# Problem in adiabatic expansion and cooling

#### gogabidzia

Hey guys. I have a problem in adiabatic cooling and expansion and there is something I didn't understand. when we are compressing air without transfering heat(so adiabatically), why does the air heat? As I know, because of moving "wall". when molecules heat on moving wall kind of baseball bat hits the ball. they are moving with more velocity(kinetic energy). and when we expand air by that wall air cools down because of ... that's right. but does temperature depend on velocity of that wall? the adiabatic expansion/compression formula (VT^..) says that not. but actually if our explanation is true, it must depend. so what is the main idea of that? #### morrobay

Conservation of energy: Air heats on compression because it had absorbed heat during expansion.
Q = (U2 -U1) + W
So the heat absorbed in this case represents mostly delta U and equals the increase in internal energy of system. That is the work done in overcoming inter molecular attraction between the gas molecules.

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#### gogabidzia

morrobay, Yes, but problem isn't that law of thermodynamics. As I know internal energy increases by collisions on that wall. But if we move that wall very very slowly, collisions won't happen yes? So why does internal energy increase?

#### morrobay

Potential energy + kinetic energy = total energy. When gas expands potential energy increases , kinetic energy decreases. Cooling by expansion.
During compression potential energy decreases and kinetic energy increases. Heating by compression.

#### gogabidzia

morrorbay, an Ideal gas has a potential energy?

#### morrobay

morrorbay, an Ideal gas has a potential energy?
In an ideal gas there are no inter molecular forces so it has only kinetic energy proportional to temperature: U = 3/2nRT.
In a real gas as the molecules approach each other the charges are disturbed and depart from usual position.
In such a way that the average distance between opposite charges is less than between like charges.
So again in answer to your original question that does not specify an ideal gas: Why does gas heat on compression ? See above.

#### THERMO Spoken Here

Heat and Temperature...

Adiabatic is a process idealization in which there is (by assumption) no heat. The sum of heats is assumed zero in consequence that ALL (and each) of the heat mechanisms are themselves (assumed) zero. Two textbook hints meaning "assume no heat" are PERFECT INSULATION and very quick, or INSTANTANEOUS event.

A baseball hit by a bat is modeled as instantaneous ~ adiabatic. As is a coin struck by a die.

http://www.thermospokenhere.com/tsh/content.php?id=C405

Good luck with your studies, TSH

#### morrobay

In an adiabatic process Q = 0. No heat exchange with surroundings. But there can be temperature changes in system.
The internal energy of system increases if work is done on the system. Compression with heating.
The internal energy of system decreases if work is done by the system. Expansion with cooling.
And again with a non ideal gas there are inter molecular forces between gas molecules in both above cases of adiabatic compression and expansion.
To quantify temperature changes in system from work done on or by the system compared to temperature changes related to inter molecular forces during compression and expansion would definitely be advanced thermodynamics

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