• Electric to be
In summary, the ideal gas law states that PV=nRT, with pressure and volume being inversely proportional at a constant temperature. However, by adding more moles of gas while keeping PV constant, the temperature will decrease. In terms of compression, the equation PV=nRT only models ideal gas behavior and does not explain the mechanism behind the temperature increase. In adiabatic processes, where there is no heat exchange, PV/T remains constant. The ideal gas law still holds as long as the number of particles is constant, and the relationship between pressure and volume remains inverse at a constant temperature.
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?

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}##

Electric to be said:
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.

Coffee_ said:
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?

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.

## 1. What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical equation that relates the pressure, volume, temperature, and amount of gas in a closed system. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.

## 2. How does adding additional gas affect the Ideal Gas Law?

Adding additional gas to a closed system will increase the number of moles (n) in the Ideal Gas Law equation. This will result in an increase in pressure (P) or volume (V) if the other variables remain constant. However, if temperature (T) is also increased, the pressure and volume may not change significantly.

## 3. Can the Ideal Gas Law be used for any type of gas?

The Ideal Gas Law is most accurate for gases that behave like ideal gases, meaning they have no intermolecular forces and take up no volume. However, it can still be used for real gases if corrections are made for deviations from ideal behavior.

## 4. How do you calculate the amount of gas using the Ideal Gas Law?

To calculate the amount of gas, or number of moles (n), using the Ideal Gas Law, rearrange the equation to solve for n. This gives us n = PV/RT, where P is pressure, V is volume, R is the ideal gas constant, and T is temperature. Plug in the given values and solve for n.

## 5. Can you use the Ideal Gas Law for gases at any temperature and pressure?

The Ideal Gas Law can be used for gases at any temperature and pressure, as long as the gas behaves like an ideal gas. However, at very high pressures or low temperatures, real gases may deviate significantly from ideal behavior and the use of the Ideal Gas Law may not be accurate.

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