This class was a little different than the previous meetings. It was heavy on lecture, with fewer experiments. We did, however, participate in the largest scale (and most interesting) experiment, to date.
The class began with a quiz. This quiz was based on one of the previous homework problems, in which the temperature of compressed air within a cylinder of a car’s engine was determined. The trick to solving this problem lies within the understanding of gauge pressure versus atmospheric pressure, which was clarified in the previous homework assignment. This should reaffirm just how important the homework assignments are.
Once the quizzes were collected, the solutions given, and our groups divided according to alphabetically listed Olympic Sports, we dove into the topic of the day: Kinetic Theory and the Definition of Temperature.
We learned that the temperature of a gas is defined as the Kinetic Energy of its molecules. By applying this information to our previous equation:
PV = (2/3) · N ·
we can determine that:
= (3/2) · kBT
We went on to discuss that molecules store internal energy through vibration and rotation, and that we should ignore gravitational and electrical potential energies for now. This leaves us with:
Eint = N ·
Through substitution with the Kinetic Energy equation, and after solving for T, we determined that:
T = [2/(3kB)] · [ Eint /N]
At this time, Professor Mason began an experiment to relate the temperature of a gas to its volume and density. He had us use heat guns to begin heating the air inside a large balloon. After a few minutes, we realized that we should have conducted this experiment outside, as the balloon nearly touched the ceiling and floor simultaneously. Professor Mason decided to move the experiment outside, but not before we were able to see the balloon was definitely floating, with no outside assistance. Once we moved the balloon outside, we were unable to duplicate these results. It seemed as though a hole developed in the top of the balloon, allowing the hot air to escape faster than it could be added.
When we returned to the classroom, Professor Mason described a high altitude balloon that he had launched with the help of previous Physics students. He went on to describe how some of the instruments had failed at high altitudes, since the cold temperature prevented the batteries from supplying sufficient voltage to these instruments. This seems like a topic that will be brought up again later in the course when we discuss electricity. There was also a brief mention of Steve Fossett, who was an explorer made famous by circumnavigating the planet in a hot air balloon. http://en.wikipedia.org/wiki/Steve_Fossett
The balloon experiment led to the discussion of buoyant forces. As the air is heated and the volume expands, the mass remains constant. Therefore, the buoyant force on the balloon is constant.
Then our groups were instructed to go back on the Active Physics website. We used an applet on this website to answer the first 5 questions of a handout that we were given. The purpose of this exercise was to understand the Root-Mean-Square Speed (Vrms) of atoms, relative to temperature, and how it differs from the average speed.
We were shown that the equation:
PV = nRT
only works for ideal gases, and that the derived equation, known as Van Der Waals Equation of State is actually:
[P + (a) · (n/V)^2] · (V – nb) = nRT
There is a chart of Van Der Waals constants that can be used to determine the “a” and “b” values for this equation.
As time was running out, we were shown that the previously established Kinetic Theory of Gases:
KEaverage = (3/2) · kT
only applies to monatomic molecules, such as Helium, and that rigid diatomic molecules use the equation:
U = N · KEaverage = (5/2) · NkT
While vibrating diatomic molecules use the equation:
U = N · KEaverage = (7/2) · NkT
Professor Mason quickly flashed the following molecular velocity equations on the screen:
Vaverage = (8/pi)^(1/2) · (kT/m)^(1/2)
Vrms = (3)^(1/2) · (kT/m)^(1/2)
Vprobable = (2)^(1/2) · (kT/m)^(1/2)
At the conclusion of class, we had completed Chapter 18 (sections 18.3, 18.4, and 18.5) and Professor Mason emphatically commanded us to READ THE BOOK!
The class began with a quiz. This quiz was based on one of the previous homework problems, in which the temperature of compressed air within a cylinder of a car’s engine was determined. The trick to solving this problem lies within the understanding of gauge pressure versus atmospheric pressure, which was clarified in the previous homework assignment. This should reaffirm just how important the homework assignments are.
Once the quizzes were collected, the solutions given, and our groups divided according to alphabetically listed Olympic Sports, we dove into the topic of the day: Kinetic Theory and the Definition of Temperature.
We learned that the temperature of a gas is defined as the Kinetic Energy of its molecules. By applying this information to our previous equation:
PV = (2/3) · N ·
we can determine that:
We went on to discuss that molecules store internal energy through vibration and rotation, and that we should ignore gravitational and electrical potential energies for now. This leaves us with:
Eint = N ·
Through substitution with the Kinetic Energy equation, and after solving for T, we determined that:
T = [2/(3kB)] · [ Eint /N]
At this time, Professor Mason began an experiment to relate the temperature of a gas to its volume and density. He had us use heat guns to begin heating the air inside a large balloon. After a few minutes, we realized that we should have conducted this experiment outside, as the balloon nearly touched the ceiling and floor simultaneously. Professor Mason decided to move the experiment outside, but not before we were able to see the balloon was definitely floating, with no outside assistance. Once we moved the balloon outside, we were unable to duplicate these results. It seemed as though a hole developed in the top of the balloon, allowing the hot air to escape faster than it could be added.
When we returned to the classroom, Professor Mason described a high altitude balloon that he had launched with the help of previous Physics students. He went on to describe how some of the instruments had failed at high altitudes, since the cold temperature prevented the batteries from supplying sufficient voltage to these instruments. This seems like a topic that will be brought up again later in the course when we discuss electricity. There was also a brief mention of Steve Fossett, who was an explorer made famous by circumnavigating the planet in a hot air balloon. http://en.wikipedia.org/wiki/Steve_Fossett
The balloon experiment led to the discussion of buoyant forces. As the air is heated and the volume expands, the mass remains constant. Therefore, the buoyant force on the balloon is constant.
Then our groups were instructed to go back on the Active Physics website. We used an applet on this website to answer the first 5 questions of a handout that we were given. The purpose of this exercise was to understand the Root-Mean-Square Speed (Vrms) of atoms, relative to temperature, and how it differs from the average speed.
We were shown that the equation:
PV = nRT
only works for ideal gases, and that the derived equation, known as Van Der Waals Equation of State is actually:
[P + (a) · (n/V)^2] · (V – nb) = nRT
There is a chart of Van Der Waals constants that can be used to determine the “a” and “b” values for this equation.
As time was running out, we were shown that the previously established Kinetic Theory of Gases:
KEaverage = (3/2) · kT
only applies to monatomic molecules, such as Helium, and that rigid diatomic molecules use the equation:
U = N · KEaverage = (5/2) · NkT
While vibrating diatomic molecules use the equation:
U = N · KEaverage = (7/2) · NkT
Professor Mason quickly flashed the following molecular velocity equations on the screen:
Vaverage = (8/pi)^(1/2) · (kT/m)^(1/2)
Vrms = (3)^(1/2) · (kT/m)^(1/2)
Vprobable = (2)^(1/2) · (kT/m)^(1/2)
At the conclusion of class, we had completed Chapter 18 (sections 18.3, 18.4, and 18.5) and Professor Mason emphatically commanded us to READ THE BOOK!
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