Converting 60KG into Light: Calculating Energy in Terms of Kilotons of TNT

[cubud]

Is light "pure" energy?

I've been working out how much energy 60KG of material is equivalent to. However it strikes me as a possibility that I should not be using E=MC^2 because what I actually want to calculate is 60KG equivalent in light.

Is there a factor I need to incorporate? I am trying to establish the consequences of being able to convert 60KG into light with 100% efficiency in terms of kilotonnes of TNT.


Thanks very much!

 

[Filip Larsen]

The factor is one. If you were to completely turn an object at rest with mass m into photons (like for instance gamma rays from mass and anti-mass annihilation) you would get photons with a total energy equal to mc².

 

[cubud]

The factor is one. If you were to completely turn an object at rest with mass m into photons (like for instance gamma rays from mass and anti-mass annihilation) you would get photons with a total energy equal to mc².

Thanks for the reply!

If I converted those photos back into 60KG of lead then that would not cause an explosion because I am converting them into a stable state. What I am trying to establish is what equivalent of kilotonnes of TNT degree of explosion I could expect if I were able to convert 60KG into light.

To convert to energy is as simple as converting 60KG into megajoules and then converting that into TNT kilotonnes, but when the 60KG is converting into light I suspect there is a factor I'd have to include. Am I correct in assuming it would result in a massive explosion?

 

[Filip Larsen]

It would indeed be a massive explosion as this is how nuclear weapons release energy. They get their energy release from the mass defect in nuclear fission or fusion processes (see for instance http://en.wikipedia.org/wiki/Binding_energy#Mass_defect). Note, that the energy release in nuclear processes does not necessarily have to be in form of photons, it could as well be kinetic energy of the particles involved, but it all still "counts" as energy.

If you compare with for instance http://en.wikipedia.org/wiki/TNT_equivalent you can calculate that your 60 kg turned into energy would correspond to around 1290 megaton of TNT.

 

[cubud]

If you compare with for instance http://en.wikipedia.org/wiki/TNT_equivalent you can calculate that your 60 kg turned into energy would correspond to around 1290 megaton of TNT.

1290 megatonnes?

I worked it out like so...

E=60 * 299792458^2
which is 5,392,531,072,420,905,840 joules
or 5,392,531,072,421 megajoules

There are 4.184 megajoules in 1 kilotonne of TNT
5,392,531,072,421 / 4.184
= 1,288,845,858,609 Kilotonnes
= 1,288,845,858 Megatonnes

 

[Filip Larsen]

My sources say that 1 ton of TNT is equal to 4.184 GJ (one million more than the value you use).

 

[Dale]

I also get 1290 megatons of TNT. The conversion I have is 4.184 GJ per 1 ton TNT, so that would be 4.184 MJ in 1 milliton of TNT instead of 1 kiloton. That is where cubud's extra factor of 10^6 came in.

 

[cubud]

I also get 1290 megatons of TNT. The conversion I have is 4.184 GJ per 1 ton TNT, so that would be 4.184 MJ in 1 milliton of TNT instead of 1 kiloton. That is where cubud's extra factor of 10^6 came in.

I think I see my error. There are 4,184 KJ in 1KG of TNT, not 1KT of TNT.

I'm glad I asked, I'd have looked pretty stupid :)

Is the general concept correct though, converting 60KG of mass into "light" would result in an explosion of this size?

 

[Dale]

Yes.

 

[Filip Larsen]

Is the general concept correct though, converting 60KG of mass into "light" would result in an explosion of this size?

Energy-wise, yes. And if converted fast enough it would be like an explosion.

 

[Lsos]

There are 4.184 megajoules in 1 kilotonne of TNT
5,392,531,072,421 / 4.184
= 1,288,845,858,609 Kilotonnes
= 1,288,845,858 Megatonnes[/QUOTE]

4.184 × 10^12 j = 4,184,000,000,000 joules in 1 kiloton of TNT.

That's 4,184,000 megajoules.Edit:
Damn...I was too slow. But yes, if you could convert 60kg of mass into light, it would be a big explosion...at least on earth. In space I guess it would just be a bunch of light rays. I'm not sure how that works in space...and I'm not sure if you can call a bunch of light an "explosion".

 

[Naty1]

yes, light IS pure energy...no mass, but it does have momentum.

I'm assuming the OP was asking a basic straightforward question.


If he/she was REALLY asking about the conversion of matter into light, not electromagnetic radiation, or was REALLY asking how much is converted to electromagnetic radiation rather than say kinetic energy of matter particles and sound waves, things get complicated quickly.

As implied earlier, it's only a few percent of the "mass" in a thermonuclear explosion that is actually converted to energy...the mass defect...and a LOT of the energy is NOT in radiation nor light but in kinetic energy of, say the 97% of the matter that remains which creates the "blast" (kinetic energy) effect which levels buildings...

A "true" conversion of mass the light energy (pure radiation) IS captured by the E = mc² NOT by the TNT equivalents used above which represents a TOATL equivalent energy.

"In space I guess it would just be a bunch of light rays...and I'm not sure if you can call a bunch of light an "explosion"."

Well it surely IS still an explosion...because, again, 97% of the output is kinetic energy of all the remaining matter particles...a difference is that there is no air as on Earth to displace...so apparently the particles emitted in space would have even greater energy than on earth...and there would be no burning of oxygen which must occur on Earth in an atmosphere.

 

[Lsos]

"In space I guess it would just be a bunch of light rays...and I'm not sure if you can call a bunch of light an "explosion".

This was meant for a 100% conversion of matter into energy, as in total annihilation...which most of this is discussion is about. In this case there would be no remaining matter particles.

But even if there is, isn't is correct to say that most of the mechanical destruction that an atomic bomb creates is due to the tremendous amount of air that it displaces, and not because of a few hundred/ thousand pounds of vaporized bomb casing?

 

[Jim1138]

If you combine hydrogen and anti-hydrogen, you would loose about half the energy/mass as neutrinos.

 

[vanesch]

It would indeed be a massive explosion as this is how nuclear weapons release energy. They get their energy release from the mass defect in nuclear fission or fusion processes

I like to nitpick here, and add that it is also the way a battery delivers its energy, or a match delivers its heat, or... It is not a particular property of nuclear reactions.
Mass defect is nothing else but "loss of energy" but only in nuclear reactions this is large enough to be measured as a change in total mass.

 

[cubud]

Hi all

Note the figure I use for tons of Tnt (907.18474) because it is "Tons" and not "Tonnes".

decimal speedOfLight = 299792458m;
decimal hiroshimaBombEnergyInKiloTons = 13m;
decimal initialMassInKG = 60m;
decimal initialMassEnergyInJoules = initialMassInKG * speedOfLight * speedOfLight;
decimal initialMassEnergyInKiloJoules = initialMassEnergyInJoules / 1000m;
decimal initialMassEnergyInMegaJoules = initialMassEnergyInKiloJoules / 1000m;
decimal initialMassEnergyInKilogramsOfTnt = initialMassEnergyInMegaJoules / 4.184m;
decimal initialMassEnergyInTonsOfTnt = initialMassEnergyInKilogramsOfTnt / 907.18474m;
decimal initialMassEnergyInKiloTonsOfTnt = initialMassEnergyInTonsOfTnt / 1000m;
decimal initialMassEnergyInHiroshimaBombs = initialMassEnergyInKiloTonsOfTnt / hiroshimaBombEnergyInKiloTons;

Speed of light: 299792458 metres/second
Hiroshima bomb energy in kilotons: 13
Initial mass: 60kg
Initial mass energy in joules: 5392531072420905840
Initial mass energy in kilojoules: 5392531072420905.84
Initial mass energy in megajoules: 5392531072420.90584
Initial mass energy in kilograms of TNT: 1288845858609.2031166347992352
Initial mass energy in tons of TNT: 1420709367.9829789868762554749
Initial mass energy in kilotons of TNT: 1420709.3679829789868762554749
Initial mass energy in Hiroshima bombs: 109285.33599869069129817349807

I think I have these figures right, do they look right to you guys?Thanks for your help!