Thermal Energy in 1 cubic meter of air at room temperature

In summary: Gravitational potential energy is just potential energy due to gravity, so PE=mgh here, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height. In summary, the thermal energy in 1 cubic meter of air at room temperature is approximately 151815 Joules, while the kinetic energy of one cubic meter of air falling 100 meters is approximately 1176 Joules. Therefore, thermal energy has a significantly greater amount of energy compared to gravitational energy.
  • #1
Bgerst103
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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.
 
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  • #2
Perhaps think about the kinetic energy of a single gas molecule (=3/2 kT).
 
  • #3
CWatters said:
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?
 
  • #4
If that's the right number of molecules (I haven't checked) then that would be the energy in Joules.
 
  • #5
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.
 
  • #6
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?
 
  • #7
Bgerst103 said:
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 "kB = 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.
 
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  • #8
phyzguy said:
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.
 
  • #9
Bgerst103 said:
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.
 

Related to Thermal Energy in 1 cubic meter of air at room temperature

1. What is the definition of thermal energy?

Thermal energy is the internal energy of a system due to the motion and vibration of its particles.

2. How is thermal energy measured in 1 cubic meter of air at room temperature?

Thermal energy is typically measured in joules (J) or calories (cal) in 1 cubic meter of air at room temperature.

3. What is the relationship between thermal energy and temperature?

Thermal energy and temperature are directly related. As the temperature of a system increases, so does its thermal energy.

4. How does thermal energy in air at room temperature affect the surrounding environment?

The amount of thermal energy in air at room temperature can affect the temperature and humidity of the surrounding environment. It is also a factor in weather patterns and air quality.

5. Can thermal energy be converted into other forms of energy?

Yes, thermal energy can be converted into other forms of energy, such as mechanical or electrical energy, through various processes like heat engines or thermoelectric generators.

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