Thermodynamics (refreshing air in airplane cabin)

[racnna]

It is thought that people develop respiratory infections during air travel because much of the airplane cabin air is recirculated. Airiines claim that using only fresh air in the cabins is too costly since at an altitude of 30 000 feet the outside conditions are -50°C and 0.1 bar, so that the air would have to be compressed and heated before being introduced into the cabin. The airplane cabin has a volume of 100 $$m^3$$ with air at the inflight conditions of 25°C and 0.8 bar. What would be the cost of completely refreshing the air every minute
if air has a heat capacity of C; = 30 J/(mol K) and energy costs, $0.2 per kW hr?

Im using the energy balance
$$\frac{dU}{dt}=\frac{dN}{dt} H +Q +W$$
i have done the derivation but the expression is complicated so i wanted to see what you guys come up with

 

[Mech_Engineer]

Have you looked at a T-S diagram for Air and the isentropic gas relations? I would model the pressure change first as an isentropic compression, and then if after compression the air needs some additional heating you can take care of that with Isentropic Ideal Gas Relations

You many be able to get some of what you need out of the NIST website:
http://webbook.nist.gov/chemistry/fluid/

Isentropic gas relations:
http://en.wikipedia.org/wiki/Isentropic_process#Table_of_isentropic_relations_for_an_ideal_gas

 

[etudiant]

Compressing the air back to close to 1 bar is painfully expensive. It requires so much energy that the air heats up more than what is desired. Moreover, the heated air is super dry, so it is minimally moisturized for passenger comfort.
Airplanes do it by stealing some of the compressor air from the jet engines, at a real sacrifice in efficiency. You need to process 8000 cubic meters of intake air every air change in your example.