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When you fill up a cabin with warm air the pressure of the cabin will rise. An outflow valve controls the desired pressure. But with pressure rising doesn't the temperature rise because you're compressing air into a space? Is this why the outflow valve is there, to regulate the pressure and temperature? Does the outflow value open and close depending on the pressure during phases like climb, cruise, and descent. Or does the outflow valve shut completely once the cabin altitude reaches 8,000ft? But then wouldn't the air get too hot because it keeps getting shoved into the cabin? Does it use the isothermal rule, if so then what is the work done?

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Pressure does not rise because keeping the cabin pressurized begins with releasing air to the outside. The flight starts low, with low cabin altitude, as the plane climbs the cabin altitude rises (lower pressure than it started).

As for the air itself. When it is compressed by the ACM, the temperature does rise, that's why it is cooled before being introduced into the cabin.

See here: Where does the final cooling take place in the air cycle machine of the air conditioning system?

Work is done on the air, then the air does work by passing through a heat exchanger, and then a turbine, which runs the ACM.

There is one plane I know of that maintains sea level pressure up to FL 410. In that case air will still be jettisoned overboard to bring in fresh air, with the same ACM cycle of temperature regulation.

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When you fill up a cabin with warm air the pressure of the cabin will rise.

You're not filling up a cabin with hot air, you're allowing sufficient air (of any temperature) into the cabin to match the air flowing out. What is important is the flow of air (~10 pounds per person per minute).

An outflow valve controls the desired pressure. But with pressure rising doesn't the temperature rise because you're compressing air into a space?

No, the outflow valve makes sure that the pressure DOESN'T rise, it stays roughly the same (allowing for climb/descent).

The classic paradigm for aircraft pressurisation is a (toy) balloon with a pin-prick leak - as long as you keep blowing it up as fast as the air is flowing oyut the leak, it will stay inflated. The outflow valves use flow as a means of controlling the pressure (differential), which then ensures the requirement for sufficient flow of breathing air per passenger.

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To maintain a comfortable temperature for the passengers, automatic systems regulate the mixture of heat from the engines and cold from the air packs. To maintain the pressure in the cabin equal to that at low altitude, even while the airplane is at 30,000 feet, the incoming air is held within the cabin by opening and closing an outflow valve, which releases the incoming air at a rate regulated by pressure sensors. Think of a pressurized cabin as a balloon that has a leak but is being inflated continuously.

On the ground, the airplane is unpressurized and the outflow valve is wide open. During preflight, the pilot sets the cruise altitude on a cabin pressure controller. As soon as the weight is off the main wheels at takeoff, the outflow valve begins to close and the cabin starts to pressurize. The airplane may be climbing at thousands of feet per minute, but inside the cabin, the rate of “climb” is approximately what you might experience driving up a hill. It might take an average airliner about 20 minutes to reach a cruise altitude of, say, 35,000 feet, at which point the pressurization system might maintain the cabin at the pressure you’d experience at 7,000 feet: about 11 pounds per square inch. Your ears may pop, but the effect is mild because the climb rate is only 350 feet per minute. When the airplane descends, the pilot sets the system controller to the altitude of the destination airport, and the process works in reverse.

The structural strength of the airplane determines how much differential pressure the cabin can tolerate—a typical figure is eight pounds per square inch—and the fuselages of new airplane designs are pressurized and depressurized many thousands of times during testing to ensure their integrity. The higher the maximum differential pressure, the closer to sea level the system can maintain the cabin. Federal Aviation Regulations say that without pressurization, pilots begin to need oxygen when they fly above 12,500 feet for more than 30 minutes, and passengers have to use it continuously above 15,000. On airliners that operate at altitudes well above that, regulations require that everyone aboard be supplied with 10 minutes of oxygen in the event the cabin pressure can’t be maintained, which brings us to the dramatic scenario known as explosive decompression.

If the door blew off a jet at altitude, all the air in the cabin would depart very quickly and a momentary thick fog would envelope the cabin as the water vapor in the air condensed instantly. Loose articles would fly around and foam rubber would burst as the tiny air bubbles within it expanded. Within a couple of seconds, oxygen masks would drop down from the overhead panels, and you would have to pull yours toward you and place it over your mouth and nose. The act of donning the mask tugs on a lanyard that starts the flow of life-sustaining oxygen.

Source: Air & Space Magazine

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    $\begingroup$ Welcome to aviation.SE! This appears to be copied from an online article. It's fine to quote other sources, but please make sure you identify them (link to them) and use the quote formatting to indicate it's a quote. $\endgroup$ – Pondlife Jul 6 at 15:33
  • $\begingroup$ Hey guys, I wish you'd clarify a bit on why my edit was rejected. I deleted the last 2 paragraphs because I thought they had to do with structural limits on pressurization and emergencies, rather than with the valve. What am I missing? I'm really curious. $\endgroup$ – Abdullah Jul 7 at 16:31

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