Find the average translational kinetic energy of nitrogen molecules

In summary, the average translational kinetic energy of nitrogen molecules at 1600K can be found using the formula 3/2kT, as translational motion can only occur in three of the molecule's five degrees of freedom. This means that the rotational and vibrational motions do not contribute to translational kinetic energy. The correct answer in the back of the book uses this formula instead of 5/2kT.
  • #1
mit_hacker
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[SOLVED] Translational Kinetic Energy

Homework Statement



(Q) Find the average translational kinetic energy of nitrogen molecules at 1600K.

Homework Equations



Translational KE per degree of freedom = 1/2kT.

The Attempt at a Solution



Since Nitrogen molecules are diatomic, it has 5 degrees of freedom so KE = 5/2kT.

The problem is that this yields the wrong answer and the answer at the back of the book uses the formula 3/2kT. Can someone please explain to me why this is so?

Thank-you very much in advance.
 
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  • #2
Yes, the nitrogen molecule has 5 degrees of freedom, but translational motion can only happen in three of them.

(i.e. The rotational and vibrational motions are not translational motion, so the kinetic energy for these types of motion is not translational kinetic energy.)

Thus, we only consider the 3 degrees of freedom for which the molecule can undergo translational motion. So, we get:

[tex] <KE> = 3/2kT[/tex]

Does this make sense?
 
  • #3
Thanks a ton!

I understand. Thanks a lot for your extremely quick help!
 
  • #4
Anytime. :smile:
 

1. What is the formula for calculating average translational kinetic energy of molecules?

The formula for calculating average translational kinetic energy of molecules is given by: K = 3/2 * (kT), where K is the average translational kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

2. How do you determine the average translational kinetic energy of nitrogen molecules?

To determine the average translational kinetic energy of nitrogen molecules, you need to know the temperature and use the formula K = 3/2 * (kT). You can find the temperature of the nitrogen molecules by using a thermometer or by looking up the temperature in a database.

3. What is the significance of finding the average translational kinetic energy of molecules?

The average translational kinetic energy of molecules is a measure of the average speed of the molecules in a substance. It is important because it helps us understand the behavior and properties of substances, such as their ability to diffuse, evaporate, or react with other substances.

4. How does the average translational kinetic energy of nitrogen molecules compare to other gases?

The average translational kinetic energy of molecules is directly proportional to the temperature. Therefore, the average translational kinetic energy of nitrogen molecules will be similar to other gases at the same temperature. However, the mass of the molecules will also affect their average kinetic energy, with lighter molecules having higher average kinetic energy at the same temperature.

5. Can the average translational kinetic energy of molecules change?

Yes, the average translational kinetic energy of molecules can change if the temperature changes. As the temperature increases, the molecules will have higher average kinetic energy and move faster. Similarly, as the temperature decreases, the molecules will have lower average kinetic energy and move slower. This is why temperature is a crucial factor in determining the average translational kinetic energy of molecules.

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