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/kg-K) |
ρ (kg/m3) |
Cp0(kJ/kg-K) |
Cv0(kJ/kg-K) |
|
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.
