Reconciling PV=NRT , with gas expansion

[unleash500]

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I know that when a gas expands it cools because it uses its own internal energy to do work on the surroundings.

However, it seems to create problems with the ideal gas equation , PV=NRT.

(based on the equation)
When we increase the Volume , the Temperature also increases (if we keep pressure constant).
Yet, I know that a gas cools upon expansion.
I am assuming that cooling means a loss of heat, which means a drop in temperature?

Can anyone point out where I went wrong?

 

[Longshanks]

I know that when a gas expands it cools because it uses its own internal energy to do work on the surroundings.

However, it seems to create problems with the ideal gas equation , PV=NRT.

When we increase the Volume , the Temperature also increases . Yet, I know that a gas cools upon expansion.
I am assuming that cooling means a loss of heat, which means a drop in temperature?

Can anyone point out where I went wrong?

It depends on the type of expansion. The temperature will increase with expansion if the pressure remains constant. Conversely, temperature can remain the same if heat transfer is allowed to the surroundings such as in an isothermal process. However, in an adiabatic expansion the internal energy decreases (as you've noted) and thus the temperature decreases, but in this case pressure is not constant.

http://en.wikipedia.org/wiki/Adiabatic_process#Ideal_gas_.28reversible_case.29

When using the ideal gas law it's important to take note of what remains constant in the problem and what type of thermodynamic process is occurring.

 

[unleash500]

It depends on the type of expansion. The temperature will increase with expansion if the pressure remains constant. .

I don't think so?
Temperature will decrease when pressure is constant. If we have a change in volume ( expansion) then work must be done in order to cause this change.

Where does the work done come from? Internal energy.
If internal energy is being converted to work, then we have a decrease in temperature.

Hmmm I think I am assuming an adiabatic process with my reply.

 

[fizzgig]

longshanks answer seems right to me. the pvnrt is just a state equation. the process that gets you from state to state is important.

if you inc volume with the same number of molecules, the only way to keep P the same is if you throw enough heat into the system that the avg collision energy stays the same. fewer molecules, farther apart, fewer collisions, so you need higher energy collisions to do it. the increase in internal energy given by heat transfer gives higher translational E and higher T, and that does it for you.

if you have an adiabatic process and the container is expanded, your internal energy does go down, cooling as you expect. the pressure will just not be the same as before in this case.

i guess you just gotta watch saying stuff like 'if you keep pressure constant'... in the latter case, you simply don't... there has to be a reason P remains constant.

 

[BerkReviewTeach]

Temperature will decrease when pressure is constant.

You should think about this physically. If the volume of the piston is increased by work (brute force pulling up the lid), then particles inside will be spread farther apart and therefore have more space to traverse before striking the wall (which now has more surface area), so the pressure must decrease.

In an adiabatic expanasion, volume goes up, internal pressure goes down, and the heat energy of the system is absorbed to carry out the work, so temperature must decrease.

Longshanks explained it quite accurately and in a thorough fashion, so I don't have much to add. Like he pointed out, PV = nRT explains why adding heat can cause expansion in a system where Pinitial = Pfinal = Pexternal.

PV = nRT could still apply to the adiabatic expansion, but you'd need to know five of the following to use it: Pinitial, Pfinal, Vinitial, Vfinal, Tinitial, and Tfinal.