Problem Involving a 2 stroke IC engine

[slasakai]

Homework Statement

A two-stroke internal combustion engine can be modeled 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.]
[
b]2. Homework Equations [/b]

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

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?

 

[mark726]

Your approach seems mostly correct, however there are a few things to note:

1. When using the first equation, you need to use the initial and final volumes and temperatures, not just the initial and final volumes. This is because the equation is a combination of the ideal gas law and the first law of thermodynamics, which takes into account changes in both temperature and volume.

2. In the work done equation, you need to use the molar heat capacity at constant volume, not the specific heat capacity. This is because the ideal gas law uses moles, not mass, as the unit of measurement. You can convert from mass to moles using the molar mass of the biofuel.

3. When calculating the work done during the adiabatic expansion, you need to use the final temperature (which is the initial temperature after the compression) and the initial temperature (which is the final temperature after the combustion).

By taking into account these factors, you should be able to get a more accurate result for the efficiency of the engine. Keep in mind that there may also be some slight discrepancies due to rounding errors or assumptions made in the model.

I hope this helps and good luck with your calculations!