Can a single nuclear bomb power the world for 2 trillion years?

[SamP37]

Helly everyone.
I'm new in physics and I don't understand many things there. What interests me the most is energy generation.
I was mostly reading Wiki articles, and I found something I couldn't understand, so I'm asking for help.
According to wiki, peak power output of the largest nuke ever was 33.8 Yottawatt. Which is 1 percent of luminosity of the Sun.
So, my first question is -- how can something that was builded and exploded on Earth be that powerful? I mean, Sun is the colossal thermonuclear reactor, that works for billions of years. And one bomb rivals that reactor? Something is not right here.
And the second question -- according to wiki, average total power consumption of the world is 16 TW, i.e that one nuke can 'feed' the world for approximately 2 trillion years. ...How? Why can't anyone put at least, I don't know, 0,00001% of that bomb power to work? That would be more than enough.
Like I said, I don't understand a lot here, so I'd really appreciate, if you will explain it to me. Thanks.

 

[Drakkith]

So, my first question is -- how can something that was builded and exploded on Earth be that powerful?

It's important to understand that power is work over time or energy over time. In other words, $power = \frac{energy}{time}$
If you do 1 joule work or release 1 joule of energy in 1 second, that's 1 watt. One joule over one millisecond is 1,000 watts. One joule released over 100 seconds is 0.01 watts. In all these cases the amount of work done or energy released is the same (1 joule), but the power changes by several orders of magnitude.

A nuke is so powerful because it releases a lot of energy very, very quickly. The Sun, on the other hand, releases a lot of energy, but it's power output isn't as high as you might expect. For example, inside the core of the Sun, the energy generated per cubic meter of space is comparable to a compost heap or a lizard. From wiki:

Theoretical models of the Sun's interior indicate a power density of approximately 276.5 W/m3,[73] a value that more nearly approximates reptile metabolism than a thermonuclear bomb.

From one of the references in the article:

A 50 kg adult human has a volume of about 0.05 m3, which corresponds to 13.8 watts, at the volumetric power of the solar center. This is 285 kcal/day, about 10% of the actual average caloric intake and output for humans in non-stressful conditions.

The colossal energy output of the Sun is due to its enormous size, not because it's a ultra powerful nuke.

And the second question -- according to wiki, average total power consumption of the world is 16 TW, i.e that one nuke can 'feed' the world for approximately 2 trillion years. ...How? Why can't anyone put at least, I don't know, 0,00001% of that bomb power to work? That would be more than enough.

A nuke releases its energy in a very small fraction of a second. This means that while its power output is very, very high, the actual energy delivered by the nuke is MUCH lower. A one megaton nuke releases 4.184 petajoules of energy, which is equivalent to the energy consumed by the world in 261.5 seconds (4.35 minutes). Tsar bomba, the largest nuke ever detonated, released the same amount of energy as the world consumes in about 3 1/2 hours.

 

[SamP37]

I'm thankful for your answer, but there's still something I don't get.
For example -- I read that 3380 Yotawatts is the total energy output of the Sun per second. But it still means, that Sun's colossal output happens because of it's size, right?
And also -- on the wiki, they estimated, that 33.8 Yotawatts of energy output was per second, right? And the nuke released energy much faster? Or there's difference between power output and energy delivered?

 

[Dale]

According to wiki, peak power output of the largest nuke ever was 33.8 Yottawatt. Which is 1 percent of luminosity of the Sun.
So, my first question is -- how can something that was builded and exploded on Earth be that powerful? I mean, Sun is the colossal thermonuclear reactor, that works for billions of years. And one bomb rivals that reactor? Something is not right here.

That is the point. The sun works for billions of years. The tsar bomba worked for about 6 ns.

 

[Drakkith]

I'm thankful for your answer, but there's still something I don't get.
For example -- I read that 3380 Yotawatts is the total energy output of the Sun per second. But it still means, that Sun's colossal output happens because of it's size, right?

The Sun's luminosity, which is the power radiated into space as light and other forms of EM radiation, is 3.828×10²⁶ watts. So in one second the Sun releases 3.828×10²⁶ joules of energy. This is primarily because of its massive surface area, which is where the radiation comes from. If the Sun were smaller and had half the surface area it has now, it would radiate half the energy.

And also -- on the wiki, they estimated, that 33.8 Yotawatts of energy output was per second, right? And the nuke released energy much faster? Or there's difference between power output and energy delivered?

Watts is already in units of power over time, so watts per second wouldn't be correct here. A 1 megaton nuke may have a power output in the yotawatt range, but the energy actually released is in the terajoule range. This is because it releases this energy in a few nanoseconds. The total energy released by a 1 megaton nuke is equivalent to the energy released by the Sun in about 10^-9 seconds.

 

[SamP37]

I'm terrible sorry for annoying you, but I still don't understand something.
Can we please compare the power and energy of that nuke to power and energy released by the Sun per second and to the power and energy, released by Three Gorges Dam? So I would understand it, with those examples?

 

[Dale]

It seems like you are having trouble distinguishing between power and energy. Roughly speaking, energy is how much you do and power is how fast you do it. The nukes get their huge power rating by doing their work very fast.

You would never talk about power released per second. Energy released per second is power

 

[davenn]

Can we please compare the power and energy of that nuke to power and energy released by the Sun per second

that has already been done for you ,,, see Drakkith's last post

now YOU go and google the energy output of the Three Gorges Dam and come back with am answer to compare with the already given other answers

 

[russ_watters]

That is the point. The sun works for billions of years. The tsar bomba worked for about 6 ns.

There is an entire chapter in "The Sum of All Fears" describing the exploding of a [failed] thermonuclear bomb. The last sentence of the chapter goes something like:
'The bomb was now "finished" exploding, yet none of its effects were yet visible outside its casing.'

My recollection is that they described the time to be a lot longer (perhaps including the implosion?) but in either case it happens really, really fast.

The relatively slow burn rate (power density) of the Sun was something I only learned of a few years ago (on PF of course!)...and it is vaguely disappointing!

 

[Dale]

My recollection is that they described the time to be a lot longer (perhaps including the implosion?) but in either case it happens really, really fast.

That could be. My number was just the Wikipedia-listed energy divided by the power. So it basically assumes a step function power output, which I am sure is simplistic.

 

[Drakkith]

You may be stuck on the difference between power and energy. Remember that power is energy per time. The power output of a nuke is high because its nuclear reactions occur very quickly. But the total energy released is a tiny, tiny, TINY fraction of that released by the Sun every day.

Energy released by the Sun per day:
3.828×10²⁶ watts x 60 seconds x 60 minutes x 24 hours = 33,073,920,000,000,000,000,000,000,000,000 joules. (3.3 x 10³¹ joules)
Energy released by the Sun per nanosecond:
3.828×10²⁶ watts x 10^-9 seconds = 382,800,000,000,000,000 joules. (3.8 x 10¹⁷ joules)

Assuming my pecking into the calculator was correct, that's a big difference in the total energy released. I really big difference. Here, the power output of the Sun remained the same, but the fact that we are looking over a longer period of time means that the total energy released changes. We're essentially doing the opposite with a nuke, where we know how much total energy was released and we're looking at the power output, which changes with the time frame.

Energy released by nuke vs Sun in one nanosecond (assuming detonation has ceased after 1 nanosecond):
Sun: 382,800,000,000,000,000 joules.
Nuke: 210,000,000,000,000,000 joules.

Since a nuke probably takes about 10 times as long to actually detonate completely, let's look at a 10 nanosecond time scale.

Energy released by nuke vs Sun in ten nanoseconds (assuming detonation has ceased after 10 nanoseconds):
Sun: 3,828,000,000,000,000,000 joules.
Nuke: 210,000,000,000,000,000 joules.

As you can see, the nuke's energy released remains the same, but the Sun's is 10 times larger than before.

Power output of a nuke on a 10 nanosecond time scale: 21,000,000,000,000,000,000,000,000 or 2.1 x 10²⁵ watts
Power output of a nuke on a 1 nanosecond time scale: 2,100,000,000,000,000,000,000,000 or 2.1 x 10²⁴ watts

The simple fact that the time scale increases by a factor of 10 means the nuke's power output is reduced by a factor of 10. The total energy released remains the same.

This is like running a gasoline generator vs blowing up the gas container. If you keep bringing the generator more gasoline to keep it running, you will constantly be generating energy yet its power output remains the same. But the gas in a single container of gasoline has a known amount of energy that cannot be changed. You can only increase or decrease the time it takes to release all that energy (blowing it up vs burning it slowly). That one gallon container of gasoline may produce MUCH more power when I blow it up than does the generator, but if I constantly use the generator for ten years and burn 100,000 gallons of gasoline, I've released FAR more energy via the generator than I did with that one gallon of gas I blew up.

 

[SamP37]

You may be stuck on the difference between power and energy. Remember that power is energy per time. The power output of a nuke is high because its nuclear reactions occur very quickly. But the total energy released is a tiny, tiny, TINY fraction of that released by the Sun every day.

Energy released by the Sun per day:
3.828×10²⁶ watts x 60 seconds x 60 minutes x 24 hours = 33,073,920,000,000,000,000,000,000,000,000 joules. (3.3 x 10³¹ joules)
Energy released by the Sun per nanosecond:
3.828×10²⁶ watts x 10^-9 seconds = 382,800,000,000,000,000 joules. (3.8 x 10¹⁷ joules)

Assuming my pecking into the calculator was correct, that's a big difference in the total energy released. I really big difference. Here, the power output of the Sun remained the same, but the fact that we are looking over a longer period of time means that the total energy released changes. We're essentially doing the opposite with a nuke, where we know how much total energy was released and we're looking at the power output, which changes with the time frame.

Energy released by nuke vs Sun in one nanosecond (assuming detonation has ceased after 1 nanosecond):
Sun: 382,800,000,000,000,000 joules.
Nuke: 210,000,000,000,000,000 joules.

Since a nuke probably takes about 10 times as long to actually detonate completely, let's look at a 10 nanosecond time scale.

Energy released by nuke vs Sun in ten nanoseconds (assuming detonation has ceased after 10 nanoseconds):
Sun: 3,828,000,000,000,000,000 joules.
Nuke: 210,000,000,000,000,000 joules.

As you can see, the nuke's energy released remains the same, but the Sun's is 10 times larger than before.

Power output of a nuke on a 10 nanosecond time scale: 21,000,000,000,000,000,000,000,000 or 2.1 x 10²⁵ watts
Power output of a nuke on a 1 nanosecond time scale: 2,100,000,000,000,000,000,000,000 or 2.1 x 10²⁴ watts

The simple fact that the time scale increases by a factor of 10 means the nuke's power output is reduced by a factor of 10. The total energy released remains the same.

This is like running a gasoline generator vs blowing up the gas container. If you keep bringing the generator more gasoline to keep it running, you will constantly be generating energy yet its power output remains the same. But the gas in a single container of gasoline has a known amount of energy that cannot be changed. You can only increase or decrease the time it takes to release all that energy (blowing it up vs burning it slowly). That one gallon container of gasoline may produce MUCH more power when I blow it up than does the generator, but if I constantly use the generator for ten years and burn 100,000 gallons of gasoline, I've released FAR more energy via the generator than I did with that one gallon of gas I blew up.

Thank you so very much for explaining. I think I'm finally starting to understand the difference. Like I said, I'm a newbie in physics, but I'm trying to dig into it.
Thanks again.

 

[NTL2009]

Thank you so very much for explaining. I think I'm finally starting to understand the difference. Like I said, I'm a newbie in physics, but I'm trying to dig into it.
Thanks again.

Maybe a more down-to-earth example, without math would help you to visualize this?

Consider a record setting 1/4 mile drag racing car. The engine produces enormous amount of power (+2000 Horsepower?), but it can only do it for a few seconds before it would destroy itself. Now consider a large truck carrying thousands of pounds of rocks or something. The engine might produce a few hundred horsepower max, but it could carry that load for many hours and a few hundred miles.

The drag racer produced a very high power, but for a very short time, so the total energy it produced was not so high.
The truck produced lower power, but for a very long time, so the total energy it produced was much higher than the racer.

A nuke bomb is like a drag racer (but millions of times shorter duration even). The sun is like a super-long haul truck driver, on a billions of years trip w/o stops or refueling.

Many other examples - the bright flash of a camera flash versus lighting a room for a day, etc. It should be clear that time is a factor. It doesn't take so much energy to do something for a short time as it does for a long time.

 

[russ_watters]

Another down-to-earth example of a real issue I'm dealing with right now (trying to avoid...): My telescope uses 5 kg counterweights, and they are suspended about 1.5m in the air. If I pick one up off the ground and attach it to my telescope in 2 seconds, that's an energy of 74 Joules or an average power of 37 watts. If I drop one on my foot and it stops in a hundredth of a second, it abosorbs that energy at an average power of 7,400 watts. Ouch.

Random, I know, but the counterweight shaft has an end cap (called a "toe saver") to avoid this problem and I recently lost it, which has me annoyed/nervous.

 

[Cutter Ketch]

This may already be obvious by now, but looking through the posts I don't see that it was stated explicitly. In addition to being confused about the difference between power and energy I suspect the OP is not aware that the unit "Watt" is power. The energy released is stated in Joules (J). The rate at which energy is released is stated in Watts (W). Where 1 W is 1 J/s

So 1 Yottawatt is an incredible power, but if it lasted only 1 yoctosecend the total released energy would be only 1 J.

 

[SamP37]

This may already be obvious by now, but looking through the posts I don't see that it was stated explicitly. In addition to being confused about the difference between power and energy I suspect the OP is not aware that the unit "Watt" is power. The energy released is stated in Joules (J). The rate at which energy is released is stated in Watts (W). Where 1 W is 1 J/s

So 1 Yottawatt is an incredible power, but if it lasted only 1 yoctosecend the total released energy would be only 1 J.

Thank you for explaining, too. Now I understand, why Tsar bomba had that insane amount of power. Because it was measure in one second, while in reality, it released energy in the matter of nanoseconds. I've been missing it.

 

[Drakkith]

Because it was measure in one second, while in reality, it released energy in the matter of nanoseconds. I've been missing it.

The measurement of its power output happens on the scale of nanoseconds. If we measured it over one second it would much lower. Just because one watt is one joule over one second doesn't mean that you have to use one second in your measurements.