globals [
  fast average slow     ;; current counts
  avg-speed avg-energy  ;; current averages
  clock vsplit vclock   ;; clock variables
  raw-width raw-height  ;; box size variables
  piston-position       ;; position of the piston at any given time
  volume area           ;; because this is 2D, area is the perimeter and volume is the area
  total-pressure        ;; pressure per unit area
  pressure-history      ;; list of 'scale' previous total-pressures
  avg-pressure          ;; mean of the pressure-history
  initspeed initmass    ;; inital speed and inital mass of the all the particles-particle mass always stays the same, but the speed changes.
  going-down?           ;; flag for whether or not the piston is moving up or down
]

turtles-own [
  speed mass energy new-speed            ;; Turtle Info    
  v1t v1l tmp-turtle                     ;; Turtle 1 -- Collide   
  heading2 mass2 speed2 v2t v2l turtle2  ;; Turtle 2 -- Collide
  theta                                  ;; Turtles 1 + 2 -- Collide
  pressure                               ;; pressure variable
]

;; precedure that setup up inital variables
to setup 
  ca
  set going-down? true
  set pressure-history []
  set initspeed 10.0
  set initmass 1.0
  set raw-width  round (0.01 * box-width  * screen-edge-x)
  set raw-height round (0.01 * box-height * screen-edge-y)
  set piston-position 0.75 * raw-height
  set area ((4 * raw-width) + (2 * (piston-position + raw-height)))
  set volume ((2 * raw-width) * (piston-position + raw-height))
  make-box
  draw-piston
  set clock  0
  set vclock 0
  ;; create the gas molecules
  cct number [
     set new-speed initspeed
     set mass initmass
     random-position
     rt random-float 360
     set shape "circle"
     recolor
     set pressure 0
  ]
  update-variables
  setup-histograms
end

;; updates variables after every time tick
to update-variables
  ;; Gas Variables
  ask turtles
    [ set speed new-speed
      set energy (0.5 * mass * speed * speed) ]
  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 values-from turtles [ speed  ]
  set avg-energy mean values-from turtles [ energy ]
  
  ;; System Variables
  calculate-pressure
  set vsplit (round (max values-from turtles [speed] * 1.2))
end

;; procedure that runs the model
to go
  ask turtles [bounce]
  ask turtles [move]
  ;; control the piston's motion
  if piston-position < (-0.75 * raw-height)
  [ set going-down? false ]
  if piston-position > (0.75 * raw-height)
  [ set going-down? true ]
  ifelse going-down?
  [ piston-down piston-speed / vsplit ]
  [ piston-up piston-speed / vsplit ]
    
  set vclock (vclock + 1)
  if (vclock = vsplit)
  [ 
    set clock  (clock + 1)
    set vclock 0
    update-variables
    do-plotting
    do-histograms
  ]
end


;; turtle procedure for bouncing off of the walls
to bounce 
  locals [ new-px new-py ]
  ; if we're not about to hit a wall (yellow patch)
  ; or the piston (gray+2 patch),
  ; we don't need to do any further checks
  if (pcolor-of patch-ahead 1 != yellow) and
     (pcolor-of patch-ahead 1 != gray + 2) [ stop ]
  ; get the coordinates of the patch we'll be on if we go forward 1
  set new-px pxcor-of patch-ahead 1
  set new-py pycor-of patch-ahead 1
  ; check: hitting left or right wall?
  if (abs new-px = raw-width)
    ; if so, reflect heading around x axis
    [ set heading (- heading) 
      set pressure pressure + abs (sin heading * mass * speed)
    ]
  ; check: hitting piston or bottom wall?
  if (abs new-py = raw-height) or (new-py = round piston-position)
    ; if so, reflect heading around y axis
    [ set heading (180 - heading) 
      set pressure pressure + abs (cos heading * mass * speed)
    ]
end

;; turtle procedure that moves all the particles
to move  
  jump (speed / vsplit)
  check-for-collision
end

;; turtle procedure to check to see if two particles collide
to check-for-collision  
  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

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

;; turtle gets mass and speed info from turtle it is colliding with
to get-turtle2-info 
  set turtle2 tmp-turtle
  set mass2 mass-of turtle2
  set speed2 new-speed-of turtle2
  set heading2 heading-of turtle2
end

;; calculates new turtle velocity after the collision
to calculate-velocity-components
  locals [ vcm ]  ;; CM vel. along dir. theta
  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))
  set 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)) 

  set new-speed-of turtle2 sqrt ((v2t * v2t) + (v2l * v2l))
  set heading-of turtle2 (theta - (atan v2l v2t))

  recolor
  ask turtle2 [ recolor ]
end

to recolor  ;; turtle procedure
  ifelse new-speed < (0.5 * initspeed)
    [ set color blue ]
    [ ifelse new-speed > (1.5 * initspeed)
        [ set color red ]
        [ set color green ] ]
end

;; patch procedure to make a box
to make-box
  ask patches with [ ((abs pxcor = raw-width) and (abs pycor <= raw-height)) or
                     ((abs pycor = raw-height) and (abs pxcor <= raw-width)) ]
    [ set pcolor yellow ]
end

;; turtle procedure to give turtles a random position within the confined area
to random-position  
  setxy ((1 - raw-width)  + random-float (2 * raw-width - 2))
        ((1 - raw-height) + random-float (raw-height + piston-position - 2))
end


;; ------ Piston ----------
to piston-up [dist]
  if (dist > 0)
  [ ifelse ((piston-position + dist) < raw-height - 1)
    [ undraw-piston
      set piston-position (piston-position + dist)
      draw-piston ]
    [ undraw-piston
      set piston-position (raw-height - 1)
      draw-piston ]
    set volume ((2 * raw-width) * (piston-position + raw-height))
    set area ((4 * raw-width) + (2 * (piston-position + raw-height)))
  ]
end

to piston-down [dist]
  if (dist > 0)
  [ ifelse (piston-position - dist) > (2 - raw-height)
    [ undraw-piston
      set piston-position (piston-position - dist)
      ask turtles
      [ if (ycor >= (piston-position - 1))
        [ bounce-off-piston ] ]
      draw-piston ]
    [ undraw-piston
      set piston-position (3 - raw-height)
      ask turtles
      [ if (pycor >= 3 - raw-height)
        [ bounce-off-piston ] ]
      draw-piston ]
    set area ((4 * raw-width) + (2 * (piston-position + raw-height)))
    set volume ((2 * raw-width) * (piston-position + raw-height))
  ]
end

to draw-piston
  ask patches with [ ((pycor = (round piston-position)) and ((abs pxcor) < raw-width)) ]
    [ set pcolor gray + 2 ]
  display
end

to undraw-piston
  no-display
  ask patches with [ (pycor = round piston-position) and ((abs pxcor) < raw-width) ]
    [ set pcolor black ]
end

to bounce-off-piston  ;; Turtles procedure particle bounces off piston
  ifelse ((((2 * piston-position) - (ycor + 2)) < (1 - raw-height)) or
          (((2 * piston-position) - (ycor + 2)) > (piston-position - 2)))
   [ set ycor ((random (raw-height + piston-position - 2)) - (raw-height - 1)) ]
   [ set ycor ((2 * piston-position) - (ycor + 2)) ]
end

to calculate-pressure  ;; Observer procedure
  set total-pressure 100 * (sum values-from turtles [pressure]) / area
  ifelse (length pressure-history < scale)
  [ set pressure-history fput total-pressure pressure-history ]
  [ set pressure-history fput total-pressure but-last pressure-history ]
  set avg-pressure mean pressure-history
  ;; rezero pressures in preparation for the next cycle
  ask turtles [ set pressure 0 ]
end

;;; plotting procedures
to setup-histograms
  ;; Speed Histogram
  set-current-plot "Speed histogram"
  set-plot-x-range 0 (initspeed * 2)
  set-plot-y-range 0 ceiling (number / 6)
  set-current-plot-pen "average"
  set-histogram-num-bars 45
  set-current-plot-pen "fast"
  set-histogram-num-bars 45
  set-current-plot-pen "slow"
  set-histogram-num-bars 45

  ;; Energy histogram
  set-current-plot "Energy histogram"
  set-plot-x-range 0 (0.5 * (initspeed * 2) * (initspeed * 2) * initmass)
  set-plot-y-range 0 ceiling (number / 6) 
  set-current-plot-pen "average"
  set-histogram-num-bars 45
  set-current-plot-pen "fast"
  set-histogram-num-bars 45
  set-current-plot-pen "slow"
  set-histogram-num-bars 45
end

;; does actual plotting (called in Go)
to do-plotting
  set-current-plot "Volume"
  plot volume
  set-current-plot "Pressure"
  plot avg-pressure
  set-current-plot "Temperature"
  plot avg-energy
  set-current-plot "Pressure vs. Volume"
  plotxy volume avg-pressure
  set-current-plot "Pressure * Volume"
  plot avg-pressure * volume / 1000
end

;; does actual histograms plotting (called in Go)
to do-histograms
  if (histogram?)
    [ histo-energy
      histo-speed ]
end

;; draw energy histogram
to histo-energy
  set-current-plot "Energy histogram"
  set-current-plot-pen "average"
  histogram-from turtles with [ color = green ] [ energy ]
  set-current-plot-pen "slow"
  histogram-from turtles with [ color = blue ] [ energy ]
  set-current-plot-pen "fast"
  histogram-from turtles with [ color = red ] [ energy ]
  set-current-plot-pen "avg-energy"
  plot-pen-reset
  draw-vert-line avg-energy
end

;; draw speed histogram
to histo-speed
  set-current-plot "Speed histogram"
  set-current-plot-pen "average"
  histogram-from turtles with [ color = green ] [ speed ]
  set-current-plot-pen "slow"
  histogram-from turtles with [ color = blue ] [ speed ]
  set-current-plot-pen "fast"
  histogram-from turtles with [ color = red ] [ speed ]
  set-current-plot-pen "avg-speed"
  plot-pen-reset
  draw-vert-line avg-speed
end

; draws a vertical line at xval on the current-plot with the current plot-pen
to draw-vert-line [xval]
  plotxy xval plot-y-min
  plot-pen-down
  plotxy xval plot-y-max
  plot-pen-up
end


; ***NetLogo Model Copyright Notice***
;
; This activity and associated models and materials were created as part of the project:
; MODELING ACROSS THE CURRICULUM.  The project gratefully acknowledges the support of the 
; National Science Foundation, National Institute of Health and the Department of Education 
; (IERI program) -- grant number REC # 0115699. Additional support was provided through the 
; project: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS 
; -- NSF (REPP program) -- grant number REC #9814682.
;
; Copyright 2002 by Uri Wilensky.  Updated 2002.  All rights reserved.
;
; Permission to use, modify or redistribute this model is hereby granted,
; provided that both of the following requirements are followed:
; a) this copyright notice is included.
; b) this model will not be redistributed for profit without permission
;    from Uri Wilensky.
; Contact Uri Wilensky for appropriate licenses for redistribution for
; profit.
;
; To refer to this model in academic publications, please use:
; Wilensky, U. (2002).  NetLogo GasLab Moving Piston model.
; http://ccl.northwestern.edu/netlogo/models/GasLabMovingPiston.
; Center for Connected Learning and Computer-Based Modeling,
; Northwestern University, Evanston, IL.
;
; In other publications, please use:
; Copyright 1998 by Uri Wilensky.  All rights reserved.  See
; http://ccl.northwestern.edu/netlogo/models/GasLabMovingPiston
; for terms of use.
;
; *** End of NetLogo Model Copyright Notice ***
@#$#@#$#@
GRAPHICS-WINDOW
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CC-WINDOW
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Command Center

BUTTON
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go
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OBSERVER
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BUTTON
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setup
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SWITCH
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clock
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MONITOR
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MONITOR
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SLIDER
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SLIDER
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PLOT
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Pressure * Volume
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PLOT
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Pressure vs. Volume
Volume
Pressure
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MONITOR
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MONITOR
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SLIDER
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scale
scale
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NIL

@#$#@#$#@
WHAT IS IT?
-----------
This model simulates the behavior of gas particles as the volume changes. In this model, the volume is slowly changing over time by a piston that is rising and falling.  As the piston lowers, the volume of the box decreases and as the piston rises, the volume of the box increases.  This systematic motion of the piston does no work on the particles inside the box.  The piston only serves a mechanism to change the volume of the box.  

The particles start with the same mass and speed upon the start of the simulation. The mass of the particles stays constant throughout the simulation, whereas, the speeds will change once particles start to collide.  Particles are in constant motion colliding with other particles and the walls. All collisions are modeled as elastic collisions, in that the total kinetic energy before and after the collision is conserved.  For example, when a fast moving particle collides with a slow moving particle, the fast moving particle will give some of its speed to the slow moving particle.  Therefore, the fast moving particle will leave the collision moving slower then when it entered the collision.  And the slow moving particle will speed up a bit.  The speed in a particle to particle collision is still conserved.  The collisions between a particle and a wall is modeled the same way.  When the particles hit the wall they transfer momentum to the wall.  After this transfer occurs, the particles then bounce off the wall with a different direction and speed. The system's pressure is calculated by averaging the number of collisions the particles have with the walls at each time step.  

The Moving Piston model is one of a collection of GasLab models that use the same basic rules for expressing what happens when gas particles collide.  Each model in this collection has different features to show the different aspects of the Gas Laws.

Multiple adaptations of this model can be found in the Chemistry folder of the Curricular Models section under the names Chem Volume 1 and 2.  It is part of a suite of models used to teach students about the chemistry of the Gas Laws.


HOW IT WORKS
------------
The particles are modeled as single particles, all with the same mass and initial velocity.  Molecules are modeled as perfectly elastic particles with no internal energy except that which is due to their motion.  Collisions with the box and between molecules 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 were two billiard balls that hit and this axis was 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 mass system.
4. Each turtle is assigned its new speed, 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.


HOW TO USE IT
-------------
Buttons:
  SETUP - puts in the initial conditions you have set with the sliders.  Be sure to wait till the SETUP button stops before pushing GO.
  GO - runs the code again and again.  This is a "forever" button.

Sliders:
  BOX-HEIGHT - height of the container
  BOX-WIDTH - width of the container
  NUMBER - number of particles
  PISTON-SPEED - rate of the piston
  SCALE - number of clock cycles over which to average the pressure

Switch:
  HISTOGRAM? - turns histograms on or off

Plots:
  VOLUME - plots the volume over time 
  PRESSURE - plots the pressure over time
  PRESSURE VS. VOLUME - plots pressure over volume 
  PRESSURE * VOLUME - plots the value of pressure * volume over time
  TEMPERATURE - plots the average temperature 
  SPEED HISTOGRAM - illustrates the number of particles at their various speeds
  ENERGY HISTOGRAM - illustrates the number of particles at their various energy levels
  
Adjust the BOX-HEIGHT, BOX-WIDTH, NUMBER, and PISTON-SPEED variable before pressing SETUP.  The SETUP button will set the initial conditions.  The GO button will run the simulation.  

In this model, though, the collisions of the piston with the particles are ignored. Note that there's a physical impossibility in the model here: in real life if you moved the piston down you would do work on the gas by compressing it, and its temperature would increase.  In this model, the energy and temperature are constant no matter how you manipulate the piston.  Nonetheless, the basic relationship between volume and pressure is correctly demonstrated here.


THINGS TO NOTICE
----------------
How does the pressure change as the volume of the box changes?  Compare the two plots of volume and pressure.

How does the pressure change as the shape of the box changes?  
  
Measure changes in pressure and volume. Is there a clear quantitative relationship? 

How can the relationship between pressure and volume be explained in terms of the collisions of molecules?

How does more particles change the relationship between pressure and volume?

What shapes do the energy and speed histograms reach after a while?  Why aren't they the same?  Do the pressure and volume affect these shapes?


THINGS TO TRY
-------------
How would you calculate pressure?  How does this code do it? 

Change the number, mass, and initial velocity of the particles.  Does this affect the pressure?   Why? Do the results make intuitive sense?  Look at the extremes:  very few or very many molecules,  high or low volumes.  

Figure out how many molecules there REALLY are in a box this size -- say a 10-cm cube.  Look up or calculate the REAL mass and speed of a typical molecule.  When you compare those numbers to the ones in the model, are you surprised this model works as well as it does?


EXTENDING THE MODEL
-------------------
Are there other ways one might calculate pressure?  

Create an isothermal piston example where the user can manually move the piston to any level in the box.  

Add in a temperature variable that allows for the particles to move the piston to the appropriate volume.


NETLOGO FEATURES
----------------  
Notice how collisions are detected by the turtles and how the code guarantees that the same two particles do not collide twice.  What happens if we let the patches detect them?


CREDITS AND REFERENCES
----------------------
To refer to this model in academic publications, please use: Wilensky, U. (2002).  NetLogo GasLab Moving Piston model. http://ccl.northwestern.edu/netlogo/models/GasLabMovingPiston. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 2002 by Uri Wilensky.  All rights reserved.  See http://ccl.northwestern.edu/netlogo/models/GasLabMovingPiston for terms of use.
@#$#@#$#@
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Polygon -7566196 true true 165 185 254 184 272 224 255 251 236 267 191 283 164 276
Line -7566196 true 167 47 159 82
Line -7566196 true 136 47 145 81
Circle -7566196 true true 165 45 8
Circle -7566196 true true 134 45 6
Circle -7566196 true true 133 44 7
Circle -7566196 true true 133 43 8

circle
false
0
Circle -7566196 true true 35 35 230

person
false
0
Circle -7566196 true true 155 20 63
Rectangle -7566196 true true 158 79 217 164
Polygon -7566196 true true 158 81 110 129 131 143 158 109 165 110
Polygon -7566196 true true 216 83 267 123 248 143 215 107
Polygon -7566196 true true 167 163 145 234 183 234 183 163
Polygon -7566196 true true 195 163 195 233 227 233 206 159

spacecraft
true
0
Polygon -7566196 true true 150 300 120 165 45 45 75 60 150 120 225 60 255 45 180 165

thin-arrow
true
0
Polygon -7566196 true true 150 300 300 150 180 150 180 4 120 4 120 150 120 150 0 150

truck-down
false
0
Polygon -7566196 true true 225 30 225 270 120 270 105 210 60 180 45 30 105 60 105 30
Polygon -8716033 true false 195 75 195 120 240 120 240 75
Polygon -8716033 true false 195 225 195 180 240 180 240 225

truck-left
false
0
Polygon -7566196 true true 120 135 225 135 225 210 75 210 75 165 105 165
Polygon -8716033 true false 90 210 105 225 120 210
Polygon -8716033 true false 180 210 195 225 210 210

truck-right
false
0
Polygon -7566196 true true 180 135 75 135 75 210 225 210 225 165 195 165
Polygon -8716033 true false 210 210 195 225 180 210
Polygon -8716033 true false 120 210 105 225 90 210

turtle
true
0
Polygon -7566196 true true 138 75 162 75 165 105 225 105 225 142 195 135 195 187 225 195 225 225 195 217 195 202 105 202 105 217 75 225 75 195 105 187 105 135 75 142 75 105 135 105

wolf-left
false
3
Polygon -6524078 true true 117 97 91 74 66 74 60 85 36 85 38 92 44 97 62 97 81 117 84 134 92 147 109 152 136 144 174 144 174 103 143 103 134 97
Polygon -6524078 true true 87 80 79 55 76 79
Polygon -6524078 true true 81 75 70 58 73 82
Polygon -6524078 true true 99 131 76 152 76 163 96 182 104 182 109 173 102 167 99 173 87 159 104 140
Polygon -6524078 true true 107 138 107 186 98 190 99 196 112 196 115 190
Polygon -6524078 true true 116 140 114 189 105 137
Rectangle -6524078 true true 109 150 114 192
Rectangle -6524078 true true 111 143 116 191
Polygon -6524078 true true 168 106 184 98 205 98 218 115 218 137 186 164 196 176 195 194 178 195 178 183 188 183 169 164 173 144
Polygon -6524078 true true 207 140 200 163 206 175 207 192 193 189 192 177 198 176 185 150
Polygon -6524078 true true 214 134 203 168 192 148
Polygon -6524078 true true 204 151 203 176 193 148
Polygon -6524078 true true 207 103 221 98 236 101 243 115 243 128 256 142 239 143 233 133 225 115 214 114

wolf-right
false
3
Polygon -6524078 true true 170 127 200 93 231 93 237 103 262 103 261 113 253 119 231 119 215 143 213 160 208 173 189 187 169 190 154 190 126 180 106 171 72 171 73 126 122 126 144 123 159 123
Polygon -6524078 true true 201 99 214 69 215 99
Polygon -6524078 true true 207 98 223 71 220 101
Polygon -6524078 true true 184 172 189 234 203 238 203 246 187 247 180 239 171 180
Polygon -6524078 true true 197 174 204 220 218 224 219 234 201 232 195 225 179 179
Polygon -6524078 true true 78 167 95 187 95 208 79 220 92 234 98 235 100 249 81 246 76 241 61 212 65 195 52 170 45 150 44 128 55 121 69 121 81 135
Polygon -6524078 true true 48 143 58 141
Polygon -6524078 true true 46 136 68 137
Polygon -6524078 true true 45 129 35 142 37 159 53 192 47 210 62 238 80 237
Line -16777216 false 74 237 59 213
Line -16777216 false 59 213 59 212
Line -16777216 false 58 211 67 192
Polygon -6524078 true true 38 138 66 149
Polygon -6524078 true true 46 128 33 120 21 118 11 123 3 138 5 160 13 178 9 192 0 199 20 196 25 179 24 161 25 148 45 140
Polygon -6524078 true true 67 122 96 126 63 144

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NetLogo 2.0alpha2
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