Avogadro's Principle and number of moles + thermodynamics problem

[Awesome-o]

Hi,
I learned recently Avogadro's principle which states " At constant temperature and pressure, equal volumes will contain the same number of molecules" this can be translated to if you double the volume, you double the number of moles. Now i don't get that at all! where does the extra particles come from as you double the volume? can't doubling the volume still hold one mole but spread out at greater area?

the other problem i have is conceptual: In thermodynamics practice i was asked: if volume is increased and pressure remains constant, what happens to temperature? My answer ws it decreases and the reasoning behind this was: as volume is spread out, average kinetic energy will spread over a larger area and temperature will decrease. I was wrong, the answer was: Temperature increase as stated by PV=nRT. why is my reasoning incorrect?

 

[Nessdude14]

Avogadro's principle doesn't imply that doubling the volume will create "extra particles." What this principle implies is that in order to double the volume of the gas with no change in pressure or temperature, you must double the gas molecules (meaning more gas must be added.) If you were to double the volume without changing the amount of gas molecules, then you'd get one of two things: a change in pressure, or a change in temperature; likely both.

As for the second question, first let's rearrange the equation PV = nRT to show the temperature:
T = PV/nR
Now, the question was about the change in temperature as the volume increases, at a constant pressure and (i assume) number of molecules, so we can remove these variables for the following equation:
ΔT = ΔV/R
So this equation shows the change in temperature corresponding to a volume change. In this equation, you can see that as the volume increases, the temperature also increases.
If this is hard for you to imagine intuitively, think of a balloon full of air or gas. If it's cooled, the balloon will shrink (its volume goes down.) If the gas in the balloon gets warmer, it expands. Hope this helps.