Find work needed to compress and heat air from -50C, .1bar to 25C, .8 bar

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Homework Statement



It is thought that people develop respiratory infections during air travel because much of the airplane cabin air is recirculated. Airiines claim that using orlly 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 air- plane cabin has a volume of 100 m3 with air at the in- flight 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 Cp; = 30 J/(mol K) and energy costs,$0.2 per kW hr?


Homework Equations


Energy Balance

The Attempt at a Solution


So far I've simply used Q/ΔT=Cp to find the heat. But I'm not sure what to do or what formulas would be applicable from this point.
 
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katieisblonde said:

Homework Statement



It is thought that people develop respiratory infections during air travel because much of the airplane cabin air is recirculated. Airiines claim that using orlly 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 air- plane cabin has a volume of 100 m3 with air at the in- flight 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 Cp; = 30 J/(mol K) and energy costs,$0.2 per kW hr?


Homework Equations


Energy Balance

The Attempt at a Solution


So far I've simply used Q/ΔT=Cp to find the heat. But I'm not sure what to do or what formulas would be applicable from this point.

You've started trying to apply the equations before even figuring out what needs to be done. Ask yourself, "what type of equipment would I need if I have to start out with air at the outside conditions and end up with air at the inside-cabin conditions? Do I need to process the air so that I change its pressure? Do I need to process the air so that I change its temperature? What kind of equipment is used for this?"
 
I think I need to heat at constant pressure, and then isothermally compress. so that would be Q=CpΔT and W=-pdv where you put P in terms of V using ideal gas law. is that a good way to approach this?
 
katieisblonde said:
I think I need to heat at constant pressure, and then isothermally compress. so that would be Q=CpΔT and W=-pdv where you put P in terms of V using ideal gas law. is that a good way to approach this?

No. You did well at identifying the two pieces of equipment needed (a compressor and a heater), but then you started messing with equations again. Before you start messing with the equations, you have to start thinking about the practical aspects of designing this system.

Please don't answer with equations again until you have thought out the practical aspects.

Ask yourself:
Which requires more compressional work (a) heating the gas first and then compressing it or (b) compressing it first and then heating it?

Which requires less equipment, adibatic compression or isothermal compression?

What happens to the temperature of a gas when you compress it adiabatically?

Can you "kill two birds with one stone" by compressing the gas adibatically, rather than isothermally?

After you answer these questions, you will be ready to start using equations.