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

In summary, the formula for the average translational kinetic energy of a gas is 3/2kT, where T is the temperature and k is a constant. However, there is no defined formula for the total translational kinetic energy of a gas. To find this, one can use the ideal gas law and the volume and pressure of the gas to determine the number of molecules and then multiply it by the average energy. The formula for total translational kinetic energy is E = (3/2)PV/N.
  • #1
UrbanXrisis
1,196
1
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:

[tex] \frac{1}{2} mv^2 = \frac{3k(300K)}{2} [/tex]

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.
 
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  • #2
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.
 
  • #3
Would it not be just 3/2NkT?
 
  • #4
dav2008 said:
Would it not be just 3/2NkT?

Ahh indeed I forgot, I've just dug out my old physics textbook now:biggrin:
 
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Likes Muskaan Gandhi
  • #5
dav2008 said:
Would it not be just 3/2NkT?

what is N?
 
  • #6
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.
 
  • #7
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?
 
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  • #8
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.
 
  • #9
PV=NkT

1 liter= 0.001m3

[tex] E= \frac{3}{2} (101.3kPa)(0.001m^3) [/tex]

would ths be correct?
 
  • #10
This is what i got;

[tex]pV=NkT[/tex]

[tex]\frac{2}{3}E = kT[/tex]

[tex]pV = N\frac{2}{3}E[/tex]

[tex]E = \frac{3pV}{2N}[/tex]

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

Regards
-Hoot
 

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

What is translational kinetic energy?

Translational kinetic energy refers to the energy associated with the movement of an object from one position to another.

How is translational kinetic energy calculated?

The formula for calculating translational kinetic energy is KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

What is the relationship between translational kinetic energy and speed?

Translational kinetic energy is directly proportional to the square of the speed of an object. This means that as the speed increases, the translational kinetic energy also increases.

What are some real-life examples of translational kinetic energy?

Some examples of translational kinetic energy include a car moving down a road, a person running, a ball rolling, and a plane flying through the air.

How is translational kinetic energy different from other forms of energy?

Translational kinetic energy is a type of mechanical energy that is specifically associated with the movement of an object. It is different from other forms of energy, such as potential energy or thermal energy, which are associated with different types of motion or interactions.

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