# Density and the ideal gas equation

## Main Question or Discussion Point

Could someone explain the connection between density, pressure, and temperature in relation to the ideal gas law to me?
(For example what happend if the Temperature/pressure is kept konstant but the density changes with temeprature.)
As I see it there are two ways to get the density into the equation: once by taking the mass from PV=mRT and inserting V*density or by taking the Volume and inserting m/density. In both cases V dissapears. Does that mean the Volume has to change with density?

Any hint on how to best think about it is appreciated. Thank you^^.

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Density IS m/V
PV=mRT <--> P = density*RT <--> P/RT = Density
If the pressure is constant and if the temp is decreasing, then the density is increasing.
If the temp is constant, then density will increase with pressure.
Usually the ideal gas law uses moles in the place of m, so if your pressure is in bars or pascals you must use moles and get n/v = concentration, you can find the density in mass by multiplying it with the average molecular weight.

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Think about a tank of gas and what temperature and pressure is.

Temperature is the kinetic energy of the fast moving molecules. So the faster the molecules are bouncing around the hotter it is. Pressure, for the walls of a tank, is how hard the molecules are bouncing off the wall and how many are bouncing off a given area per second.

If you put the same molecules with the same speed in a smaller tank then more will bounce off the per second. Also the kinetic energy per molecule is the same but they are in a smaller area so the temperature is higher.

This is how and air conditioner works. It work far better if the expansion rate of the gas is not linear with temperature like an ideal gas, but the principle is the same. You compress the gas which make it hotter than the outdoor summer heat. So now move it outside where even in the summer heat it cools off. Now move this cooled compressed gas back inside the house and let it expand again. Since it is expanded it gets much cooler because there are fewer kinetic molecules per square inch. Then blow indoor air over this cold indoor tank to cool it off. Repeat. The house gets cooler than the outdoor summer air which was cooled off by the outdoor summer air.

In an ideal gas if you cool it off it means the gas molecules are slowed down. That means it is not bouncing off the tank walls as fast or with as much energy. So the pressure drops. If you compress the gas then, even with less energy per molecule, you get more molecules per inch per second bouncing off the walls. So the pressure is returned. In a ideal gas where the pressure stays constant the volume will change in proportional to temperature, or temperature in proportion to volume. Where volume it held constant the temperature will change in proportion to pressure, or pressure in proportion to temperature.