Thermodynamics concept question

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An ideal gas cools when it expands adiabatically and reversibly because it does work during the expansion, which draws energy from its internal energy. As the gas does work, its internal energy decreases, leading to a reduction in the average kinetic energy of its molecules. This decrease in kinetic energy results in a lower temperature. Since the process is adiabatic, no heat is exchanged with the surroundings, further contributing to the cooling effect. Thus, the temperature drops as the gas expands due to the loss of internal energy.
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Problem: Why does an ideal gas cool when it expands adiabatically and reversibly?

Is the volume of the container expanding? so the total kinetic energy of the gas is getting smaller as it occupies more space making the temperature cool?
 
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The gas does work in order to expand. This work is done at the expense of the internal energy of the gas. (KE of its molecules)
 
Is that all? so when the gas is doing work, it will loose energy? is that because the system is loosing energy and the temperature willl decrease??
 
still unsure...
 
The gas does work.
The energy to do this comes from the internal energy of the gas.
The temperature of the gas depends on the (average) KE of the molecules.
If internal energy is lost, KE is reduced, temperature goes down.
(Because its adiabatic, no heat energy is allowed into the gas from outside.
If it was allowed, this heat energy would appear as internal energy and cause the temperature to rise.)
 
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