Compressed Air Car: Is My Thermodynamics Calculation Correct?

[jamesasteven]

Background:

This is my first post here on physics forums. I have perused for quite a while. I am a Chem Eng. student at University of Houston and this question is from my Thermodynamics class. I have enjoyed working on this problem (for hours) but am certain i have made a mistake,

Question:

A compressed air car has several advantages over conventional vehicles -it has zero emissions, refueling can be done at home and there are no hazardous chemicals to deal with. The engine relies on the expansion of compressed air from a tank to provide power. According to a magazine article a car can achieve 68 mph with a range of 125 miles. It will take only a few minutes to refuel using a custom air compressor. It should cost $2 to fill the cars carbon fiber tanks with 340 liters or air at 4350 psi.

A) Obtain the maximum amount of work that can be obtained from the compressed air tank with the volume and pressure stated above. What is the effective mileage of this engine (miles per gallon of gasoline equivalent)? One gallon of gasoline provides 130MJ of energy when burned.

B) Calculate the power required to run the custom compressor unit mentioned, in order to allow refilling of the tank in 5 min. What is the cost of electricity (in $/kWh) given the $2 cost estimate for refilling.

My full attempt is attached. Any advice would be much appreciated.

 

[mfb]

(A) looks good.

(B): 1.09J/s is certainly not right, and I don't see how you "converted" this to kWh (a unit of energy, not a unit of power). The first Power= has inconsistent units or missing brackets.
In addition, please try to avoid mixing text and formulas. Define some variable (like P) as power, and use the variable afterwards instead of "power=".

 

[rude man]

Max work out = work in. So if the compression is done isothermally your answer is OK.

But if the compression is done adiabatically the work to compress would be greater due to the increase in temperature & therefore internal energy, so the theoretical max available work output would presumably also be greater, although I don't know how the added internal energy could be harnessed to provide extra mechanical energy.

 

[jamesasteven]

Thank you for your replies. I have still been working on part B and will post an updated solution.