Name: ______________________________________ Date: ________________________
Student Exploration: Temperature and Particle Motion
Vocabulary: absolute zero, Kelvin scale, kinetic energy, Maxwell-Boltzmann distribution, molar
mass, molecule, temperature, universal gas constant
Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
1. Why is hot air hot? __________________________________________________________
_________________________________________________________________________
2. Why is cold air cold? ________________________________________________________
_________________________________________________________________________
3. Air consists of tiny particles called molecules. How do you think the molecules move in hot
and in cold air? ____________________________________________________________
_________________________________________________________________________
Gizmo Warm-up
The Temperature and Particle Motion Gizmo™ illustrates
how the molecules of gas move at different temperatures. In
this Gizmo, temperature is measured on the Kelvin scale,
which measures temperature from absolute zero, the
coldest possible temperature (-273.15 °C). Each unit on the
Kelvin scale is equivalent to 1 °C: 273.15 K = 0 °C, and
373.15 K = 100 °C.
Check that the selected gas is Hydrogen and the
Temperature is 300 K.
1. Describe the motion of the hydrogen molecules: __________________________________
_________________________________________________________________________
_________________________________________________________________________
2. Are all of the molecules moving at the same speed? _______________________________
Hannah Sonnentag
10/07/11
Hot air is hot because of the time of the year and the temperature, also depending on where you are.
Cold air is cold because if it is winter time or in a naturally cold area or the surrounding temperature.
I think the hot air will move fast and the cold air will be more slow
moving.
The molecules are moving fast and rapid.
No
Check that the selected gas is Hydrogen and the
Temperature is set to 300 K.
Question: How is the temperature of a gas related to the motion of gas molecules?
1. Observe: Move the Temperature slider back and forth. Focus on the particle motion at left.
What do you notice? ________________________________________________________
_________________________________________________________________________
2. Analyze: The temperature of a substance is a measure of the average kinetic energy of its
particles (kinetic energy is the energy of motion). The kinetic energy (KE) of a particle is
equal to its mass times the square of its velocity, divided by two:
KE = mv
2
/ 2
A. Based on the formula for kinetic energy, how will the temperature change if you
increase the average velocity of the molecules in a gas? ______________________
___________________________________________________________________
B. How will the temperature change if you increase the mass of the gas molecules?
___________________________________________________________________
3. Predict: Oxygen molecules are sixteen times as massive as hydrogen molecules. At the
same temperature, which type of molecule would you expect to move faster? Explain.
_________________________________________________________________________
_________________________________________________________________________
4. Check: Test your prediction by choosing Oxygen from the Select a gas menu.
What do you see? __________________________________________________________
5. Explain: Based on the definition of temperature given above, explain why oxygen molecules
move more slowly than hydrogen molecules at the same temperature. _________________
_________________________________________________________________________
_________________________________________________________________________
When the temperature is more cold the air molecules move
slowly and when the air is hot the air molecules move very fast.
Hydrogen molecules, because they would be more lighter then the oxygen
molecules and be able to move faster.
The oxygen molecules moving slower then the hydrogen molecules.
The oxygen molecules are more loaded and heavier which weighs down and the
molecules and don't allow the same amount of moving ability as the hydrogen
moles have.
Select Hydrogen gas.
Set the Temperature to 300 K.
Introduction: The graph on the right side of the Gizmo represents the Maxwell-Boltzmann
distribution of particle velocities. The curve represents the probability of a particle moving at
the velocity shown on the x-axis of the graph. The higher the curve, the greater the probability of
finding a particle moving at that velocity will be.
Question: How are particle velocities distributed?
1. Observe: Move the Temperature slider back and forth. This time focus on the graph at right.
What do you notice about the shape of the graph? _________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
2. Analyze: Look at the left side of the graph as you raise the temperature from 50 to 1,000 K.
A. Even at the highest temperatures, are there still a few slow particles? ____________
B. At what temperature do you see the widest variety of particle velocities? __________
C. In general, is the Maxwell-Boltzmann curve a symmetrical or an asymmetrical curve?
___________________________________________________________________
3. Estimate: Because particles have a range of velocities at any given temperature, it is useful
to calculate the average velocity. Physicists express the average velocity in three ways:
most probable velocity (v
p
), mean velocity ( ), and root mean square velocity (v
rms
).
Set the temperature to 200 K (the selected gas should still be Hydrogen).
A. Estimate the most probable velocity by looking at the peak of the curve. What is your
estimate? ______________
B. Turn on Show most probable velocity. What is the actual value? ______________
C. Base on the shape of the curve, do you think most of the particles are moving faster
or slower than the most probable velocity? ______________
(Activity B continued on next page)
When the temperature is low and colder the graph has a high peak and doesn't
stretch out in length very much. When the temperature is high and hotter the graph
has a low stretched line that exceed very high.
yes
750c
symmetrical
1357m/s
1284m/s
faster but somewhat
slowly at the same time
Activity B (continued from previous page)
4. Predict: The mean velocity is the average velocity of all of the particles. Based on the shape
of the curve and your answer to the previous question, do you expect the mean velocity to
be greater than or less than the most probable velocity? Explain your reasoning.
_________________________________________________________________________
_________________________________________________________________________
5. Check: Turn on Show mean velocity. What is the mean velocity? ____________________
6. Experiment: Try a variety of other gases and temperatures. Is the mean velocity always
greater than the most probable velocity? ________________________________________
Explain why this is so: _______________________________________________________
_________________________________________________________________________
_________________________________________________________________________
7. Calculate: Turn off Show most probable velocity and Show mean velocity. Select
Hydrogen and set the Temperature to 100 K. You can calculate the most probable velocity
(v
p
), mean velocity ( ), and root mean square velocity (v
rms
) using the following formulas:
In each formula, R stands for the universal gas constant, or 8.3144 J / K mol, T stands for
Kelvin temperature, and M stands for the molar mass, in kg / mol. Hydrogen gas (H
2
) has a
molar mass of 0.002016 kg / mol.
A. Calculate the most probable velocity (v
p
): ____________________
B. Check by turning on Show most probable velocity. Were you correct? __________
C. Calculate the mean velocity ( ): ____________________
D. Check by turning on Show mean velocity. Were you correct? __________
E. Calculate the root mean squared velocity (v
rms
): ____________________
F. Check by turning on Show root mean square velocity. Were you correct? _______
Less then because when you do the mean you usually have to divide.
1449m/s
no
yes