# A Silly Question but a Good Physics Question



## RobynC (Jun 10, 2011)

Anybody here's seen Star Trek which with a NY accent is said "Stah Track", and everybody's seen the phasers in action probably. Of course the amount of power varies from episode to episode based on the law of plot and the rule of cool.

Still, there were some figures that were actually listed which are of course certifiably insane


Level 8: Vaporizes human beings
Level 11: 10 cubic meters of rock vaporized per 0.2 second discharge
Level 12: 50 cubic meters of rock vaporized per 0.1 second discharge
Level 13: 90 cubic meters of rock are vaporized per discharge
Level 14: 160 cubic meters of rock are vaporized per discharge
Level 15: 370 cubic meters are vaporized per discharge
Level 16: 650 cubic meters of rock are vaporized by a 0.28 second discharge

The numbers are absurd but it's an interesting physics question: How much energy would it take to vaporize this much stuff? 

BTW: Yes I'm in a silly mood


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## stargazing grasshopper (Oct 25, 2013)

Dr Brown says you'd require exactly 1.21 gigawatts of energy for all applications distributed at differing frequencies.


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## Thomas60 (Aug 7, 2011)

Level 8: 80kg x (300,000,000 m/s)^2
= 7.2 x 10^18 J
ergo: 114000 Hiroshima's of power to disintegrate a human into pure energy.

Or if you just wish to oxidize and vaporize (into a gas)
300 Gj (300*10^9j)
Complete Vaporisation of a Human Body | Stylianidis | Journal of Interdisciplinary Science Topics


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## RobynC (Jun 10, 2011)

@_Thomas60_

Firstly: Good question, the key word is to vaporize which is to turn into a gas: Not turn into pure energy.

Secondly: You have to remember orders of magnitude, the amount is 2.99 gigajoules. This however fails to factor in potential interactions in the body between various chemicals such as lipids, sugars, and proteins & byproducts if subjected to a massive energy burst.

Thirdly: If I do my math right that's about 143 pounds of TNT to yield that much energy for a summary vaporization of a human being.


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## Thomas60 (Aug 7, 2011)

In star trek I never see shockwaves when someone is vaporized, and yet the expansion ratio of water to steam is 1-1700!


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## RobynC (Jun 10, 2011)

@Thomas60

Well a summary and total vaporization of a person would be like a bomb going off!


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## Psychosmurf (Aug 22, 2010)

RobynC said:


> Anybody here's seen Star Trek which with a NY accent is said "Stah Track", and everybody's seen the phasers in action probably. Of course the amount of power varies from episode to episode based on the law of plot and the rule of cool.
> 
> Still, there were some figures that were actually listed which are of course certifiably insane
> 
> ...


Well "rock" is very variable in composition, so let's just say it's 650 cubic meters of iron at standard temperature and pressure.

Now, the density of iron is 7.874 g*cm^(-3), and 650 cubic meters is 650,000,000 cubic centimeters. Multiplying that by the density of iron, we get 5.1181*10^9 grams of iron.

Next we need to figure out the number of mols of iron of that mass. The atomic weight of iron is 55.845, so we get 9.16483*10^7 mols. 

Now, the heat of vaporization of iron is 340 kJ per mol, which gives us 3.11604*10^10 kJ, which is close to the amount of energy contained in 1 pound of Uranium 235.


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## MNiS (Jan 30, 2010)

Psychosmurf said:


> Well "rock" is very variable in composition, so let's just say it's 650 cubic meters of iron at standard temperature and pressure.
> 
> Now, the density of iron is 7.874 g*cm^(-3), and 650 cubic meters is 650,000,000 cubic centimeters. Multiplying that by the density of iron, we get 5.1181*10^9 grams of iron.
> 
> ...


Don't forget to divide by 0.28.

Edit: Or do you multiply by 0.28^2? Hmm...


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## Psychosmurf (Aug 22, 2010)

MNiS said:


> Don't forget to divide by 0.28.
> 
> Edit: Or do you multiply by 0.28^2? Hmm...


You don't have to divide by 0.28 since the OP's question asks for the amount of energy released, not the amount of power.


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## RobynC (Jun 10, 2011)

@Psychosmurf

Firstly, rock can be variable so for the sake of the argument you could assume the most common rock to be sandstone or shale...

Secondly: No, I asked for how much energy to vaporize... not released in vaporization


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## Psychosmurf (Aug 22, 2010)

RobynC said:


> @_Psychosmurf_
> 
> Firstly, rock can be variable so for the sake of the argument you could assume the most common rock to be sandstone or shale...
> 
> Secondly: No, I asked for how much energy to vaporize... not released in vaporization


I meant released from the laser gun itself, not the iron.


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## azdahak (Mar 2, 2013)

RobynC said:


> @_Psychosmurf_
> 
> Firstly, rock can be variable so for the sake of the argument you could assume the most common rock to be sandstone or shale...
> 
> Secondly: No, I asked for how much energy to vaporize... not released in vaporization



What @Psychosmurf did was give you the enthalpy of vaporization (or sublimation) -- the amount of energy required to induce a phase change from liquid(solid) to gas. That takes a certain amount of energy to make happen -- to essential boil someone away.

I guess what you want to know is how much energy would you need for the method of disintegrating something? Like, can you pop a 9V in a "phaser" and blow up rocks?

I'm not sure that can be effectively answered without knowing the method. 

For instance you could use a laser pulse to create a ionized canal in the air and then channel a stream of anti-protons at a target...that would be relatively energy cheap....if you don't count the energy costs of producing and containing the antimatter.


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## RobynC (Jun 10, 2011)

@azdahak

1. The energy would be released from a laser weapon...
2. The rock I was thinking of would be sandstone or shale, not iron


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## azdahak (Mar 2, 2013)

RobynC said:


> @_azdahak_
> 
> 1. The energy would be released from a laser weapon...
> 2. The rock I was thinking of would be sandstone or shale, not iron



I think you're using the word "energy" in a very wide way and it's confusing we poor scientists who mean something very specific by it.

Again I _think_ what you're asking is something like this:

I can put a triple A battery in a penlight laser and it can't disintegrate anything.

What size battery would I have to put into a laser to vaporize rock.

If that's what you mean, the question is not really answerable because it depends on the technology involved.


If you just want to know the amount to energy it takes to turn a given amount to rock into vapor, then @Psychosmurfs answer is in the correct order of magnitude for people, iron or sandstone.

It's the same as asking how much "energy" you have to apply to a pot of water to get it to boil.

That energy can come from a microwave oven, an immersion heater, or a propane flame....but the amount of energy needed is fixed.

Now the _efficiency_ of all those technologies are different in how they convert electricity/gas into heat.

You can compare them all directly by calculating how many _dollars_ it takes to heat up a pot of water by all those methods.


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