Homework Help: Problem Involving a 2 stroke IC engine

1. Nov 21, 2013

slasakai

1. The problem statement, all variables and given/known data

A two-stroke internal combustion engine can be modelled by the following cycle. The cycle starts with the piston chamber at maximum volume V1 = 1000 cm3, filled with an air-fuel mixture – which we treat as an ideal gas – at atmospheric pressure and room temperature (p1 = 101 kPa; T1 = 20.0 °C). The air is then adiabatically compressed into a volume V2 = 140 cm3. At this point the fuel is ignited, causing a rapid heating of the gas at constant volume, followed by an adiabatic expansion to the original volume of the piston chamber. Finally, the hot exhaust gases are vented and replaced by air-fuel mixture at room temperature and atmospheric pressure with the piston chamber at maximum volume, as before.
The air-fuel mixture taken into the piston chamber in each cycle contains 5.00 mg of a particular biofuel. Determine the efficiency of the engine by calculating the work done in each separate stage of the cycle.
[Air has a molar heat capacity at constant volume CV = 20.8 J mol-1 K-1. The energy liberated per unit mass on burning the biofuel is 30.0 MJ kg-1.]
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b]2. Relevant equations[/b]

(1) TV^(γ-1)=constant , (2) Work Done(adiabatic expansion)= nCv(T1-T2)

3. The attempt at a solution

my approach was to use the first equation to to work out the temparature after the first compression and then calculate work done with eq2. I got the answer of T2=643 k appx, and work done as -302 J (appx) , I repeated a similar calculation for the expansion. I am unsure of whether or not this is the correct approach to use in this situation. My ultimate answer was e=0.213 for efficieny and this seems to be about correct. Can anyone please help me to see whether my approach to this problem was correct?