When a gas is compressed, its temperature goes up, yes? Makes sense, since the gas molecules are now closer together and therefore more likely to bump into each other. But if we look the ideal gas equation (simplified to remove the constants), pV=T, or as pressure goes up and volume goes down, temperature should stay constant, no? Or is it the case that p and V are not 1/1 inversely proportional to each other, so that T always increases with compression? Does the speed of compression matter?
Or is my problem that I’m just looking at an equation and not thinking about real gases?
If you want to maintain a constant temperature, T, then you must vary BOTH pressure and volume to do so. If you change the pressure of a system, but maintain the same volume, then you will also see a change in temperature. Likewise, if you change the the volume, but maintain a constant pressure, then the temperature will change too. They are all interrelated, so a change in one automatically demands a change in at least one other term.
In most systems that you’re familiar with, like balloons or tires, compression is accompanied by other physical effects. When you blow up a balloon, the gas isn’t just expanding the volume, it’s being compressed by the elasticity of the balloon. You’re doing work on the balloon, and therefore on the system (you’re also increasing “n,” the amount of gas in the system, which you’ve left out of your equation).
When you compress a gas with a pump or piston, simultaneously increasing pressure and reducing volume, you are doing work on the system – adding energy, which increases the temperature. The ideal gas equation is an equation of state – it doesn’t accurately describe system with work being done on them, it only describes systems in equilibrium.
No, that is not what the equation says at all. Not al all. If you keep temperature constant then P*V is . . . well , constant. But you could keep pressure constant and let only V and T change in which case P is constant, by definition.
I think your question is regarding adiabatic compression and in that case all three change.