Average translational kinetic energy of nitrogen molecule

In summary, 2.0 moles of nitrogen (N2) gas with a volume of 8.4e-3 m3 and a pressure of 4.7e5 Pa has an average translational kinetic energy of 3/2 kT, where k is the Boltzmann constant. This is found by using the ideal gas law and then solving for the kinetic energy using the formula KE=3/2kT.
  • #1
physics4u
4
0

Homework Statement



2.0 moles of nitrogen (N2) gas are placed in a container whose volume is 8.4 10-3 m3. The pressure of the gas is 4.7 105 Pa. What is the average translational kinetic energy of a nitrogen molecule?

average KEN2 = WebAssign will check your answer for the correct number of significant figures. J


Homework Equations





The Attempt at a Solution

 
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  • #2
No equations, no attempt at solving?
 
  • #3
Attempt

2.0 moles of nitrogen (N2) gas are placed in a container whose volume is 8.4e-3 m3. The pressure of the gas is 4.7e5 Pa. What is the average translational kinetic energy of a nitrogen molecule?

So I used PV=nRT and solved for T, after solving for Temperature, I used KE=3/2kT and solved for the total kinetic energy. Now is this my final answer or are there more steps to this problem?
 
  • #4
physics4u said:
2.0 moles of nitrogen (N2) gas are placed in a container whose volume is 8.4e-3 m3. The pressure of the gas is 4.7e5 Pa. What is the average translational kinetic energy of a nitrogen molecule?

So I used PV=nRT and solved for T, after solving for Temperature, I used KE=3/2kT and solved for the total kinetic energy. Now is this my final answer or are there more steps to this problem?

the *total* kinetic energy due to translational motion is 3/2 NkT

you have solved for the kinetic energy of a typical molecule. which is what you want.
 
  • #5
physics4u said:
2.0 moles of nitrogen (N2) gas are placed in a container whose volume is 8.4e-3 m3. The pressure of the gas is 4.7e5 Pa. What is the average translational kinetic energy of a nitrogen molecule?

So I used PV=nRT and solved for T, after solving for Temperature, I used KE=3/2kT and solved for the total kinetic energy. Now is this my final answer or are there more steps to this problem?

For a diatomic gas, you should use 5/2 KT.
 
  • #6
Shooting star said:
For a diatomic gas, you should use 5/2 KT.

mmm... no, he/she used PV=nRT to solve for the temperature which holds for any kind of ideal gas, be it composed of molecules or not... cf. Landau + Lif****z Stat Mech Volume I, section 42. then the translational kinetic energy is just 3/2 kT. cheers.
 
  • #7
Quite right upto the point of finding T. But after finding T, he/she has used E_av = 3/2 KT, which will be true for point masses with only 3 degrees of freedom. The rotational energy is being neglected. So, E_av = 5/2 KT will give the correct answer.
 
  • #8
but the question in the original post asks only for the average *translational* kinetic energy.
 
  • #9
OK, I missed the "translational". In that case, it should be 3/2 KT. Thanks.
 
  • #10


and what is K? is that the same as nr?
 

What is the average translational kinetic energy of a nitrogen molecule?

The average translational kinetic energy of a nitrogen molecule is approximately 5.92 x 10^-21 Joules at room temperature (25°C or 298 K).

How is the average translational kinetic energy of a nitrogen molecule calculated?

The average translational kinetic energy of a nitrogen molecule can be calculated using the formula 1/2 * m * v^2, where m is the mass of the molecule and v is its average velocity.

What factors affect the average translational kinetic energy of a nitrogen molecule?

The average translational kinetic energy of a nitrogen molecule can be affected by temperature, pressure, and the mass of the molecule. Higher temperatures and pressures will result in higher kinetic energy, while a heavier molecule will have a lower kinetic energy.

Why is the average translational kinetic energy of a nitrogen molecule important?

The average translational kinetic energy of a nitrogen molecule is important because it helps us understand the behavior and properties of gases. It is also a key factor in determining the temperature and pressure of a gas.

How does the average translational kinetic energy of a nitrogen molecule compare to other molecules?

The average translational kinetic energy of a nitrogen molecule is similar to other diatomic molecules with similar masses, such as oxygen and hydrogen. However, it may differ from larger molecules or molecules with different shapes or structures.

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