All AP Physics 2 Resources
Example Question #1 : Kinetic Molecular Theory
What is the average molecular kinetic energy of a gas at a temperature of ?
We know that the expression for average kinetic energy is:
Where average velocity of a gas is:
Plugging this into our expression for kinetic energy, we get:
Plugging in our values, we get:
Example Question #2 : Kinetic Molecular Theory
A mixture of methane and oxygen is held at a constant temperature of and a pressure of . What is the ratio of the average velocity of methane to that of oxygen?
For gases at equal temperatures, we know that they both have the same average kinetic energy:
Note that is the molecular weight of each molecule, and is the average velocity of each molecule. Then rearranging for the ratio of velocities:
Then taking the square root of each side:
Now all we need is the molecular weight of each molecule:
Plugging these in, we get:
Example Question #3 : Kinetic Molecular Theory
What is the ratio of the rate of effusion of carbon dioxide to nitrogen ?
We can use Graham's law to solve this problem, which states that the ratio of effusion between to gasses is the square root of the inverse of the gases' molecular masses:
Therefore, in this problem we get:
Now we just need to determine the molecular masses of the two gasses, starting with carbon dioxide:
Plugging these in: