Q. An engine working on the Otto cycle is supplied with air at 0.1 MPa, 35°C. The compression
ratio is 7. The heat supplied is 2500 kJ/kg. Draw the P-V diagram of the Otto cycle. Assuming
Cp=1.005 kJ/kg K, Cv=0.717 kJ/kg K, γ=1.4, and R = 0.287 kJ/kg K, calculate:
(i) the cycle efficiency,
(ii) the maximum pressure and temperature of the cycle,
(iii) the mean effective pressure.
[10 Marks; Test time:15min]
(i) Cycle efficiency
T1= 308 K; P1= 0.1 MPa; r = 7 ; Qs = 2500 kJ/kg
1 mark
1
πππ‘π‘π = 1 − π ϒ−1 ;
πππ‘π‘π = 54%
1 mark
(ii) Maximum pressure and temperature of the cycle
π£1
=7
π£2
π2
π£1 πΎ−1
=( )
= (7)0.4 = 2.17
π1
π£2
π2 = 2.17 × 308 = 670.8 πΎ
ππ = ππ£ (π3 − π2 ) = 2500
π3 − 670.8 =
1 mark
ππ½
ππ
2500
0.717
π3 = ππππ₯ = 3486.7 + 670.8 = ππππ. π π²
π2
π£1 πΎ
= ( ) = (7)1.4 = 15.24
π1
π£2
π2 = 1.524 πππ
π3 π2
=
π3 π2
1 mark
1 mark
π3 = ππππ₯ = 1.524 ×
4157.5
= π. ππ π΄π·π
670.8
1 mark
(iii) Mean effective pressure
ππ =
ππππ‘
(π£1 − π£2 )
πnet = ππ × πππ‘π‘π = 2500 × 0.54 = 1350
ππ½
ππ
1 mark
π£1 =
π
π1 0.287 × 308
3
=
= 0.883 π ⁄ππ
π1
100
π£2 =
0.883
3
= 0.126 π ⁄ππ
7
πm =
1350
= 1783 πππ = π. πππ π΄π·π
(0.883 − 0.126)
1 mark
1 mark
1 mark