# How hot would pressurized air get if the air conditioning failed?

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.

• 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. – Peter Kämpf May 22 '14 at 19:17
• @PeterKämpf do you have any references to back that claim? It would appear from the answers that it isn't accurate, and pressurizing the air would bring it up to several hundred degrees which is a lot to loose by just piping it into the cabin. – falstro May 23 '14 at 8:05
• @PeterKämpf then why am I always uncomfortably hot when traveling on an airliner? – jwenting May 23 '14 at 10:31
• @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? – falstro May 23 '14 at 17:57
• @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! – Lnafziger May 24 '14 at 11:27

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.

Image from ECS

• 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. – casey May 23 '14 at 20:02

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 $$\frac{P_1}{T_1}=\frac{P_2}{T_2}$$

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).

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

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)

• $1082°F\approx583°C$ – ratchet freak May 22 '14 at 14:18
• 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. – fooot Dec 18 '14 at 22:37