Let us look at the ideal gas law, which does not apply perfectly to any case, but it shows us the relationships between variables. ..
PV = nRT … R is a constant, T is temperarue, P is pressure, V is volume and n in the number of moles..
If we increase temperature (keeping R and n constant), we are expecting the volume to increase as well (directly proportional) and the pressure will descrease slighty. This is all assuming an open system that allows the solid/liquid/gas to get bigger. In this case, since n is staying the same as well as mass and volume is increasing, and density = mass/volume.. density would get smaller.
The opposite would happen if the temperature is falling.
In the case that we treat volume as a fixed variable, not allowing the solid/liquid/gas to get bigger or smaller, we are only looking at pressure as what changes. If temperature increases, the pressure will increase, but volume will stay the same and since density is only dependent on mass and volume, it will also not change.
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