12------1.0000
oxygen-16-----0.99968
sodium-23----0.99952
calcium-40----0.99906
iron-56------0.99884
silver-107----0.99911

So there are some sample points on the curve. you can fill in
some more. Personally I expect the curve to not be a curve!
I expect it to be jagged and jittery because so much is going
on as you proceed up the nuclear weight scale. But they CALL
it a curve, as you would expect of people for whom everything
is curves----unless its a Lie Group. Just kidding.
Do you have a web source for the nuclear binding energy?
It might be a pretty thing to see online.
I should really be saying the binding energy for iron is maximal
because the binding energy is the deficit---how much the nucleons are in hock for. But I rushed into it and did things
upside down I guess. For me it is more intuitive to think of
iron as minimal.
Do you have a table of the weights of the isotopes?
Or know of one online?

#### kyle_soule

Originally posted by marcus
Hi Kyle, I just got back to the computer and saw your post. I have not checked the math but am responding impulsively impromptu.
I believe we should look at a few sample points on the curve first.
Like, be very empirical.
I have my fat CRC Handbook out and Im opening it to
the table of isotopes. Everybody should have the CRC Handbook of chemstry and physics----or is this stuff on the web?

It fell open to sodium-23----22.9898
Flip the page oxygen-16----15.9949
Have to have hydrogen-1---1.00797
And of course carbon-12----12.0000
Another at random silver-107---106.9051

I chose these more or less randomly but
they are common isotopes in each case---stable.
Now I could be wrong. What I expect is that if
in each case I divide the weight by the nucleon number
I will get a minimum at iron.

hydrogen-1----1.00797
carbon-12------1.0000
oxygen-16-----0.99968
sodium-23----0.99952
calcium-40----0.99906
iron-56------0.99884
silver-107----0.99911

So there are some sample points on the curve. you can fill in
some more. Personally I expect the curve to not be a curve!
I expect it to be jagged and jittery because so much is going
on as you proceed up the nuclear weight scale. But they CALL
it a curve, as you would expect of people for whom everything
is curves----unless its a Lie Group. Just kidding.
Do you have a web source for the nuclear binding energy?
It might be a pretty thing to see online.
I should really be saying the binding energy for iron is maximal
because the binding energy is the deficit---how much the nucleons are in hock for. But I rushed into it and did things
upside down I guess. For me it is more intuitive to think of
iron as minimal.
Do you have a table of the weights of the isotopes?
Or know of one online?
http://science-park.info/periodic/ [Broken]
Clicking on the elements brings up information, which includes isotopes.

Also, I see what you calculated, what I calculated was different, it was this...

http://cfa160.harvard.edu/~rmcgary/binding.gif [Broken]

Your method is much easier, I will do both. Tomorrow will be a boring day in school, I'll just do it during school

EDIT: As the second link shows, I was calculating the binding energy per nucleon.

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#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
http://science-park.info/periodic/ [Broken]
Clicking on the elements brings up information, which includes isotopes.

Also, I see what you calculated, what I calculated was different, it was this...

http://cfa160.harvard.edu/~rmcgary/binding.gif [Broken]

Your method is much easier, I will do both. Tomorrow will be a boring day in school, I'll just do it during school

EDIT: As the second link shows, I was calculating the binding energy per nucleon.
Frankly I am thrilled to be dealing with someone who has this
much gumption. Go for it. I am confident your results will be
right and (partly for lack of time) will not check them.

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#### Alexander

Marcus, so how about Hawkins radiation? Can you derive its power, spectrum distribution and peak wavelength without cutting and pasting from a textbook?

#### kyle_soule

Originally posted by Alexander
Marcus, so how about Hawkins radiation? Can you derive its power, spectrum distribution and peak wavelength without cutting and pasting from a textbook?
Why do you have to be so negative and sarcastic. You should have gotten the idea on PF2 when so many of the threads you commented on were locked. If you have nothing to contribute to this conversation, we would all appreciate it very much if you did not comment at all.

How would anybody learn if you did not use a textbook at one time? Do you (or have you), I believe you said you were a teacher, not use a textbook?

EDIT: If you had a problem with how you think marcus is performing it is much more appropriate to pm him...but who cares about manners or rudeness, right? of course you wouldn't.

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#### marcus

Gold Member
Dearly Missed
Heh heh,

"Marcus, so how about Hawkins radiation? Can you derive its power, spectrum distribution and peak wavelength without cutting and pasting from a textbook?"

Alexander certainly is argumentative isnt he?
I didnt know about the events of PF2 that you refer to, Kyle.
Havent been around that long.

I feel respect and even a kind of gratitude towards major discoveries in physics---make life so much more interesting---and have no need to pretend that I can derive them on my own.

In the discussion so far of Hwkng radiation I havent needed any textbook because just happen to remember that, in the units I use, the temp is g/2pi.

This little fact T = g/2pi tells a lot because starting from the mass M one can get the radius 2M and so g must clearly be 1/4M, just by the classical nwtnian law-----GM/R2

So temp is 1/8piM, and so on. You just need to remember that the temp is g/2pi and the rest follows from classical freshman physics or highschool physics.

And Boltzmann's law is classical too----sigma T4
and sigma is just pi-square over 60.

the power spectrum for thermal radiation at a certain temperature is just the old Planck blackbody curve for things
at that temperature. Once you know the temperature you know a lot---and it doesnt take a lot of fishing in the textbook.

What did Alexander used to do that would get threads locked?
Sounds like it might be a riot.

#### kyle_soule

Originally posted by marcus
What did Alexander used to do that would get threads locked?
Heated debates and he was insulting.

This is, of course, only if it is the same Alexander.

I looked at this CRC Handbook of Chemistry and Physics...a little too pricey with my current income, college coming up in a month, car payments, insurance, etc. I have no given up hope on a free, or much cheaper, version on the internet somewhere

#### marcus

Gold Member
Dearly Missed
Originally posted by kyle_soule
Heated debates and he was insulting.

This is, of course, only if it is the same Alexander.

I looked at this CRC Handbook of Chemistry and Physics...a little too pricey with my current income, college coming up in a month, car payments, insurance, etc. I have no given up hope on a free, or much cheaper, version on the internet somewhere
about CRC handbook, if you are a college student you never need
it because it is in the reference section or at the reference desk of the places you spend your time----the physics library or chem library or engineering library! It is a book that is always around when you need it.

also nowadays so much of that information is, as you indicate, available on web.
there is no need to have all the tables in one book or at one website. most likely you simply keep track of which website to go to for which data.
planets here, elements there, properties of materials the other place, chemical reactions and molecules yet a fourth place etc.

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