Question

A gasoline engine operates on the air standard Otto cycle. The air intake to the engine is at 300K and 95kPa (State 1). The air is compressed in the engine to an unknown pressure. Heat is then added during combustion at an amount of 1100 kJ/kg. At the end of the heat addition process, the temperature reaches 2200K. Compute the following: (a) the temperature at the end of the compression process, (b) the volumetric compression ratio of this engine, (c) the amount of work done during the compression process per kg of air, (d) the temperature at the end of the expansion process, (e) the net work of the cycle per kg of air, and (f) the cycle thermal efficiency. Assume air to be an ideal gas with constant specific heats [Cpo=1.004 kJ/(kg K) and Cy..=0.717 kJ/(kg K)]. Also, assume that the compression and expansion processes are isentropic. (5 points)

Answer 1

T1 = 300 K

P1 = 95 kPa

Q2-3 = 1100 kJ/kg

T3 = 2200 K

Q2-3 = Cv (T3 - T2)

1100 = 0.717 (2200 - T2)

T2 = 665.8298 K

Isentropic compression 1 - 2

P2/P1 = (T2/T1)k/k-1

P2/95 = (665.8298 / 300)1.4/1.4-1

P2 = 1547.2857 kPa

V1/V2 = (T2/T1)1/k-1

V1/V2 = (665.8298 / 300)1/1.4-1

V1/V2 = 7.33846

W1-2 = Cp (T2 - T1)

W1-2 = 1.004 (665.8298 - 300)

W1-2 = 367.2931 kJ/kg

Isentropic Expansion 3-4

V4/V3 = (T3/T4)1/k-1

7.33846 = (2200 / T4)1/1.4-1

7.338460.4 = 2200 / T4

T4 = 991.2443 K

Wnet = W3-4 - W1-2

Wnet = Cp (T3 - T4) - 367.2931

Wnet = 1.004 (2200 - 991.2443) - 367.2931

Wnet = 846.2976 kJ/kg

Eff.th = Wnet / Q2-3

Eff.th = 846.2976 / 1100

Eff.th = 0.76936 or 76.936%

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