Math/Physics question

Gef · 11-24-2015, 02:20 PM

A player character in a supers campaign has the ability to open portals at very long range. He hasn't done it yet, but he's thinking of opening a portal into the sun. One effect of the portal is to limit the speed of material passing through it to 1 yard per second. The portal's 9'x3', so if open for 1 second to the bottom of the convective layer, the solar plasma (about ¾ H, ¼ He) has a density 100 times air, and a temperature around 3300 times as great. On earth, it immediately drops to standard pressure, so I figure by the gas law it want's to expand from 3 cubic yards to 2 million. After an expansion of 100 times (5½yard radius), it's lighter than air and begins to rise. Meanwhile, it's combusting which allows interpenetration, so even though it wants to expand to 2 million cubic yards, it'll displace only 1.6 ,illioon cubic yards of air. But actually, it immediately begins to cool, reducing its expansion but superheating the ambient air. The average molecular weight of air is an order of magnitude greater than the plasma, so that'll reduce expansion accordingly. On top of the heat and gale, there's radiation.

I'm pretty sure that being in the immediate neighborhood of the portal is destructive to anything important, and that being above the portal is bad news at any reasonable altitude. What I can't figure out with half-remembered college classes (I flunked fluid dynamics in the first place) is how far out from the portal the destruction extends. What would be useful to know is how far away you need to be, in order to survive in a) an armored vehicle, b) an NBC suit, c) a normal building, and d) unprotected.

Any ideas? The super with this power has a friend who's a genius with Intuitive Mathematician to help him model the effect.

whswhs · 11-24-2015, 02:35 PM

You need to take radiative cooling into account. Look up the Stefan-Boltzmann law to approximate the rate at which energy will be emitted.

Anthony · 11-24-2015, 02:47 PM

Well, the obvious problem with a speed limit of 1 yard per second is that it implies that gases basically can't pass through, as the average molecular velocity exceeds 1 yard per second. This lets you ignore the entire idea. Assuming you want to allow this idea, the center of the sun has a pressure of about 2.5e+11 bar or 2.5e+16 pascals; if we assume it's an ideal gas that amounts to 3.7e+16J/m^3; we're letting through 2.3 cubic meters so total energy is 8.5e+16J, which is about 20 megatons. Going further out will reduce the energy by whatever amount is desired.

ericthered · 11-24-2015, 02:48 PM

I'm tempted to take a shortcut and try to just figure out how much energy is in the 'bomb' (which is what this looks like) and then see if there's a nearby nuke I can compare it to. Because I'm thinking about things and this is actually really close to a nuclear explosion.

Of course, I start looking into the specific heat of hydrogen at high temperatures and I no longer feel so clever.

EDIT: Anthony, what about energy from temperature?

Bruno · 11-24-2015, 02:59 PM

I'm thinking, even if you ignore individual molecular motion and go for a larger scale average, that 1yd/s cap is going to stop this from going FAWOOOSH. Or at least not so psychotically.

9' x 3' x 0' != 3 cubic yards, among other things. That's about zero cubic yards :) You're imagining a 1 yard deep chunk being extruded before it gets depressurizied, but with the (weird and sorta aphysical) 1yd/s limit, I think you have to look at the first infinitesimal depth layer - I'm not sure it can expand at more than 1yd/s, which means it can't advance out of the way for the next "strip" until it finishes expanding to its full volume. So on and so forth, so you're only going to be getting 9' x 3' x 1' at 1ATM coming out every turn, not at 100 ATM. Which is a much less exciting energy density, even if it's still pretty dang hot.

Anthony · 11-24-2015, 03:04 PM

Quote:

Originally Posted by ericthered

EDIT: Anthony, what about energy from temperature?

That's what the number I gave was.

ericthered · 11-24-2015, 03:09 PM

Quote:

Originally Posted by Anthony

That's what the number I gave was.

oh, then what about pressure? An object expanding 100 times still has a lot of potential energy.

Anthony · 11-24-2015, 03:43 PM

Quote:

Originally Posted by ericthered

oh, then what about pressure? An object expanding 100 times still has a lot of potential energy.

The pressure comes from the temperature. There isn't any real distinction to be made there.

Flyndaran · 11-24-2015, 04:40 PM

Ha, using magic to do the opposite of science; using a giant fusion "bomb" to make a tiny "fission" bomb.

11-24-2015, 02:20 PM	#1
Gef Join Date: Sep 2004 Location: Yucca Valley, CA	Math/Physics question A player character in a supers campaign has the ability to open portals at very long range. He hasn't done it yet, but he's thinking of opening a portal into the sun. One effect of the portal is to limit the speed of material passing through it to 1 yard per second. The portal's 9'x3', so if open for 1 second to the bottom of the convective layer, the solar plasma (about ¾ H, ¼ He) has a density 100 times air, and a temperature around 3300 times as great. On earth, it immediately drops to standard pressure, so I figure by the gas law it want's to expand from 3 cubic yards to 2 million. After an expansion of 100 times (5½yard radius), it's lighter than air and begins to rise. Meanwhile, it's combusting which allows interpenetration, so even though it wants to expand to 2 million cubic yards, it'll displace only 1.6 ,illioon cubic yards of air. But actually, it immediately begins to cool, reducing its expansion but superheating the ambient air. The average molecular weight of air is an order of magnitude greater than the plasma, so that'll reduce expansion accordingly. On top of the heat and gale, there's radiation. I'm pretty sure that being in the immediate neighborhood of the portal is destructive to anything important, and that being above the portal is bad news at any reasonable altitude. What I can't figure out with half-remembered college classes (I flunked fluid dynamics in the first place) is how far out from the portal the destruction extends. What would be useful to know is how far away you need to be, in order to survive in a) an armored vehicle, b) an NBC suit, c) a normal building, and d) unprotected. Any ideas? The super with this power has a friend who's a genius with Intuitive Mathematician to help him model the effect.

11-24-2015, 02:35 PM	#2
whswhs Join Date: Jun 2005 Location: Lawrence, KS	Re: Math/Physics question You need to take radiative cooling into account. Look up the Stefan-Boltzmann law to approximate the rate at which energy will be emitted. __________________ Bill Stoddard I don't think we're in Oz any more.

11-24-2015, 02:47 PM	#3
Anthony Join Date: Feb 2005 Location: Berkeley, CA	Re: Math/Physics question Well, the obvious problem with a speed limit of 1 yard per second is that it implies that gases basically can't pass through, as the average molecular velocity exceeds 1 yard per second. This lets you ignore the entire idea. Assuming you want to allow this idea, the center of the sun has a pressure of about 2.5e+11 bar or 2.5e+16 pascals; if we assume it's an ideal gas that amounts to 3.7e+16J/m^3; we're letting through 2.3 cubic meters so total energy is 8.5e+16J, which is about 20 megatons. Going further out will reduce the energy by whatever amount is desired. __________________ My GURPS site and Blog.

11-24-2015, 02:48 PM	#4
ericthered Hero of Democracy Join Date: Mar 2012 Location: far from the ocean	Re: Math/Physics question I'm tempted to take a shortcut and try to just figure out how much energy is in the 'bomb' (which is what this looks like) and then see if there's a nearby nuke I can compare it to. Because I'm thinking about things and this is actually really close to a nuclear explosion. Of course, I start looking into the specific heat of hydrogen at high temperatures and I no longer feel so clever. EDIT: Anthony, what about energy from temperature? __________________ Be helpful, not pedantic Worlds Beyond Earth -- my blog Check out the PbP forum! If you don't see a game you'd like, ask me about making one!

11-24-2015, 02:59 PM	#5
Bruno Join Date: Sep 2004 Location: Canada	Re: Math/Physics question I'm thinking, even if you ignore individual molecular motion and go for a larger scale average, that 1yd/s cap is going to stop this from going FAWOOOSH. Or at least not so psychotically. 9' x 3' x 0' != 3 cubic yards, among other things. That's about zero cubic yards :) You're imagining a 1 yard deep chunk being extruded before it gets depressurizied, but with the (weird and sorta aphysical) 1yd/s limit, I think you have to look at the first infinitesimal depth layer - I'm not sure it can expand at more than 1yd/s, which means it can't advance out of the way for the next "strip" until it finishes expanding to its full volume. So on and so forth, so you're only going to be getting 9' x 3' x 1' at 1ATM coming out every turn, not at 100 ATM. Which is a much less exciting energy density, even if it's still pretty dang hot. __________________ All about Size Modifier; Unified Hit Location Table A Wiki for my F2F Group A neglected GURPS blog

11-24-2015, 04:40 PM	#9
Flyndaran Untagged Join Date: Oct 2004 Location: Forest Grove, Beaverton, Oregon	Re: Math/Physics question Ha, using magic to do the opposite of science; using a giant fusion "bomb" to make a tiny "fission" bomb. __________________ Beware, poor communication skills. No offense intended. If offended, it just means that I failed my writing skill check.