Question

I'm learning about the combined gas law, and while doing calculations, I found that a doubling in the quantity of moles causes the temperature to be cut in half (all other things being equal).

I don't understand the mechanics of the change. Why does twice as much gas in the same amount of space cause the temperature to drop?
I would assume that there would be no change, since the total heat mass of the gas is unchanged. The particles in the gas are moved closer together, true, and more influenced by intermolecular bonds; but that seems to cut both ways, as a more crowded cluster of particles might produce more collisions? All in all, I understand the formula, but I don't get how the particles are interacting.
Also, is it true to say, mechanistically, that an increase in volume produces an increase in temperature? I don't understand how that would work, but it seems like a parallel to the example above (particles with less space to move have less energy; you can either shrink the container or crowd it, and reduce the temperature accordingly).
I understand how Charles' Law works in the other direction: increasing temperature gives the particles more energy, which causes them to collide harder and more frequently with their container, which will then expand.
But does merely making a container larger cause the gas within to rise in temperature? How would more space increase the total heat mass contained within the system? Where is the extra energy coming from?
A decrease in V causes an increase in P, and an increase in P causes an increase in T, but a decrease in V does not increase T?
I would appreciate your help very much, this is driving me a little crazy.
ps. Down voting questions is rather ungenerous. It's a question, not an assertion. I am confessing that I don't understand. If I know too little to ask the question well, forgive me. Your help is appreciated.

Answer 1

Doubling the moles of gas in a container at constant temperature will double the pressure according to Avogadro's law. However, if pressure must remain constant, then the temperature must decrease to accommodate the increase in moles. Expanding the volume doesn't inherently raise temperature; energy must be added for the temperature to increase, as per Charles's law.

Step-by-step explanation:

When we talk about the effects of changing the number of moles of gas in a container, we are exploring concepts rooted in the ideal gas law and the kinetic molecular theory (KMT). According to Avogadro's law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. If the number of moles in a fixed volume doubles, the pressure would also double to maintain the same temperature, based on the kinetic molecular theory, and vice versa. However, if instead of allowing the pressure to change, you adjust the temperature to keep the pressure constant, the temperature must decrease to accommodate the doubling of moles while maintaining the same volume. This is because the total energy of the system does not change simply by adding more particles unless heat is added or removed from the system.

Mechanistically, increasing the volume does not inherently increase the temperature of the gas. Instead, when a gas expands without the input of energy (as in an elastic expansion), its temperature usually drops as the molecules do work during expansion. This underlines that just making a container larger doesn't increase the temperature unless there is heat added to the system. This aligns with Charles's law, which states that at constant pressure, the volume of a gas changes directly with temperature. Remember, temperature is a measure of the average kinetic energy of molecules, therefore, when we increase temperature, molecules move faster, and if contained, they need more space to maintain the same pressure, which results in an increase in volume.