# Why temperature increase when I fill a container with more particles?

If I have an adiabatic and rigid container with air , and if I fill it more with air, according to Ideal Gas law, the number of moles, temperature, and pressure would increase. Why would temperature increase?

Per example, if I have a piston and adiabatic cylinder, and if I push the piston, due to my work, particles will gain velocity and Kinetic Energy will increase, which means more Temperature. In the case of my rigid container, I would like to know why it would increase the temperature. I know there are more particles, they are tighter and they collide more, but I'm not providing any bonus energy, as heat or work, so their kinetic energy would mantain constant, and since an ideal gas only have elastic collisions, the temperature of whole system would be the same. Would the explanation for this be the fact that there are entering new particles with energy too, that can share with other particles?

## 1 Answer

If you add gas particles to an insulated container of fixed volume, what happens to the temperature depends entirely on what energy you give those particles when you add them. If you give them the same average kinetic energy as the ideal gas particles already in the container, the temperature will not change.

Perhaps what is confusing you is that you are trying to use the ideal gas law to infer the temperature. That law is just a constraint on pressure, temperature, and density, but it isn't necessarily telling you the temperature, that depends on additional details. For example, in the Earth's atmosphere, the ideal gas law sets the density of the air, because the temperature and pressure are set by other considerations.

• that's correct. Ideal Gas Law works here. According to Ideal Gas Law, if the number of particles increase on the container, pressure will increase, due to the increase of collision, yet, temperature doesn't have necessarily to increase, and you have just told me why... Thanks – VitorAguiar68 Apr 22 '17 at 23:11
• My question was based on the Ideal Gas Law, and I could see mathematically that temperature would increase or keep constant, I just wasn't understanding why... On the second paragraph, you mean that I can't relate how pressure, volume and temperature increase with height, per example? Maybe because due to the effects of gravity, solar radiation, atmospheric ionization processes, etc.. right? – VitorAguiar68 Apr 22 '17 at 23:15
• The ideal gas law is a relationship under the umbrella of thermal physics. Usually in thermal physics we don't assume a near magical ability to manipulate the microstate of the system (by, say, inserting low energy atoms without disturbing the existing gas). If the additional gas is to be introduced using macroscopic tools and techniques then there are consequences from that restriction. – dmckee Apr 22 '17 at 23:47
• In the atmosphere, the ideal gas law does apply, but it relates three variables, pressure, temperature, and density. So it cannot by itself be used to solve for all three, it only gives you one if you already know the other two. So which other two you already know depends on the situation, and the ideal gas law then gives you the third. In the atmosphere, temperature is given by heat transport, while pressure is from weight, so the ideal gas law gives density. If you compress a fixed amount of gas adiabatically with given applied pressure forces, that's when the ideal gas law gives T. – Ken G Apr 23 '17 at 12:06