GasLab Second Law

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Uri_dolphin3 Uri Wilensky (Author)

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WHAT IS IT?

This model is one in a series of GasLab models. They use the same basic rules for simulating the behavior of gases. Each model integrates different features in order to highlight different aspects of gas behavior.

The basic principle of the models is that gas particles are assumed to have two elementary actions: they move and they collide --- either with other particles or with any other objects such as walls.

This model simulates the Second Law of Thermodynamics via the behavior of gas particles in a box. The Second Law of Thermodynamics states that systems tend towards increased entropy. Essentially what this means is that over time ordered systems become less ordered unless work is done on the system to keep it ordered.

HOW IT WORKS

Particles are modeled as perfectly elastic particles with no energy except their kinetic energy --- that which is due to their motion. Collisions between particles are elastic. Particles are colored according to speed -- blue for slow, green for medium, and red for high speeds.

The exact way two particles collide is as follows:

  1. Two turtles "collide" if they find themselves on the same patch.
  2. A random axis is chosen, as if they are two balls that hit each other and this axis is the line connecting their centers.
  3. They exchange momentum and energy along that axis, according to the conservation of momentum and energy. This calculation is done in the center of mass system.
  4. Each turtle is assigned its new velocity, energy, and heading.
  5. If a turtle finds itself on or very close to a wall of the container, it "bounces" -- that is, reflects its direction and keeps its same speed.

The propeller is modeled such that it shows the effect of the flux of the particles between the two sides of the box, but does not effect or interact with the particles as they pass through. When particles move from the left side to the right side they accelerate the propeller clockwise, and likewise, when particles move from the right side to the left side they accelerate the propeller counter-clockwise.

HOW TO USE IT

SETUP: sets up the initial conditions and distributes the particles in one of three different modes. Be sure to wait till the Setup button stops before pushing go.
CORNER: all the particles are created in the lower left corner of the box and diffuse outwards from there.
ONE SIDE: all the particles are created in the left side of the box evenly distributed.
BOTH SIDES: all the particles are created evenly distributed throughout the entire box.
GO: runs the code again and again. This is a "forever" button.
NUMBER: the number of gas particles
PROPELLER-RADIUS: the radius of the propeller in the opening between the sides of the box. The size of the opening is based on the size of the propeller.

About the plots

PARTICLE COUNTS: plots the number of particles on each side of the box.
PROPELLER VELOCITY: plots the velocity of the propeller: positive is clockwise, negative is counter-clockwise.
PRESSURES: plots the pressure of the gas on each side of the box.
ENTROPY: plots a measure of the entropy of the system. As the particles become more evenly and randomly distributed the entropy will increase.

THINGS TO NOTICE

When the particles are evenly distributed throughout the box, what do you notice about the behavior of the propeller?

In what ways is this model a correct or incorrect idealization of the real world?

In what ways can you quantify entropy? What is the best way to quantify entropy in this model? Does this model use this method? If not, what is wrong with the method being used?

THINGS TO TRY

Set all the particles in part of the world, or with the same heading -- what happens? Does this correspond to a physical possibility?

Are there other interesting quantities to keep track of?

EXTENDING THE MODEL

Could you find a way to measure or express the "temperature" of this imaginary gas? Try to construct a thermometer.

What happens if there are particles of different masses? (See GasLab Two Gas model.)

How does this 2-D model differ from the 3-D model?

If more than two particles arrive on the same patch, the current code says they don't collide. Is this a mistake? How does it affect the results?

Is this model valid for fluids in any aspect? How could it be made to be fluid-like?

RELATED MODELS

The GasLab suite of models, especially GasLab Maxwell's Demon, which models a theoretical system that seems to violate the Second Law of Thermodynamics.

CREDITS AND REFERENCES

Thanks to Brent Collins and Seth Tisue for their work on this model.

This model was developed as part of the GasLab curriculum (http://ccl.northwestern.edu/curriculum/gaslab/) and has also been incorporated into the Connected Chemistry curriculum (http://ccl.northwestern.edu/curriculum/ConnectedChemistry/)

HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

  • Wilensky, U. (2002). NetLogo GasLab Second Law model. http://ccl.northwestern.edu/netlogo/models/GasLabSecondLaw. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
  • Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

Copyright 2002 Uri Wilensky.

CC BY-NC-SA 3.0

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.

Comments and Questions

Click to Run Model

globals [
  fast average slow               ;; current counts
  avg-speed avg-energy            ;; current averages
  avg-speed-init avg-energy-init  ;; initial averages
  vsplit vclock                   ;; clock variables
  left-count right-count          ;; # of particles on each side
  propeller-velocity              ;; current velocity of the propeller
  left-pressure right-pressure    ;; pressure in each chamber
  left-walls right-walls          ;; agentsets of the walls on each side (used when calculating pressure)
  propeller-angle                 ;; current angular position of the propeller
]

turtles-own [
  speed mass energy new-speed           ;; turtle info
  v1t v1l tmp-turtle                    ;; collision info (turtle 1)
  heading2 mass2 speed2 v2t v2l turtle2 ;; collision info (turtle 2)
  theta                                 ;; collision info (both particles)
]

patches-own [
  wall?       ;; is this patch part of the wall?
  pressure    ;; sum of momentums of particles that have bounced here during this time slice
]

to setup [mode]
  clear-all
  make-box
  set vclock  0
  crt number
  [ set new-speed 10.0
    set shape "circle"
    set mass 1.0
    setup-position mode
    recolor ]
  update-variables
  set avg-speed-init avg-speed
  set avg-energy-init avg-energy
  rotate-propeller
  reset-ticks
end 

to setup-position [mode]  ;; turtle procedure
  if mode = "corner"
    [ setxy (- (max-pxcor - 1)) (- (max-pycor - 1))
      set heading random-float 90
      fd random-float 8 ]
  if mode = "one side"
    [ setxy (- (1 + random-float (max-pxcor - 2)))
            (random-float (world-height - 3) + min-pycor + 1) ]
  if mode = "both sides"
    [ setxy (random-float (world-width - 3) + min-pxcor + 1)
            (random-float (world-height - 3) + min-pycor + 1) ]
end 

to update-variables
  ask turtles
    [ set speed new-speed
      set energy (0.5 * speed * speed * mass) ]
  set average count turtles with [color = green]
  set slow    count turtles with [color = blue]
  set fast    count turtles with [color = red]
  set avg-speed  mean [speed] of turtles
  set avg-energy mean [energy] of turtles
  set vsplit (round ((max [speed] of turtles) * 1.2))
  set left-count count turtles with [xcor < 0]
  set right-count count turtles with [xcor >= 0]
  set left-pressure sum [pressure] of left-walls
  ask left-walls [ set pressure 0 ]
  set right-pressure sum [pressure] of right-walls
  ask right-walls [ set pressure 0 ]
end 

to go
  ask turtles [ bounce ]
  ask turtles [ move ]
  ask turtles [ check-for-collision ]
  set vclock (vclock + 1)
  rotate-propeller
  ifelse (vclock = vsplit)
  [
    tick
    set vclock 0
    update-variables
  ]
  [ display ]
end 

to rotate-propeller
  set-current-plot "Propeller"
  plot-pen-reset
  set propeller-angle propeller-angle - propeller-velocity / 2
  plot-pen-up
  plotxy cos propeller-angle sin propeller-angle
  plot-pen-down
  plotxy 0 - cos propeller-angle 0 - sin propeller-angle
  plot-pen-up
  plotxy cos (propeller-angle + 90) sin (propeller-angle + 90)
  plot-pen-down
  plotxy 0 - cos (propeller-angle + 90) 0 - sin (propeller-angle + 90)
  ;; slow down the propeller due to friction
  set propeller-velocity propeller-velocity * 0.999
end 

to bounce ;; turtle procedure
  ; if we're not about to hit a wall (yellow patch),
  ; we don't need to do any further checks
  if [pcolor] of patch-ahead 1 != yellow [ stop ]
  ; get the coordinates of the patch we'll be on if we go forward 1
  let new-px [pxcor] of patch-ahead 1
  let new-py [pycor] of patch-ahead 1
  let pressure-increment mass * speed
  ask patch new-px new-py [ set pressure pressure + pressure-increment ]
  ; check: hitting left, right, or middle wall?
  if (abs new-px = max-pxcor) or (pxcor != 0 and new-px = 0)
    ; if so, reflect heading around x axis
    [ set heading (- heading) ]
  ; check: hitting top or bottom wall?
  if (abs new-py = max-pycor) or (pxcor = 0)
    ; if so, reflect heading around y axis
    [ set heading (180 - heading) ]
end 

to move  ;; turtle procedure
  let old-xcor xcor
  jump (speed / vsplit)
  if (old-xcor < 0) and (xcor >= 0)
    [ set propeller-velocity propeller-velocity + 0.03 * speed ]
  if (old-xcor > 0) and (xcor <= 0)
    [ set propeller-velocity propeller-velocity - 0.03 * speed ]
end 

to check-for-collision  ;; turtle procedure
  if count other turtles-here = 1
    [ set tmp-turtle one-of other turtles-here
      if ((who > [who] of tmp-turtle) and (turtle2 != tmp-turtle))
        [ collide ] ]
end 

to collide  ;; turtle procedure
  get-turtle2-info
  calculate-velocity-components
  set-new-speed-and-headings
end 

to get-turtle2-info  ;; turtle procedure
  set turtle2 tmp-turtle
  set mass2 [mass] of turtle2
  set speed2 [new-speed] of turtle2
  set heading2 [heading] of turtle2
end 

to calculate-velocity-components  ;; turtle procedure
  set theta (random-float 360)
  set v1l (new-speed * sin (theta - heading))
  set v1t (new-speed * cos (theta - heading))
  set v2l (speed2 * sin (theta - heading2))
  set v2t (speed2 * cos (theta - heading2))
  ;; CM vel. along dir. theta
  let vcm (((mass * v1t) + (mass2 * v2t)) / (mass + mass2))
  set v1t (vcm + vcm - v1t)
  set v2t (vcm + vcm - v2t)
end 

;; set new speed and headings of each turtles that has had a collision

to set-new-speed-and-headings
  set new-speed sqrt ((v1t * v1t) + (v1l * v1l))
  set heading (theta - (atan v1l v1t))

  let new-speed2 sqrt ((v2t * v2t) + (v2l * v2l))
  let new-heading (theta - (atan v2l v2t))
  ask turtle2 [
    set new-speed new-speed2
    set heading new-heading
  ]

  recolor
  ask turtle2 [ recolor ]
end 

to recolor  ;; turtle procedure
  ifelse new-speed < 5.0
    [ set color blue ]
    [ ifelse new-speed > 15.0
        [ set color red ]
        [ set color green ] ]
end 

to make-box
  ask patches
    [ set pressure 0
      set wall? false
      if count neighbors != 8 or
         ((pxcor = 0) and (abs pycor > propeller-radius))
        [ set pcolor yellow
          set wall? true ]
      if (pxcor = 0) and (abs pycor <= propeller-radius)
        [ set pcolor gray ] ]
  set left-walls patches with [wall? and (pxcor < 0)]
  set right-walls patches with [wall? and (pxcor > 0)]
end 

to-report calculate-order
  let x-patches-per-grid-cell (world-width / 5)
  let y-patches-per-grid-cell (world-height / 5)
  let counts-list []
  let gridx -2
  repeat 5
    [ let gridy -2
      repeat 5
        [ let gridcount count turtles with [int (pxcor / x-patches-per-grid-cell) = gridx
                                            and int (pycor / y-patches-per-grid-cell) = gridy]
          set counts-list lput gridcount counts-list
          set gridy gridy + 1 ]
      set gridx gridx + 1 ]
   ;; show counts-list
  report variance counts-list
end 


; Copyright 2002 Uri Wilensky.
; See Info tab for full copyright and license.

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