Average translational kinetic energy of nitrogen molecule

[physics4u]

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

 

[Shooting Star]

No equations, no attempt at solving?

 

[physics4u]

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?

 

[olgranpappy]

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.

 

[Shooting Star]

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.

 

[olgranpappy]

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.

 

[Shooting Star]

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.

 

[olgranpappy]

but the question in the original post asks only for the average *translational* kinetic energy.

 

[Shooting Star]

OK, I missed the "translational". In that case, it should be 3/2 KT. Thanks.

 

[name_ask17]

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