# AP Physics 2 : Kinetic Molecular Theory

## Example Questions

### Example Question #11 : Thermodynamics

What is the average molecular kinetic energy of a gas at a temperature of ?

Possible Answers:

Correct answer:

Explanation:

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 #1 : 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?

Possible Answers:

Correct answer:

Explanation:

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 #1 : Kinetic Molecular Theory

What is the ratio of the rate of effusion of carbon dioxide  to nitrogen ?

Possible Answers:

Correct answer:

Explanation:

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: