How Do You Calculate the Total Translational Kinetic Energy of Oxygen Gas?

[UrbanXrisis]

Compute the total translational kinetic energy of one liter of oxygen gas at atmospheric pressure.

<E>=3/2 kT

assuming that the T is about the temperature of Earth's surface, 300K, then:

$$\frac{1}{2} mv^2 = \frac{3k(300K)}{2}$$

what I am wondering is, is this the total translational kinetic energy? I think the book defines it as the average energy but does not give a formula for total translational kinetic energy.

 

[Hootenanny]

That indeed is the formula for average translational kinetic energy, however, I have not come across any formula for the total kinetic energy of a gas.

 

[dav2008]

Would it not be just 3/2NkT?

 

[Hootenanny]

Would it not be just 3/2NkT?

Ahh indeed I forgot, I've just dug out my old physics textbook now

 

[UrbanXrisis]

Would it not be just 3/2NkT?

what is N?

 

[dav2008]

N is the number of molecules.

I mean it makes sense that if the average translational kinetic energy of each molecule is 3/2kT then to get the total energy you would just multiply by the total number of molecules.

 

[UrbanXrisis]

how would I determine how many molecules are in 1 liter of oxygen? and how would one take into account the temperature when it is given inpressure?

 

[dav2008]

Are you familiar with the ideal gas law?

PV=NkT

P=pressure in pascals, V=volume in m³.

Since you know the pressure and the volume, and you are looking for the term "3/2NkT" I think you can see how you can get it.

 

[UrbanXrisis]

PV=NkT

1 liter= 0.001m³

$$E= \frac{3}{2} (101.3kPa)(0.001m^3)$$

would ths be correct?

 

[Hootenanny]

This is what i got;

$$pV=NkT$$

$$\frac{2}{3}E = kT$$

$$pV = N\frac{2}{3}E$$

$$E = \frac{3pV}{2N}$$

I think you've just missed out the number of molecules

Regards
-Hoot