How Does Room Temperature Affect Air Molecule Energy from Winter to Summer?

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Room temperature significantly affects the kinetic energy of air molecules, with an increase from approximately 34 J/mole at 5°C in winter to about 37 J/mole at 25°C in summer, resulting in a difference of 3 J per mole. For a room measuring 3m x 3m x 4m, this translates to a total energy difference of 4573 J between winter and summer. However, this energy is not equivalent to power, as it does not represent energy loss or gain per second; rather, it is an average kinetic energy retained by the molecules until collisions occur. The discussion clarifies that the energy is dependent on pressure and temperature but does not change over time in a stable system. Overall, the relationship between temperature, pressure, and energy in gases is complex and does not imply a constant energy transfer rate.
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According to KMT, Avarage kinetic energy of 1 mole gas is=(3/2) x R x T
So , in winter in my cold room ,
the gases have Kea=34J/mole (T=5oC)

and in summer that figure climbs to, -roughly- 37J/mole, (T=25oC)
Difference is , 3J per mole.

If my rooms dimensions are 3m x 3m x 4m, volume is 36m^3, so
n is = PV/RT=(1)(36.000)/(0.082)(15+273) (avg temp of 15oC taken to compute number of moles)
n=1524 mole ==> 3J x 1524= 4573J That's the difference of Energy between winter and summer for my room.

So, does that mean the air molecules in my room carries 4573J more energy in summer compared to winter?

How can I put time factor? Can I say they carry that per second?
Power=E/t=4573/1=4573 Watts??
Can I assume they hit my body constantly it's as if 4573W heater is in the room and warms me up??
 
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The number of moles is not the same. The room is not a sealed container but one in equilibrium with the atmospheric pressure.
If you do the calculation right you will see that the total energy is independent of temperature but dependent of pressure.
Time does not come into the picture.
 
Can you elaborate on that pls?
 
The number of moles in a room of volume V, at pressure p and temperature T is
N=pV/RT
If you multiply this by the energy per mole, u=3/2 RT, the temperature simplifies. There is nothing more to "elaborate".
 
skepticwulf said:
Can I say they carry that per second?

No, the energy is not 'per second'. Energy per second would be power, and would imply that the gas is losing or gaining that much energy per second. A gas molecules with X joules of kinetic energy will retain that energy until a collision causes it to either give up or gain energy. As the molecule bounces around over time, it will randomly gain or lose energy with each bounce. If the gas is in equilibrium then all of these collisions tend to cancel themselves out and you can assign an average value.
 
nasu said:
The number of moles in a room of volume V, at pressure p and temperature T is
N=pV/RT
If you multiply this by the energy per mole, u=3/2 RT, the temperature simplifies. There is nothing more to "elaborate".
Thank you!, you're such a nice person.
 
You are welcome. :smile:
 

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