globals [ fast average slow ;; current counts avg-speed avg-energy ;; current averages clock vsplit vclock ;; clock variables raw-width raw-height ;; position of the box walls width height ;; dimensions of gas chamber volume area ;; size of gas chamber total-pressure ;; average of pressure inside the box pressure-history ;; previous pressure values initspeed initmass ;; initial speed and mass of particles wall-position ;; position of the gray wall wall-speed ;; speed of the gray wall walls ;; holds the wall patches was-locked? ;; whether the wall was previously locked ] turtles-own [ speed mass energy ;; turtle info v1t v1l tmp-turtle ;; collision info (turtle 1) heading2 mass2 speed2 v2t v2l turtle2 ;; collision info (turtle 2) theta ;; collision info (both turtles) pressure ;; pressure vars ] ;; The setup reads all the variables for the setup of the box and particles. to setup ca set raw-width round (0.90 * screen-edge-x) set raw-height round (0.80 * screen-edge-y) set wall-position 0 set was-locked? wall-is-locked? set width raw-width - 1 set height 2 * raw-height - 1 set wall-speed 0 make-box draw-wall set initspeed 10.0 set initmass 1.0 set clock 0 set vclock 0 set pressure-history [] cct number [ set speed initspeed set mass initmass random-position rt random-float 360 set shape "circle" recolor ] update-variables setup-plots do-plotting end ;; procedure to ask all turtles to update their energy/speed and ;; also update the pressure inside the box to update-variables ask turtles [ 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] if any? turtles [ set avg-speed mean values-from turtles [speed] set avg-energy mean values-from turtles [energy] set total-pressure sum values-from turtles [pressure] ] set width wall-position + raw-width - 1 set area 2 * width + 2 * height set volume width * height calculate-pressure ask turtles [ set pressure 0 ] set vsplit max list 1 (round ((max values-from turtles [speed]) * 1.2)) end ;; vsplit allows for the particles of different speeds to travel in a path that ;; will ensure a collision between particles if they are on the same patch to recalculate-vsplit ;; this needs to be done without-interruption to be sure that nothing tries to ;; use vsplit or vclock before they've been recalculated without-interruption [ set vsplit 2 * vsplit set vclock 2 * vclock ] end ;; runs the simulation ;; determines wall speed and how the inside and outside pressure move the wall. to go ask turtles [ bounce ] ask turtles [ move ] ifelse wall-is-locked? [ if not was-locked? [ set was-locked? true draw-wall ] ask walls with [pxcor != (round wall-position)] [ set pcolor temperature-color ] ] [ if was-locked? [ set was-locked? false ] ask walls [ set pcolor temperature-color ] if (outside-pressure > total-pressure and wall-speed > (- avg-speed)) [ set wall-speed wall-speed - 1 ] if (total-pressure > outside-pressure and wall-speed < avg-speed) [ set wall-speed wall-speed + 1 ] if wall-speed > 0 [ wall-right wall-speed / vsplit ] if wall-speed < 0 [ wall-left (- wall-speed) / vsplit ] ] set vclock (vclock + 1) if (vclock = vsplit) [ set clock (clock + 1) set vclock 0 update-variables do-plotting do-histograms ] end ;; a turtle procedure that keeps the particles inside the box and ;; also recalculates the energy and direction after the bounce to bounce locals [ new-px new-py ] ; if we're not about to hit a box wall (red patch) or ; the moveable wall (gray+2 patch) we don't need to do any more checks if (not shade-of? red pcolor-of patch-ahead 1) 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) or (new-px = round wall-position) ; if so, reflect heading around x axis [ set heading (- heading) set pressure pressure + abs (sin heading * mass * speed) set energy mean list energy outside-temperature set speed sqrt (2 * energy / mass) recolor ] ; check: hitting top or bottom wall? if (abs new-py = raw-height) ; if so, reflect heading arouny y axis [ set heading (180 - heading) set pressure pressure + abs (cos heading * mass * speed) set energy mean list energy outside-temperature set speed sqrt (2 * energy / mass) recolor ] end ;; turtle procedure used to move turtles using the vsplit modification to move ;; turtle procedure while [(speed / vsplit) >= 1.0] [ recalculate-vsplit ] jump (speed / vsplit) check-for-collision end ;; turtle procedure to check and see if turtle will collide with other turtles ;; if they move forward to check-for-collision if count other-turtles-here = 1 [ set tmp-turtle random-one-of other-turtles-here if ((who > who-of tmp-turtle) and (turtle2 != tmp-turtle)) [ collide ] ] end ;;turtle collision procedure to collide 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 speed-of turtle2 set heading2 heading-of turtle2 end ;; turtle procedure that calculates the speed of the two turtles ;; before they collide to calculate-velocity-components locals [vcm] ;; CM vel. along dir. theta set theta (random-float 360) set v1l (speed * sin (theta - heading)) set v1t (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 ;; turtle procedure that sets new speed and headings used for after ;; the collision of two turtles. to set-new-speed-and-headings set speed sqrt ((v1t * v1t) + (v1l * v1l)) set heading (theta - (atan v1l v1t)) set speed-of turtle2 sqrt ((v2t * v2t) + (v2l * v2l)) set heading-of turtle2 (theta - (atan v2l v2t)) recolor ask turtle2 [ recolor ] end ;; turtle procedure to recolor the turte to its new speed color ;; after a collision to recolor ifelse speed < (0.5 * initspeed) [ set color blue ] [ ifelse speed > (1.5 * initspeed) [ set color red ] [ set color green ] ] end ;; patch procedure to make the box to make-box set walls patches with [ ((pxcor = (- raw-width)) and (abs pycor <= raw-height)) or ((pxcor = raw-width) and (abs pycor = (raw-height - 1))) or ((abs pycor = raw-height) and (abs pxcor <= raw-width)) ] ask walls [ set pcolor temperature-color ] set plabel-of patch raw-width raw-width "outside" end to random-position ;; turtle procedure setxy (1 - raw-width + random-float (width - 1)) (1 - raw-height + random-float (height - 1)) end to-report temperature-color report scale-color red outside-temperature -200 600 end ;; moveable wall to undraw-wall no-display ask patches with [(pxcor = round wall-position) and (abs pycor < raw-height)] [ set pcolor black ] ask patches with [(pxcor = round wall-position) and (abs pycor = raw-height)] [ set pcolor temperature-color ] end to draw-wall ask patches with [(pxcor = round wall-position) and (abs pycor < raw-height)] [ set pcolor gray + 2 ] if wall-is-locked? [ ask patches with [(pxcor = round wall-position) and (abs pycor = raw-height)] [ set pcolor gray + 2 ] ] display end ;;this procedure ensures that the wall will not move past the already defined edges of the box to bounce-off-wall ifelse ( ( ((2 * wall-position) - (xcor + 2)) < (1 - raw-width) ) or ( ((2 * wall-position) - (xcor + 2)) > (wall-position - 2)) ) [ set xcor ((random-float (raw-width + wall-position - 2)) - (raw-width - 1)) ] [ set xcor ((2 * wall-position) - (xcor + 2)) ] end to wall-right [dist] if (dist > 0) [ ifelse (wall-position < raw-width - 1) [ undraw-wall set wall-position (wall-position + dist) draw-wall ] [ undraw-wall set wall-position (raw-width - 1) set wall-speed 0 draw-wall ] set width wall-position + raw-width - 1 set volume width * height set area 2 * width + 2 * height ] end ;; wall movement procedure to wall-left [dist] if (dist > 0) [ ifelse (wall-position - dist) > (2.5 - raw-width) [ undraw-wall set wall-position (wall-position - dist) ask turtles [ if (xcor >= (wall-position - 1)) [ bounce-off-wall ] ] draw-wall ] [ undraw-wall set wall-position (3 - raw-width) set wall-speed 0 ask turtles [ if (pxcor >= 3 - raw-width) [ bounce-off-wall ] ] draw-wall ] set width wall-position + raw-width - 1 set volume width * height set area 2 * width + 2 * height ] end ;;; pressure calculations to calculate-pressure set total-pressure (sum values-from turtles [pressure]) / area ;ifelse length pressure-history < 1 ;[ set pressure-history fput total-pressure pressure-history ] ;[ set pressure-history fput total-pressure (but-last pressure-history) ] ;set avg-pressure mean pressure-history end ;;; plotting procedures to setup-plots set-current-plot "Speed" set-plot-y-range 0 ceiling (number / 6) end to do-plotting set-current-plot "Speed" set-current-plot-pen "fast" plot fast set-current-plot-pen "average" plot average set-current-plot-pen "slow" plot slow set-current-plot "Temperature vs Time" set-current-plot-pen "temperature" plot avg-energy set-current-plot "Pressure vs Time" set-current-plot-pen "pressure" plot total-pressure set-current-plot "Volume vs Time" set-current-plot-pen "volume" plot volume set-current-plot "Outside vs Inside Temperature" set-current-plot-pen "outside" plot outside-temperature set-current-plot-pen "inside" plot avg-energy end ;;histogram procedures to do-histograms if (histogram?) [ histo-energy ] end to histo-energy set-current-plot "Energy histogram" set-current-plot-pen "fast" histogram-from turtles with [color = red] [ energy ] set-current-plot-pen "medium" histogram-from turtles with [color = green] [ energy ] set-current-plot-pen "slow" histogram-from turtles with [color = blue] [ energy ] set-current-plot-pen "avg-energy" plot-pen-reset draw-vert-line avg-energy end ;; histogram procedure 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. (2003). NetLogo GasLab Heat Box model. ; http://ccl.northwestern.edu/netlogo/models/GasLabHeatBox. ; 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/GasLabHeatBox ; for terms of use. ; ; *** End of NetLogo Model Copyright Notice *** @#$#@#$#@ GRAPHICS-WINDOW 386 24 680 339 35 35 4.0 0 10 1 1 1 CC-WINDOW 367 366 691 493 Command Center BUTTON 20 42 101 75 NIL setup NIL 1 T OBSERVER T BUTTON 20 83 101 116 NIL go T 1 T OBSERVER NIL SLIDER 109 42 317 75 number number 0 500 207 1 1 particles MONITOR 131 232 238 281 NIL clock 0 1 MONITOR 23 555 103 604 NIL avg-speed 3 1 MONITOR 241 136 363 185 inside-temperature avg-energy 3 1 MONITOR 9 232 122 281 volume volume 3 1 MONITOR 241 185 363 234 inside-pressure total-pressure 3 1 SLIDER 7 151 238 184 outside-temperature outside-temperature 0 500.0 42.0 1 1 NIL SWITCH 108 82 247 115 wall-is-locked? wall-is-locked? 1 1 -1000 SLIDER 7 185 238 218 outside-pressure outside-pressure 1 20.0 2.0 1 1 NIL PLOT 112 506 356 664 Speed time count 0.0 100.0 0.0 200.0 true true PENS "fast" 1.0 0 -65536 true "average" 1.0 0 -11352576 true "slow" 1.0 0 -16776961 true PLOT 24 306 329 492 Outside vs Inside Temperature time temperature 0.0 500.0 0.0 500.0 true true PENS "outside" 1.0 0 -16776961 true "inside" 1.0 0 -6524078 true PLOT 370 504 600 663 Energy histogram Energy Number 0.0 500.0 0.0 10.0 true false PENS "fast" 10.0 1 -65536 true "medium" 10.0 1 -11352576 true "slow" 10.0 1 -16776961 true "avg-energy" 1.0 0 -7566196 true SWITCH 620 563 747 596 histogram? histogram? 0 1 -1000 PLOT 697 42 933 203 Temperature vs Time time temperature 0.0 100.0 0.0 100.0 true true PENS "temperature" 1.0 0 -65281 true PLOT 697 204 933 354 Pressure vs Time time pressure 0.0 100.0 0.0 10.0 true true PENS "pressure" 1.0 0 -44544 true PLOT 697 355 932 505 Volume vs Time Time Volume 0.0 100.0 0.0 100.0 true true PENS "volume" 1.0 0 -16777216 true @#$#@#$#@ WHAT IS IT? ----------- This model is illustrating the relationship between pressure, volume, temperature and number of particles as noted in the (PV = nRT) equation of the Ideal Gas Laws. (P=pressure, V=volume, n=number of particles, R=constant value, T=temperature) A constant number of particles are trapped within a box that can change its volume. As the walls of the box are heated, the sides of the walls will change color from a deep red (cool) to a bright red, to pink to a pale pink white (hot). The walls contain a constant heat value throughout the simulation. The gray wall is movable if the WALL-IS-LOCKED? switch is off. When this switch is off, competing pressures (inside and outside pressures) move the wall. If the pressure on the inside of the box is greater than the pressure on the outside of the box, then the wall will move to the right, increasing the volume of the box. But if the pressure on the outside is greater than the pressure on the inside, then the wall will move to the left, decreasing the volume of the box. When the wall lock is on volume and numbers of particles are being held constant to illustrate the relationship between pressure and temperature. When the wall lock is off and the wall is able to move freely, pressure and number of particles are held constant to illustrate the relationship between volume and temperature. 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 between molecules are elastic. Particles are colored according to speed -- blue for slow, green for medium, and red for high speeds. In this model, pressure is calculated by adding up the momentum transferred to the walls of the box by the particles when they bounce off the wall. This is averaged over all of the walls and recorded as the pressure. When the OUTSIDE-TEMPERATURE slider is increased, this increases the temperature of the walls. The increase in temperature of the walls will directly affect the behavior of the particles. As the particles hit the walls, they will conduct heat from the walls increasing their speed. This increase in speed, increases the chance of hitting the walls more often. Since the average number of total collisions between the particles and the walls measures pressure, faster particles will result in an increase in pressure. If the wall is not locked and the pressure on the inside of the box exceeds the pressure on the outside of the box, the wall will move. When the volume increases, the number of collisions between the particles and walls decreases which lowers the pressure and sometimes the wall will move, decreasing the volume of the box. The Heat Box models are one in a collection of GasLab models that uses the same basic rules for expressing what happens when particles collide. Each of the GasLab models has different features to show the different aspects of the Gas Laws. Adaptations of this model can be found in the Chemistry folder of the Curricular Models section under the name Chem Heat Box. This model is part of a suite of models used to teach students about the Gas Laws from a chemistry prospective. HOW IT WORKS ------------- The exact way two particles collide is as follows: 1. Two turtles "collide" when 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 but exchanges energy with the wall if they're different. The exact way particles gain energy from the walls of the box is as follows: 1. Particles check their state of energy. 2. They hit or bounce off the wall. 3. They find wall energy and recalculate their new energy. 4. They change their speed and direction after the collision. HOW TO USE IT ------------- Buttons: SETUP - sets up the model with the current values of the sliders and switch GO - runs the model Sliders: NUMBER - number of particles within in the box OUTSIDE-TEMPERATURE - temperature of the outside of the box and the wall of the box OUTSIDE-PRESSURE - the outside pressure put on the wall (pressure to the right of the wall) Switch: WALL-IS-LOCKED? - Determines if the wall is locked in place or moving Plots: PRESSURE VS. TIME - average pressure of the inside of the box over time VOLUME VS. TIME - volume of the box over time TEMPERATURE VS. TIME - average particle temperature inside the box over time OUTSIDE VS. INSIDE TEMPERATURE - average particle temperature and wall temperature over time SPEED VS. TIME - plots the speeds of the particles over time ENERGY HISTOGRAM - illustrates the number of particles at their various energy levels Adjust the NUMBER, WALL-IS-LOCKED?, OUTSIDE-TEMPERATURE, OUTSIDE-PRESSURE variables 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 ---------------- What happens to the wall when the inside pressure is greater than the outside pressure? What happens to the wall when the outside pressure is greater than the inside pressure? How does locking the wall and not locking the wall affect pressure? How does the volume of the box change as the outside pressure increases? Decrease? How can the relationship between pressure and volume be explained in terms of the collisions of molecules? How does adding heat to the box walls affect the pressure with volume constant? With the volume variable? How does adding heat to the wall affect the particle behavior? THINGS TO TRY ------------- Determine the conditions needed to have the wall sit to the far right of the box? Far left of the box? Try to get the pressure on either side of the wall to equalize. Try to get the wall to not bounce. Try to get the wall to equalize in the middle of the box. EXTENDING THE MODEL ------------------- Give the wall a mass and see how that affects the behavior of the model. Close off the right side of the box. Create two values on either side to the wall that allow the user to "spurt" particles into the chambers to see how number of particles affects pressure. NETLOGO FEATURES ---------------- Notice how the collisions are detected by the turtles and how the code guarantees 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. (2003). NetLogo GasLab Heat Box model. http://ccl.northwestern.edu/netlogo/models/GasLabHeatBox. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL. In other publications, please use: Copyright 2003 by Uri Wilensky. All rights reserved. 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