Why is it that gas compression leads to an increase in temperature under adiabatic process?

[m25]

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Why is it that gas compression leads to an increase in temperature under adiabatic process?
It just does not seem to fit with the PV=nRT equation? And since adiabatic process neither loses or gain heat, how is it even possible that the temperature increases?

 

[Jumb0]

U = Q + W
Q = Zero in this case, so U = W
The gas is compressed, so its work function is positive.
That means U is also positive. The internal energy of the gas increased.
The internal energy of an ideal gas is given by U = 3nRT/2
U and T are directly proportional. Therefore, as U increases, T will increase too.
🙂

 

[kraskadva]

Adiabatic means the system can't exchange heat with its surroundings, not that the temperature can't increase.
So, with PV=nRT, if you increase the pressure (through compression) then something on the other side of the equation has to increase as well. R is a constant, and you're not adding more moles of gas, so it has to be T that increases.

 

[m25]

Adiabatic means the system can't exchange heat with its surroundings, not that the temperature can't increase.
So, with PV=nRT, if you increase the pressure (through compression) then something on the other side of the equation has to increase as well. R is a constant, and you're not adding more moles of gas, so it has to be T that increases.

But in that case, isn't volume V also decreasing because it's a compression?

 

[kraskadva]

Maybe, maybe not. There are different ways to do a compression.
Either way though, the change in PV has to be reciprocated by a change in T during an adiabatic process.