Well the easiest answer I can think of is to use the ideal gas equation and look at the terms and their effect on pressure. PV=nRT == P=(nrRT)/V, as can been seen from the equation: Pressure is directly proportional to Temperature and inversly proportional to Volume. So you trap air inside a fixed volume container. (Note: not every container will work. The walls of the container must be able to withstand the imbalance between the new inner air pressure and the atmospheric pressure.) Then simple cool the container. If you have gauge fixed to the rigid container (measuring the interior) you will see a drop in air pressure inside the container.