Thermodynamics Miscellaneous
- Air enters a diesel engine with a density of 1.0 kg/m3. The compression ratio is 21. At steady state, the air intake is 30 × 10–3 kg/s and the net work output is 15 kW. The mean effective pressure (kPa) is_____.
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mep = work output swept volume = 12 30 × 10- 3 
1 - 1 
21
= 525 kPaCorrect Option: B
mep = work output swept volume = 12 30 × 10- 3 1 - 1 21
= 525 kPa
- In a compression ignition engine, the inlet air pressure is 1 bar and the pressure at the end of isentropic compression is 32.42 bar. The expansion ratio is 8. Assuming ratio of specific heats (γ) as 1.4, the air standard efficiency (in percent) is
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Compression ratio,
rk= v1 = p2 1/γ v2 p1
= (32.42) 1/1.4 = 11.9999 ≅ 12
cutoff ratio,rk = compression ratio expansion ratio = 12 = 1.5 8
η = 1 - 1 reγ - 1 rcγ - 1 γ(rc - 1) η = 1 - 1 151.4 - 1 120.4 1.4(1.5 - 1)
η = 59.599%.Correct Option: C
Compression ratio,
rk= v1 = p2 1/γ v2 p1
= (32.42) 1/1.4 = 11.9999 ≅ 12
cutoff ratio,rk = compression ratio expansion ratio = 12 = 1.5 8
η = 1 - 1 reγ - 1 rcγ - 1 γ(rc - 1) η = 1 - 1 151.4 - 1 120.4 1.4(1.5 - 1)
η = 59.599%.
- A diesel engine has a compression ratio of 17 and cut-off takes place at 10% of the stroke. Assuming ratio of specific heats (γ) and the air standard efficiency (in%) is –.
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Compression ratio
= 17 = V1 = V1 = 17V2 V2
where ρ = cut-off ratio= V3 V2 
V3 - V2= 10 Vs 100
V3 – V2 = 0.1(V1 – V2)
= 0.1(17V2 – V2)
= 0.1(16V2)
V3 = 1.6V2 + V2
V3 = 2.6V2= V3 = ρ = 2.6 V2 η = 1 - 1 × 
ργ - 1 
γ(r)γ - 1 ρ - 1 = 1 - 1 × 2.61.4 - 1 1.4(17)1.4 - 1 2.6 - 1
= 0.5960 = 59.60%.Correct Option: A
Compression ratio
= 17 = V1 = V1 = 17V2 V2
where ρ = cut-off ratio= V3 V2 V3 - V2= 10 Vs 100
V3 – V2 = 0.1(V1 – V2)
= 0.1(17V2 – V2)
= 0.1(16V2)
V3 = 1.6V2 + V2
V3 = 2.6V2= V3 = ρ = 2.6 V2 η = 1 - 1 × ργ - 1 γ(r)γ - 1 ρ - 1 = 1 - 1 × 2.61.4 - 1 1.4(17)1.4 - 1 2.6 - 1
= 0.5960 = 59.60%.
- In an air-standard Otto cycle, air is supplied at 0.1 MPa and 308 K. The ratio of the specific heats (γ) and the specific gas constant (R) of air are 1.4 and 288.8 J/kgK, respectively. If the compression ratio is 8 and the maximum temperature in the cycle is 2660 K, the heat (in kJ/kg) supplied to the engine is ______.
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Otto cycle
Given: P1 = 0.1 MPa
T1 = 308 K
γ = 1.4
R = 0.2888 kJ/kg.k
T3 = 2660 K
(1-2) Isentropic compression
PVr = constant= T2 = (r)γ - 1 T1
T2 = 308 × 80.4 = 698.40 k
(2-3) Isochoric Heat addition process= Cp = 1.4 Cv
R = 0.2888 kJ/kg
Cp – Cv = 0.2888Cv Cp - 1 = 0.2888 Cv Cv = 0.2888 = 0.722 kJ /kg 1.4 - 1
Qin = Cv (T3 – T2) = 0.722 (2660 – 698.40)
= 1416.27 kJ/kgCorrect Option: C
Otto cycle
Given: P1 = 0.1 MPa
T1 = 308 K
γ = 1.4
R = 0.2888 kJ/kg.k
T3 = 2660 K
(1-2) Isentropic compression
PVr = constant= T2 = (r)γ - 1 T1
T2 = 308 × 80.4 = 698.40 k
(2-3) Isochoric Heat addition process= Cp = 1.4 Cv
R = 0.2888 kJ/kg
Cp – Cv = 0.2888Cv Cp - 1 = 0.2888 Cv Cv = 0.2888 = 0.722 kJ /kg 1.4 - 1
Qin = Cv (T3 – T2) = 0.722 (2660 – 698.40)
= 1416.27 kJ/kg
- The crank radius of a single-cylinder IC engine is 60 mm and the diameter of the cylinder is 80 mm. The swept volume of the cylinder in cm3 is
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Stroke of the cylinder, l = 2r = 2 × 60 = 120 mm
Swept volume = π d2 × l 4 = π 802 × 120 = 603 cm3 4 Correct Option: D
Stroke of the cylinder, l = 2r = 2 × 60 = 120 mm
Swept volume = π d2 × l 4 = π 802 × 120 = 603 cm3 4
