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I understand that aircraft are pressurized by pushing air into the cabin using the engines, and using a valve to let the air escape at a controllable rate thus achieving the desired pressure differential. However, when air is compressed, it heats up and if I understand correctly, all pressurized aircraft have air conditioning units to keep the temperatures at a reasonable level.

If all air conditioning units were to fail, how hot would the air being shoved into the cabin actually be? If this depends on aircraft and or engine type, any example as a ballpark figure would be appreciated.

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  • $\begingroup$ In reality, heat loss through the air ducting and cabin insulation is so strong that cabin temperatures tend to be lower than what is considered comfortable. In order to save fuel, on many airlines the air flow into the cabin is reduced, and the little heat this air carries into the cabin is not enough to keep the cabin warm enough. $\endgroup$ May 22 '14 at 19:17
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    $\begingroup$ @PeterKämpf then why am I always uncomfortably hot when traveling on an airliner? $\endgroup$
    – jwenting
    May 23 '14 at 10:31
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    $\begingroup$ @PeterKämpf what do you mean "[not] pressurized instantly"? Air is taken from outside, and compressed to the pressure inside the cabin; that's a pretty quick process, wouldn't you say? $\endgroup$
    – falstro
    May 23 '14 at 17:57
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    $\begingroup$ @PeterKämpf I have been in two different airplanes where the packs have failed, and I can assure you that the air coming into the cabin gets quite hot! $\endgroup$
    – Lnafziger
    May 24 '14 at 11:27
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    $\begingroup$ @falstro: I do not dispute that the air out of the ACM is hot. But this heat can only be felt when the air flow from the ACM fills the whole cabin instantly. In reality, the flow is just enough to replenish what is leaked away plus some amount for ventilation. Thus, the heat is dissipated in the cabin air, and the big surface area of the cabin cools the whole cabin air down. If the ventilating flow is low, the cabin air becomes really cold, given an outside temperature of -50°C and lower. $\endgroup$ Aug 24 '14 at 9:52
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The air conditioning is in a so called "air cycle machine" (ACM). If it fails, the air will not be compressed (done in the same machine).

Temperature goes up and down as the air passes through the machine's heat exchangers, compressors and turbines, reaching 250$^\circ$C at peak.

Wikipedia article http://www.thisisecs.com

Image from ECS

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    $\begingroup$ For most airplanes the air entering the ACM comes is already hot and compressed from its source. E.g the EMB-145 draws bleed air from the 9th or 14th compressor stages of the engines (or the APU). This is similar in other airplanes, though the particular compressor stages may differ. If the ACM was inop, the resulting cabin temperature should have the same equivalent potential temperature ($\theta_e$) as the ambient atmospheric air. $\endgroup$
    – casey
    May 23 '14 at 20:02
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The exact values depend on the specific aircraft and engine setup, of course, but I'll talk about a 767-300ER with P&W4000 engines at cruise altitude.

The first thing to take in to account is Gay-Lussac's law \begin{equation} \frac{P_1}{T_1}=\frac{P_2}{T_2} \end{equation}

The pressure outside the aircraft @ cruise is around -70°F (~216 K) and 2.9 psi (~20 kPa). The pressure inside the aircraft (we'll talk about the compressing stage in a moment) is around 11.5 psi (~79.3 kPa).

\begin{equation} \frac{20\ kPa}{216\ K}=\frac{79.3\ kPa}{T_2} \end{equation} \begin{equation} T_2 = 856.44\ K (1082°F) \end{equation}

In reality, its a bit more complicated than this, because this assumes that the volume of air is constant, which in this case it is not. In the low-stage compressor, the air is compressed to 30 psi (~206.8 kPa) and 400°F (~477.6 K). That is what is piped through the bleed valve and into the air conditioning units and is most likely what the temperature of the air would be if the bleed valve was closed and the air conditioning units were disabled.

Source (PDF Warning)

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    $\begingroup$ $1082°F\approx583°C$ $\endgroup$ May 22 '14 at 14:18
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    $\begingroup$ This is in the neighborhood of the bleed air from the engine, but it goes through a precooler before being used for things like wing anti-ice or the AC packs. $\endgroup$
    – fooot
    Dec 18 '14 at 22:37
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what nobody is considering here at all is the bleed air is highly compressed when taken from the engine. 400 to 600 degrees Celsius are not uncommon. But, what happens when you expand gases? Yes the opposite than when compressing it, it cools down. So the it would even without cooling get close to a reasonable temperature and, since the plane is not pressurized same level as the bleed air is in the engine before leaving it.

And as somebody mentioned in a comment, "the little air exchanged" in the cabin. In most airliners today the air inside the cabin is completely exchanged every around 3 to 4 minutes, so the airflow is quite considerable.

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  • $\begingroup$ Welcome to the site Björn. Actually before getting to the pack (ACM), the bleed passes through a pre-cooler (heat exchanger) that ensures that a certain temp (typically 200°C) is reached before sending the air to the pack, so it's not really just expansion from 400–600°C. You can improve this post by adding references. - From Review $\endgroup$
    – ymb1
    Nov 7 '21 at 16:18
  • $\begingroup$ Another thing that no one seems to have considered is that the heat in the cabin of an airliner is mostly generated by its human cargo. It's that heat that the A/C system needs to remove, just as it would need to remove the heat from that many humans in a room on the ground. $\endgroup$
    – jamesqf
    Nov 7 '21 at 17:50

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