Compressed air help (adiabatic processes)

[sikatriz]

Homework Statement

i'm trying to work out how much energy can be extracted from a compressed air system using an adiabatic process. given how small scale the system is(an most likely unrealistic), the values for the energy that can be extracted seem very high from my calculations.

Homework Equations

these equations were taken from wikipedia (hopefully not my first error) http://en.wikipedia.org/wiki/Adiabatic_process#Derivation_of_discrete_formula

(P₂/P₁) = (V₂ / V₁)^-$$\gamma$$

work done = P₁V₁^$$\gamma$$((V₂^1-$$\gamma$$ - V₁^1-$$\gamma$$) / (1 - $$\gamma$$)) (last bit should read 1 minus gamma rather than 1 to the power minus gamma)

The Attempt at a Solution

the volume of the tank is 8.4cc and i want the air to be compressed to 3cc. initial pressure is 1 bar. $$\gamma$$ = 7/5

firstly i used equation 1 to find out the pressure when the air is compressed ie. P₂,

P₁ = 1e5
V₁ = 8.4
V₂ = 3

and found P₂ = 422689 Pa

then to find out how much work can be extracted as the piston is pushed forward i used the second formula using

P₁ = 422689
V₁ = 3
V₂ = 8.4
$$\gamma$$ = 7/5

putting these values into the formula i found a value of ~1MJ for the work done. is this right? if not where am i going wrong? thank you in advance.

 

[Valkarie]

EDIT:i figured out the mistake i made. i had P1 in the first equation as 1 bar which should have been 1e5.