A gasoline engine has a piston/cylinder with 0.1 kg air at 4 MPa, 1527°C after combustion, and this is expanded in a polytropic process with n = 1.5 to a volume 10 times larger. Find the expansion work and heat transfer using the heat capacity value in Table A.5.
TABLE A.5
Properties of Various Ideal Gases at 25°C, 100 kPa*(SI Units)
Gas 
ChemicalFormula 
Molecular Mass(kg/kmol) 
R(kJ/kgK) 
ρ (kg/m3) 
Cp0(kJ/kgK) 
Cv0(kJ/kgK) 

Steam 
H2O 
18.015 
0.4615 
0.0231 
1.872 
1.410 
1.327 
Acetylene 
C2H2 
26.038 
0.3193 
1.05 
1.699 
1.380 
1.231 
Air 
— 
28.97 
0.287 
1.169 
1.004 
0.717 
1.400 
Ammonia 
NH3 
17.031 
0.4882 
0.694 
2.130 
1.642 
1.297 
Argon 
Ar 
39.948 
0.2081 
1.613 
0.520 
0.312 
1.667 
Butane 
C4H10 
58.124 
0.1430 
2.407 
1.716 
1.573 
1.091 
Carton dioxide 
CO2 
44.01 
0.1889 
1.775 
0.842 
0.653 
1.289 
Carton monoxide 
CO 
28.01 
0.2968 
1.13 
1.041 
0.744 
1.399 
Ethane 
C2H6 
30.07 
0.2765 
1.222 
1.766 
Solution 156HP
Step 1 of 3</p>
We are required to calculate the expansion work and heat transfer during the given process.
Step 2 of 3</p>
The mass of air in the cylinder is kg
The given process is polytropic and the value of is 1.5.
The initial specific volume is
The final specific volume is
The initial pressure is MPa
kPa
Let the final pressure be .
In a polytropic process,
constant
Thus,
kPa
The work done in a polytropic process is,
, where and are initial and final temperatures.
C = 1800 K
From the ideal gas equation, ,
and
Therefore,
K
Substitute and values in
J [R for air is (8.314/ air molar mass= 28.97 g/mol)]
kJ
Therefore, the work done is 70.6 kJ.