Ask me about the Universe (Earth, stars, light, Sun)
Please register to participate in our discussions with 2 million other members - it's free and quick! Some forums can only be seen by registered members. After you create your account, you'll be able to customize options and access all our 15,000 new posts/day with fewer ads.
So using 11.2 km/s, it would be 6.272E+10 Joules per second for a total of 1.786 seconds to reach an altitude of 20 km, or a total of 1.120E+11 Joules to move 1 kg.
That would mean it would require 8.185E-15 Joules to move one molecule of CO2 that 20 km distance. Or, to put it in your favorite terms: It would require a 1.956E-30 megaton TNT explosion.
The danger of formulas without understanding the problem
Quote:
Originally Posted by Glitch
I would not consider 400 ppm as "plenty". The optimum CO2 levels should be between 800 and 1,200 ppm for plants. If CO2 levels drop below 200 ppm, photosynthesis stops, plants die, and the food chain collapses.
The bulk of the atmospheric CO2 is located in the troposphere. In order to have a global impact the molecule must be in the stratosphere. We know that volcanic eruptions can put huge quantities of CO2 and SO2, among other gases, into the stratosphere. Those gases then circle the planet in the jet streams (see note below) and it can effect the climate of the entire planet. The 1991 Pinatubo eruption is a perfect example. That eruption put so much Sulfur Dioxide, Methane, and other particulates into the atmosphere that the surface temperature of the entire planet dropped by more than 1°F for over a year.
What I want to know is how much energy is required to put CO2 into the stratosphere. There must be a certain minimum amount of energy to move CO2 20 km into the stratosphere from sea level. CO2 would normally fall back to Earth or be absorbed by the oceans, because it is heavier than air. But if there was sufficient energy propelling that CO2 molecule skyward, it could eventually reach the stratosphere and be carried around the planet. If it does not reach the stratosphere, and stays within the troposphere, then there is no way it can effect global climate. Only the local weather may be effected, as in acid rain for example.
Discounting for winds, water vapor, or any uneven distribution of gases in the atmosphere, how many Joules of energy would it require to lift a 44.01 g/mol molecule 20 km into the atmosphere? If you do not want to work out the answer, I can understand that. Just point me to the appropriate equations and I will happily do the grunt work.
NOTE: We discovered the jet streams in 1883 after the Krakatoa eruption. Vessels crossing the Pacific described a "River of Smoke" in the sky.
Quote:
Originally Posted by beninfl
25,000 mph = (2.5E4 mph)(0.447 m/s per mph) = 1.1175E4 m / s
W = ((1 Kg)(1.1175E4)2) / 2 = 6.24E7 Joules
1Kg would require 6.24E7 Joules. Now you need to adjust for your weight and your answer is there.
If you're asking how much energy it would take for someone to transport a molecule of CO2 into the stratosphere from the surface of the Earth, the problem I alluded to earlier, you'd have to say how you were going to transport the CO2 there.
If you tried to simply shoot the CO2 molecule from a magical CO2 accelerator, you'd find that it would have to be going really fast to stop from being slowed down by the rest of the atmosphere. You can't ignore fluid resistance (especially at this scale) because that's the dominant force in the problem. The mean free path of the lower atmosphere is tiny (measured in nm), so our CO2 molecule would have to have enough momentum to overcome all those collisions over 10km. I'm too lazy to calculate it (because it's totally irrelevant and not technically achievable) but know that the initial velocity would be a small fraction away from c.
Your statement that CO2 falls back to the Earth is not quite correct. The atmosphere is a dynamic system in approximate thermodynamic equilibrium, so no matter what you do it will tend to that equilibrium state. Whether you release the CO2 at ground level or transport it to the tropopause and release it there, it will eventually come to the same distribution. To get a sense of what that distribution is, it's important to know that the troposphere is considered "well mixed" in the sense that various gases have a relatively uniform composition up to the tropopause. Since the density decreases approximately exponentially, that means that the CO2 concentration decreases similarly (with a fixed concentration). Release one molecule of CO2 on the surface and it will eventually sample all those altitude, spending more of its time closer to the surface but by no means all of its time there.
So, given all that above, it's not clear to me what you're actually asking. I've given you the difference in energy of a CO2 molecule on Earth versus one ten miles up, but that's not a very relevant answer to what would actually happen in a real atmosphere. I've shown you how to calculate the change in concentration of CO2 given a release in the troposphere--is that what you're looking for? Do you want to know the change in temperature of the atmosphere given a surface release of a certain amount of CO2 (the temperature would go down every so slightly as some of the CO2 went up)?
The Law of Entropy where Entropy always increases (even though that's actually wrong, it "usually" increases) would indeed dictate you have a chance in hell of tracking that Co2 mole. Speaking of Entropy, that's what the "s = k log w" is in my status.
If you're asking how much energy it would take for someone to transport a molecule of CO2 into the stratosphere from the surface of the Earth, the problem I alluded to earlier, you'd have to say how you were going to transport the CO2 there.
If you tried to simply shoot the CO2 molecule from a magical CO2 accelerator, you'd find that it would have to be going really fast to stop from being slowed down by the rest of the atmosphere. You can't ignore fluid resistance (especially at this scale) because that's the dominant force in the problem. The mean free path of the lower atmosphere is tiny (measured in nm), so our CO2 molecule would have to have enough momentum to overcome all those collisions over 10km. I'm too lazy to calculate it (because it's totally irrelevant and not technically achievable) but know that the initial velocity would be a small fraction away from c.
The method of transport is not important. If you want to use a magical CO2 accelerator, that works for me.
I was hoping to avoid fluid dynamics, but I suppose you are right. There is no avoiding it because we are dealing with an atmosphere. Although, I do not think it needs to be as fast as you are stating. After all, erupting volcanoes are quite capable of putting up huge quantities of CO2 20+ km into the atmosphere and the CO2 is not being accelerated anywhere close to even 3% the speed of light.
Quote:
Originally Posted by jayrandom
Your statement that CO2 falls back to the Earth is not quite correct. The atmosphere is a dynamic system in approximate thermodynamic equilibrium, so no matter what you do it will tend to that equilibrium state. Whether you release the CO2 at ground level or transport it to the tropopause and release it there, it will eventually come to the same distribution. To get a sense of what that distribution is, it's important to know that the troposphere is considered "well mixed" in the sense that various gases have a relatively uniform composition up to the tropopause. Since the density decreases approximately exponentially, that means that the CO2 concentration decreases similarly (with a fixed concentration). Release one molecule of CO2 on the surface and it will eventually sample all those altitude, spending more of its time closer to the surface but by no means all of its time there.
So, given all that above, it's not clear to me what you're actually asking. I've given you the difference in energy of a CO2 molecule on Earth versus one ten miles up, but that's not a very relevant answer to what would actually happen in a real atmosphere. I've shown you how to calculate the change in concentration of CO2 given a release in the troposphere--is that what you're looking for? Do you want to know the change in temperature of the atmosphere given a surface release of a certain amount of CO2 (the temperature would go down every so slightly as some of the CO2 went up)?
I understand what you are saying, and you are right. I was hoping it might be easier to determine the energy required to put CO2 into the stratosphere. The E=0.5Mv^2 equation really only works in a vacuum. Once you bring an atmosphere, or another external factor into the equation it changes the dynamics of everything.
Location: where you sip the tea of the breasts of the spinsters of Utica
8,298 posts, read 14,133,459 times
Reputation: 8104
Quote:
Originally Posted by Lunar Delta
Space is indeed "something". It can be warped and bent by massive bodies, and it has properties that can be measured and described. If you want to know more about space you should check out this video, it's incredibly informative, and the narrator isn't boring.
The method of transport is not important. If you want to use a magical CO2 accelerator, that works for me.
I was hoping to avoid fluid dynamics, but I suppose you are right. There is no avoiding it because we are dealing with an atmosphere. Although, I do not think it needs to be as fast as you are stating. After all, erupting volcanoes are quite capable of putting up huge quantities of CO2 20+ km into the atmosphere and the CO2 is not being accelerated anywhere close to even 3% the speed of light.
I understand what you are saying, and you are right. I was hoping it might be easier to determine the energy required to put CO2 into the stratosphere. The E=0.5Mv^2 equation really only works in a vacuum. Once you bring an atmosphere, or another external factor into the equation it changes the dynamics of everything.
Fluid dynamics is not linear. It's not possible to describe the behavior of one molecule of CO2 by describing the behavior of 44 grams and dividing by Avogadro's number. It's important to specify exactly what you want to understand, because length scales are important to the problem. In the case of a volcano, the hot gas will cause a convective instability in the atmosphere which will quickly transport the gas to the tropopause. That is not what would happen with one molecule of CO2.
I still think you need to clarify your question if you want a sensible answer. How much CO2 is being released? What temperature is it? Will you let natural processes carry it up or will you use some external means? If you do use external means to transport the CO2, what will they be? Will you need to continually work to transport the CO2 up or will you transport it once and let the system relax?
I have read that planets and other large pieces of matter in the solar system cannot accumulate a net electric charge due to solar wind, which carries away any excess charge.
Can meteors, or other objects outside of the solar system accumulate a huge static electric charge? Could this charge cause them to be accelerated to relativistic velocities? If one of them approached a planet with an atmosphere would it cause super lightning? Could it potentially ionize the entire atmosphere to plasma?
Please register to post and access all features of our very popular forum. It is free and quick. Over $68,000 in prizes has already been given out to active posters on our forum. Additional giveaways are planned.
Detailed information about all U.S. cities, counties, and zip codes on our site: City-data.com.