Thermal Energy in 1 cubic meter of air at room temperature

[Bgerst103]

Homework Statement

How much thermal energy was in 1 cubic meter of air at room temperature. Give your answer in Joules.

How much kinetic energy does one cubic meter of air have if it were to hit the ground after falling 100 m? Give your answer in Joules.

Which has more energy? Gravitational energy or thermal energy?

Homework Equations

The Attempt at a Solution

I'm not really sure how to calculate thermal energy of air. Room temperature is 25C I believe.

 

[CWatters]

Perhaps think about the kinetic energy of a single gas molecule (=3/2 kT).

 

[Bgerst103]

Perhaps think about the kinetic energy of a single gas molecule (=3/2 kT).

So, there are about 2.5 x 10^25 molecules in 1m3 of air. K is 1.381 x 10^-23. I've decided to use 293.15 K as my temperature. So the kinetic energy of one molecule is 6.0726 x 10^-21. So do I multiply this by 2.5 x 10^25? That would come out to 151815. If this is right how would I turn this into joules?

 

[CWatters]

If that's the right number of molecules (I haven't checked) then that would be the energy in Joules.

 

[Bgerst103]

Thermal energy in one cubic meter of air

Homework Statement

How much thermal energy was in 1 cubic meter of air at room temperature. Give your answer in Joules.

How much kinetic energy does one cubic meter of air have if it were to hit the ground after falling 100 m? Give your answer in Joules.

Which has more energy? Gravitational energy or thermal energy?

Homework Equations

2/3kT

The Attempt at a Solution

So, there are about 2.5 x 10^25 molecules in 1m3 of air. K is 1.381 x 10^-23. I've decided to use 293.15 K as my temperature. The kinetic energy of one molecule is 6.0726 x 10^-21. So, I multiplied by 2.5 x 10^25 would come out to 151815 J, is this thermal energy? How do i calculate the kinetic energy after falling 100m? I'm assuming i just compare the two to answer the third question.

 

[phyzguy]

I think your calculation of the thermal energy is correct. Can you calculate the mass of 1 m^3 of air? Do you know how to calculate the gravitational potential energy gained when a mass m falls a distance h under the influence of gravity?

 

[dauto]

So, there are about 2.5 x 10^25 molecules in 1m3 of air. K is 1.381 x 10^-23. I've decided to use 293.15 K as my temperature. So the kinetic energy of one molecule is 6.0726 x 10^-21. So do I multiply this by 2.5 x 10^25? That would come out to 151815. If this is right how would I turn this into joules?

That's already in Joules (You would know that if you kept better track of units. That's a very important point that for some reason most student blow off as unimportant or trivial. Don't make that mistake. Instead of "K is 1.381 x 10^-23" say "k_B = 1.381 x 10^-23 J/K" Note all the changes I've made to your statement. They were all intentional). I didn't check your math, it but seems to be in the right ball park.

 

[Bgerst103]

I think your calculation of the thermal energy is correct. Can you calculate the mass of 1 m^3 of air? Do you know how to calculate the gravitational potential energy gained when a mass m falls a distance h under the influence of gravity?

The density of air at room temp is about 1.2 kg/m3 so mass would be M=DV so I guess the mass is just 1.2 as well? Gravitional potential energy is just PE=mgh correct? So then, 1.2(9.8)(100)=1176 meaning thermal energy is much greater than gravitational.

 

[phyzguy]

The density of air at room temp is about 1.2 kg/m3 so mass would be M=DV so I guess the mass is just 1.2 as well? Gravitional potential energy is just PE=mgh correct? So then, 1.2(9.8)(100)=1176 meaning thermal energy is much greater than gravitational.

I think that's correct.