The combustion process in a diesel engine may be modeled as

The combustion process in a diesel engine may be modeled as an isobaric heat addition process. The cylinder contents may be approximated as van der Walls gas. The temperature and total volume of the engine cylinder before combustion are 950 K and 75 cm^3, while total volume after combustion is 150 cm3. If for every 22 kg of air 1 kg of diesel fuel is used for combustion, determine the work done by the engine.

Solution

Given T₁ = 950K ;V₁ = 75 cm3

V₁ = 150 cm3

Air Fuel ratio = 22:1 ; calorific value of diesel is 44800 kJ/kg

r =1.4 ;R = 8.314 KJ/KgK

For adiabatic process

T₁V₁^r-1 =T₂ V₂^r-1

so by solving   
T₂ = 1253.5 K

now work done is
  
W = nR( T₁-T₂ )/(r-1)

W =(8.314)(950-1253.5)/(1.4-1)

W = -6308.24 J/Kg

W = -6.308 KJ/Kg

so,
Total work done by engine = engergy by fuel + work by piston cylinder
  
= 44800 +(-6.308)
  
= 44793.7 KJ/Kg