Mechanical Engineering > GATE 2022 SET-1 > Otto Cycle
An engine running on an air standard Otto cycle has a displacement volume 250 cm³ and a clearance volume 35.7 cm³. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg.. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).

Correct : 4500

Given:
Displacement volume Vd = 250 cm³
Clearance volume Vc = 35.7 cm³
P1 = 100 kPa, T1 = 300 K
Qin = 800 kJ/kg, Cv = 0.718 kJ/kg.K, γ = 1.4
Compression Ratio (r):
V1 = Vd + Vc = 250 + 35.7 = 285.7 cm³
V2 = Vc = 35.7 cm³
r = V1 ÷ V2 = 285.7 ÷ 35.7 = 8.0

Temperature after isentropic compression (T2):
T2 = T1 × rγ−1
T2 = 300 × (8)0.4
(8)0.4 = 2.2974
T2 = 300 × 2.2974 = 689.2 K
Pressure after isentropic compression (P2):
P2 = P1 × rγ
P2 = 100 × (8)1.4
(8)1.4 = 18.379
P2 = 100 × 18.379 = 1837.9 kPa
Temperature after constant volume heat addition (T3):
Qin = Cv × (T3 − T2)
800 = 0.718 × (T3 − 689.2)
T3 − 689.2 = 800 ÷ 0.718 = 1114.2
T3 = 689.2 + 1114.2 = 1803.4 K

Maximum Pressure (P3):
Since heat addition is at constant volume, V2 = V3
P3 ÷ P2 = T3 ÷ T2
P3 = P2 × (T3 ÷ T2)
P3 = 1837.9 × (1803.4 ÷ 689.2)
P3 = 1837.9 × 2.616
P3 = ≈ 4500 kPa
∴ The maximum pressure in the cycle = 4500 kPa

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