PV=nRT AND PV work?

[zogoto]

It seems that when a gas expands (keeping pressure constant) adiabatically, then the temperature of the gas should go down. But then PV = nRT says that temperature should go up. What am I missing here?

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[GoldShadow]

PV=nRT is the relationship for a gas in one state, not for a gas that has changed from one state to another. The relationship you want is:

(P1)(V1)/(T1) = (P2)(V2)/(T2)

Here you can clearly see that it's an inverse relationship.

edit: on second thought, I might be mixing something up

edit2: never mind this, see my next post

 

[GoldShadow]

Alright, I got it. One way of looking at it is in terms of internal energy. For an adiabatic expansion:

ΔU = -W = -PΔV

Then, using the ideal gas law:

-PΔV = nRΔT

Since it's an adiabatic expansion, W (and therefore, ΔU and PΔV) will be negative, which means nRΔT also has to be negative. Since n and R are both positive, then it means ΔT must be negative. The only way this can be true is if the initial temperature T1 is larger than the final temperature T2.

 

[zogoto]

Thanks. I get that part now. But what about when you have those PV diagrams with cycles and stuff. When do you know the expansion is adiabatic and not? I'm looking at an EK 1001 problem where they say that after V increases, T must increase. This is implying heat has entered, right? How would I have known to say that?

 

[Zanzibar]

It seems that when a gas expands (keeping pressure constant) adiabatically, then the temperature of the gas should go down. But then PV = nRT says that temperature should go up. What am I missing here?

so, this is the way i see it;

we have a gas expanding (and thus increasing its volume). if we want to keep the pressure constant throughout, then the force exerted per unit area must be constant, and in a larger volume of gas, the only way to keep the average force per unit area the same as before it expanded is to increase the number of collisions. This is done by increasing the temperature.

 

[spyderracing32]

It seems that when a gas expands (keeping pressure constant) adiabatically, then the temperature of the gas should go down. But then PV = nRT says that temperature should go up. What am I missing here?

If you keep pressure constant the KE must go up with the expanded volume to maintain the same pressure (P = F/A), so yes the temperature will go up. Now if pressure is not constant and something external to the system increases the volume of the vessel, the pressure goes down as well as the temperature, but I think the ideal gas law deals only with things within the system.


edit: guy above me beat me to it, i didn't read the thread before posting this.