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summer_2019:ideal_gas_law [2019/08/01 22:46]
wellerd 		summer_2019:ideal_gas_law [2019/08/06 15:27] (current)
wellerd
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-<​code>​ +====== Ideal Gas Law Activity ​====== 
-GlowScript 2.8 VPython +**Follow this link for the activity and the instructions:​ [[https://​trinket.io/​glowscript/​575630aab8?​showInstructions=true|link]]**
-# Constants +
-R=8.314 # Gas constant +
-N_A=6.02E23 # Avogodro'​s constant +
-L = 0.1 # Our container is a cube with L=0.1m on each side +
-Ratom = 0.001 # wildly exaggerated size of a gas atom+
  
-# Properties of the gas atoms we are working with +**Or, read the instructions after the image below, and copy the code into your own GlowScript file.**
-N_atoms = 500 # change this to have more or fewer atoms +
-n=N_atoms/​N_A # number of moles of gas atoms+
  
-Molar_mass = 4E-3 # molar mass of helium in kg/mol+You should see something that looks like this:
  
-T = 300 # temperature in Kelvin+{{:​summer_2019:​idealgasparticle.png?​800|}}
  
-# Create ​a container ​for our gas atoms +If you click on the "​Instructions"​ tab in the upper right, ​a set of instructions ​for the activity should pop up. Click between "​Instructions"​ and "​Result"​ to alternately view the instructions and the animation. If you prefer, the same instructions are also listed below.
-container = box(pos=vec(0,​0,​0),​size=vec(L,​L,​L),​ color=color.white, opacity=0.1)+
  
-v_avg = sqrt(8*R*T/​(pi*Molar_mass)) # average velocity of gas atoms +  ​* Try runnning your code. You'll notice that our gas particle is currently escaping the box. 
-#v_rms = sqrt(3*R*T/​(Molar_mass)) # root mean squared velocity of gas atoms +  
-Velocity=v_avg+  ​* Add an '​if'​ statement to check for when the gas particle collides with a wall, and make the particle move in th opposite direction after contacting the wall.
  
-Theoretical_Pressure=n*R*T/​(L*L*L*1000) # Calculate the theoretical pressure based on the ideal gas law+  ​* Enter the equation for v_rms of a gas particle and correct that value in your particle'​s velocity.
  
-# The lines below create a graph for the heigh vs time. Try creating a graph for the velocity and acceleration +  * The pressure of an ideal gas comes from collisions between particles and the walls of the container. The pressure is equal to the force (mass times delta_velocity) divided by the area. Add a line to the code that calculates ​the pressure ​from our gas atom colliding with the wall. 
-Grph1 = graph(title='​Pressure vs Time', xtitle='​Time (s)', ytitle='​Pressure (atm)',​ fast=False,​ymin=0,​ ymax=5*Theoretical_Pressure) #ymin=0, ymax=2*Theoretical_Pressure +  * Hint: Everytime that a particle-wall collision ​occurs, you should increase your pcount, and then average ​the total pressure ​by dividing by pcount.
-ExperimentalPressureGraph = gcurve(color=color.red, label='​Experimental_Pressure'​) +
-TheoreticalPressureGraph = gcurve(color=color.blue,​ label='​Theoretical_Pressure'​) +
-     +
-t=0 # initialize ​the time variable +
-dt = 2.5E-9 #time-step interval +
-pressure=0 # initialize ​the pressure tracker +
-pcount=0 # This counter will track when a particle-wall collision ​adds to the pressure+
  
-# The following lines create ​all the particles +  * Try to create ​a pressure vs. time graph that adds another data point for every particle-wall collision. In this simplified model, the pressure versus time graph should be horizontal. 
-ListOfParticles = [] # Empty list of particles +   
-for i in range(0,​N_atoms):​ +  ​* For an extra challenge, try making ​the particle collisions work in three dimensions. This will build into a more complicated model to be used later.
-    newparticle = sphere(pos=vector(L*random()-L/​2,​L*random()-L/​2,​L*random()-L/​2),​radius=Ratom,​ color=color.green,opacity=0.7, visible = True) #Create a spherical particle at a random postion +
-    ​newparticle.velocity = vector(Velocity*sin(pi*random())*cos(2*pi*random()),Velocity*sin(pi*random())*sin(2*pi*random()),​Velocity*cos(pi*random())) #Randomize velocity +
-    newparticle.mass = Molar_mass/​N_A #Give the particles the atomic mass of your gas +
-    ListOfParticles.append(newparticle) #Append the particle ​to our list of particles+
  
-# The following lines simulate random motion and particle-wall collisions +For more information ​on glowscript tools, check out: [[https://www.glowscript.org/docs/GlowScriptDocs/index.html]]
-while True: +
-    rate(9999) +
-    for particle in ListOfParticles:​ +
-        particle.pos = particle.pos + particle.velocity*dt #Update position of every particle based on its velocity +
-         +
-        #Check for particle-wall collisions in x,y,z. If there are collisions, add some pressure to the total. +
-        if abs(particle.pos.x) >= L/2: +
-            particle.velocity.x = - particle.velocity.x  +
-            pcount+=1  +
-            pressure+=particle.mass*abs(particle.velocity.x)/(L*L*dt) +
-        if abs(particle.pos.y) >= L/2: +
-            particle.velocity.y = - particle.velocity.y ​  +
-            pcount+=1  +
-            pressure+=particle.mass*abs(particle.velocity.y)/(L*L*dt) +
-        if abs(particle.pos.z) >= L/2: +
-            particle.velocity.z = - particle.velocity.z  +
-            pcount+=1  +
-            pressure+=particle.mass*abs(particle.velocity.z)/(L*L*dt) +
-     +
-    #The following lines calculate the experimental pressure measured due to particle-wall collisions +
-    if pcount>​=1:​ +
-        Experimental_Pressure=pressure/​pcount # Average the total pressure over the number of particle-wall collisions +
-        Experimental_Pressure=Experimental_Pressure*101325 # Convert from Pa to atm +
-        ExperimentalPressureGraph.plot(t,​Experimental_Pressure) #Graph the experimental pressure +
-        pressure=0 # Reset the pressure tracker +
-        pcount=0 # Reset the pressure counter+
  
-    TheoreticalPressureGraph.plot(t,​Theoretical_Pressure) ​#Graph theoretical pressure+<​code>​ 
 +GlowScript 2.7 VPython 
 +## Constants 
 +L=0.1 #Give our container a length of 0.1m on each side 
 +N_Avogodro=6.02E23 # Avogodro'​s constant 
 +k_B=1.38E-23 # Boltzmann constant
  
-    ​t=t+dt+## Gas information 
 +mass = 4E-3/​N_Avogodro # helium mass in kg/atom 
 +Ratom=0.01 # exaggerated size of helium atom 
 +T=300 # Temperature equals 300 K 
 + 
 +v_rms=0 # Calculate the root-mean square speed 
 + 
 +## Setup a container with a gas particle inside 
 +container = box(pos=vec(0,​0,​0),​ size=vec(L+2*Ratom,​L+2*Ratom,​L+2*Ratom),​ color=color.white,​ opacity=0.1) 
 +particle = sphere(pos=vec(0,​0,​0),​ radius = Ratom, color = color.red) 
 +particle.velocity=vec(500,​0,​0) 
 + 
 +## Create a graph to track pressure 
 +Grph1 = graph(title='​Pressure vs Time', xtitle='​Time (s)', ytitle='​Pressure (Pa/​atom)',​ fast=False, ymin=0, ymax=1E-20) #initialize our graphs. Useful boundaries: ymin=0, ymax=5*Theoretical_Pressure 
 +ExperimentalPressureGraph = gcurve(color=color.red,​ label='​Experimental_Pressure'​) #Make a graph for measured pressure 
 + 
 +## Set up the time variables for the while loop 
 +dt = 1E-7 # Time-step 
 +t = 0 # Initialize time variable 
 +pressure=0 # initialize the pressure variable 
 +pcount = 0 # initialize a pressure counter 
 + 
 +## While loop to iterate over time 
 +while True: 
 +    rate(1000) # Determines how fast the simulation runs 
 +    particle.pos = particle.pos + particle.velocity*dt # Update the particle'​s position 
 +     
 +    ## Add if statement for particle-wall collision here 
 +     
 +     
 +    ## Add a graph for experimental pressure here 
 +     
 +     
 +    ​t = t + dt
 </​code>​ </​code>​
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  • Last modified: 2019/08/01 22:46
  • by wellerd