Ideal Gas Law - Adding additional gas & additional question

[Electric to be]

Hello, I know this has been fairly discussed to death, but I've had relative trouble finding a response that specifically addresses the n, in PV= nRT, the ideal gas law.

Out of relatively common sense, by adding additional moles of gas, the pressure in the gas should increase as there are more molecules, and therefore more collisions with the container the gas is held in. However, is it possible that by increasing n, the temperature will drop, as seen by their inversely proportional relationship in the equation? (somehow keeping PV constant)

Also, in regards to simply compressing a gas. I understand that if a gas is compressed, pressure is increased and work is done to the gas molecules and thus more energy is transferred into them, increasing their average kinetic energy and temperature. However, in this increase of pressure through compression, volume also decreases. I understand that PV = nRT is simply a way to model ideal gas law behavior, and that work does actually occur and the temperature of the gas should increase, but if the pressure increases, and the volume decreases, keeping PV equal to nRT, why would there be a need, according to the equation, for the temperature to also increase? Does the pressure increase in an amount that is more than proportional to the decrease in volume, which would require an increase in the temperature, according to the equation?

 

[Coffee_]

For your second question look up adiabatic processes, if we assume that the system is fully isolated and can't have any heat flow going on then indeed the volume and pressure and not proportional as $\frac{1}{x}$

 

[jbriggs444]

Hello, I know this has been fairly discussed to death, but I've had relative trouble finding a response that specifically addresses the n, in PV= nRT, the ideal gas law.

Out of relatively common sense, by adding additional moles of gas, the pressure in the gas should increase as there are more molecules, and therefore more collisions with the container the gas is held in. However, is it possible that by increasing n, the temperature will drop, as seen by their inversely proportional relationship in the equation? (somehow keeping PV constant)

Somehow keeping PV constant -- that's the key. If the equation is to hold, the temperature must be reduced. Maybe somebody is rubbing ice cubes all over the outside of your container. The equation does not tell you what is happening to reduce the temperature. It simply tells you that if you add gas, hold volume constant and observe that pressure is constant then you can correctly conclude that temperature has been reduced -- somehow.

 

[Electric to be]

For your second question look up adiabatic processes, if we assume that the system is fully isolated and can't have any heat flow going on then indeed the volume and pressure and not proportional as $\frac{1}{x}$

So if I roughly understand it correctly, under conditions where temperature can change, PV ≠ P'V', but PV/T will still be equal to P'V'/T', correct? Also pressure and volume are still inversely proportional if the temperature is constant right?

 

[Coffee_]

Yes it's been a while but I'm pretty sure the ideal gas law still holds and as long as the amount of particles don't change pV/T is constant that is just a property of the gas. The $PV^{\gamma}=c$ is a property of the proces where no heat can be exhanged.