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--- summer_2019:ideal_gas_law [2019/08/05 18:53]
wellerd
+++ summer_2019:ideal_gas_law [2019/08/06 15:27] (current)
wellerd
@@ Line 1: / Line 1: @@
 ====== Ideal Gas Law Activity ======
+**Follow this link for the activity and the instructions: [[https://trinket.io/glowscript/575630aab8?showInstructions=true|link]]**
-===== Part A (Non-Computation) =====
+**Or, read the instructions after the image below, and copy the code into your own GlowScript file.**
-<WRAP info>
+You should see something that looks like this:
-==== Learning Goals ====
+{{:summer_2019:idealgasparticle.png?800|}}
-  * Ideal gas particles move with a distribution of different speeds.
+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.
-  * Temperature of ideal gas particles is directly proportional to the average kinetic energy of the gas particles.
-  * No energy is lost during particle-particle and particle-wall collisions.
-</WRAP>
+  * Try runnning your code. You'll notice that our gas particle is currently escaping the box.
+  * 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.
-===== Part B (Computation) =====
+  * Enter the equation for v_rms of a gas particle and correct that value in your particle's velocity.
-Copy and paste the following code into Glowscript to model the ideal gas law.
+  * 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.
+  * Hint: Everytime that a particle-wall collision occurs, you should increase your pcount, and then average the total pressure by dividing by pcount.
+  * 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.
+  * 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.
+For more information on glowscript tools, check out: [[https://www.glowscript.org/docs/GlowScriptDocs/index.html]]
 <code>
-GlowScript 2.8 VPython
+GlowScript 2.7 VPython
 ## Constants
-R=8.314 # Gas constant
+L=0.1 #Give our container a length of 0.1m on each side
-N_Avo=6.02E23 # Avogodro's constant
+N_Avogodro=6.02E23 # Avogodro's constant
-L = 0.1 # Our container is a cube with L=0.1m on each side
+k_B=1.38E-23 # Boltzmann constant
-Vol=L*L*L # Volume of our cube is 1 Liter
-Atomic_radius = 0.001 # wildly exaggerated size of a gas atom
-container = box(pos=vec(0,0,0),size=vec(L,L,L), color=color.white, opacity=0.1) # Create a container for our gas atoms
+## 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
-N_atoms = 300 # Number of gas atoms in your simulation
+v_rms=0 # Calculate the root-mean square speed
-n=N_atoms/N_Avo # number of moles of gas atoms
-Molar_mass = 4E-3 # molar mass of helium in kg/mol
+## 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)
-T = 300 # temperature in Kelvin
+## 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
-#v_avg = sqrt(8*R*T/(pi*Molar_mass)) # average velocity of gas atoms
-v_rms = sqrt(3*R*T/(Molar_mass)) # root mean squared velocity of gas atoms
-Velocity=v_rms #Which velocity would you like to assign your gas atoms: v_avg or v_rms?
-Theoretical_Pressure=n*R*T/Vol # Calculate the theoretical pressure based on the ideal gas law
-## The lines below create a graph for the heigh vs time. Try creating a graph for the velocity and acceleration
-Grph1 = graph(title='Pressure vs Time', xtitle='Time (s)', ytitle='Pressure (atm)', fast=False, ymin=0, ymax=5*Theoretical_Pressure) #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
-TheoreticalPressureGraph = gcurve(color=color.blue, label='Theoretical_Pressure') #Make a graph for theoretical pressure
-t=0 # initialize the time variable
-dt = 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
+## Set up the time variables for the while loop
-ListOfParticles = [] # Empty list of particles
+dt = 1E-7 # Time-step
-for i in range(0,N_atoms): #Loop over all of the atoms
+t = 0 # Initialize time variable
-    newparticle = sphere(pos=vector(L*random()-L/2,L*random()-L/2,L*random()-L/2),radius=Atomic_radius, color=color.green,opacity=0.7, visible = True) #Create a spherical particle at a random postion
+pressure=0 # initialize the pressure variable
-    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
+pcount = 0 # initialize a pressure counter
-    newparticle.mass = Molar_mass/N_Avo #Assign particles the atomic mass (in kg/atom) of your gas
-    ListOfParticles.append(newparticle) #Append the particle to our list of particles
-## The following lines simulate random motion and particle-wall collisions
+## While loop to iterate over time
-while True: #Run infinitely
+while True:
-    rate(9999) #Determines how fast the code runs
+    rate(1000) # Determines how fast the simulation runs
-    for particle in ListOfParticles: #Loop over all partciles
+    particle.pos = particle.pos + particle.velocity*dt # Update the particle's position
-        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 is a collision, reverse the velocity direction and add some pressure to the total.
-        if abs(particle.pos.x) >= L/2:
-            particle.velocity.x = - particle.velocity.x
-            pressure+=particle.mass*abs(particle.velocity.x)/(L*L*dt)
-            pcount+=1
-        if abs(particle.pos.y) >= L/2:
-            particle.velocity.y = - particle.velocity.y
-            pressure+=particle.mass*abs(particle.velocity.y)/(L*L*dt)
-            pcount+=1
-        if abs(particle.pos.z) >= L/2:
-            particle.velocity.z = - particle.velocity.z
-            pressure+=particle.mass*abs(particle.velocity.z)/(L*L*dt)
-            pcount+=1
-    #The following lines calculate the experimental pressure measured due to particle-wall collisions
+    ## Add if statement for particle-wall collision here
-    if pcount>=10: #After at least 10 particle-wall collisions occur
-        Experimental_Pressure=pressure/pcount # Average the total pressure over the number of particle-wall collisions
-        Experimental_Pressure=Experimental_Pressure/101.325 # Convert from kPa to atm
+    ## Add a graph for experimental pressure here
-        ExperimentalPressureGraph.plot(t,Experimental_Pressure) #Graph the experimental pressure
-        pressure=0 # Reset the pressure tracker
-        pcount=0 # Reset the pressure counter
+    t = t + dt
-    TheoreticalPressureGraph.plot(t,Theoretical_Pressure) #Graph theoretical pressure
-    t=t+dt #move on to the next time-step
 </code>