One reason is because they are required to. Transport category aircraft are required to maintain an 8000' cabin. This is adequate for passenger comfort, without incuring too great of a performance penalty due to excess weight.
It varies, but it's up to about 7000-8000 feet at FL350ish. The cabin pressure is determined by the differential, which is about 7.5 psi or so there, and most aircraft have their altitude maximum defined by their pressurization systems. The 737-300 for instance is limited to 8 psi, that works out to a max of FL370.
Remember 8000 feet is only the max. When we fly at FL210, our cabin altitude is only about 3000 feet. Our maximum differential is 7.5 as well. Our average differential is in the 3.0-4.5 range, with altitudes between 1000 and 2000 feet cabin altitude.
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I understand that an airliner is pressurized to 8000 ft. Is there any reason for why they use 8000 ft specifically as opposed to pressurizing to sea level?
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Pressurizing an airplane is a little more complicated. Most have a engineered max differential of around 8-9 psi. This equates to around an 8,000ft cabin at 35,000ft. The newer aircraft have a cabin "scheduled" altitude. This means that for every altitude the aircraft is flying at there is a corresponding scheduled altitude the system tries to maintain the cabin up to it's max differential. This is done at a "scheduled" rate of climb or descent.
Keep in mind that simply lowering the cabin to sea level would create it's own problems. What if I took off from MIA and were flying to DEN? Denver is some 5400ft above sea level. Upon landing the outflow valves would fully open as the cabin air tried to match the outside pressure almost a mile above sea level. That would be an ear popper.
Usually, prior to takeoff, we select the destination's field elevation in the pressurization's mode selector. The pressurization system is automatic from there on. It'll maintain max differential pressure for the lowest cabin altitude during cruise.
Starting down the system adjust the cabin pressure to reach field elevation prior to landing. Landing at DEN means it only has to lower the cabin altitude from around 8000' to 5400'. Landing in MIA it'll continue max differential pressure until the cabin altitude is almost sea level prior to landing.