Re: Please explain the relationship between temperature of air and pressure

In a closed container the air pressure will rise if you increase the
temperature, because the molecules bounce off each other and the walls of
the container with greater speed - they 'push more' against each other and
the walls. If the container is fixed so that the walls cannot move the
density will stay the same because density is just mass divided by volume,
and the mass of the heated air is the same as that of the cooler air.

In free air (like our atmopshere) a heated parcel of air will be able to
expand. This will cause the density to go down, and, assuming that the
parcel of air was at rest with respect to other parcels of surrounding air
before you started heating it, it will now rise until its density matches
that of the surroundings and will then come to a rest.

If you cool air it will contract and descend, if in the free atmosphere.