The figure shows the diesel cycle. It is similar to the Otto cycle, but there ar

Question

The figure shows the diesel cycle. It is similar to the Otto cycle, but there are two important differences. First, the fuel is

not admitted until the air is fully compressed at point 2. Because of the high temperature at the end of an adiabatic compression, the

fuel begins to burn spontaneously. (There are no spark plugs in a diesel engine) Second, combustion takes place more slowly, with

fuel continuing to be injected. This makes the ignition stage a constant-pressure process. The cycle shown, for one cylinder of a

diesel engine, has a displacement (V_max - V_min) of 1000 cm^3 and a compression ratio r = (V_max/V_min) = 21. These are

typical values for a diesel truck. The engine operates with intake air (gamma = 1.4) at 25 degrees Celcius and 1.0 atm pressure. The

quantity of fuel injected into the cylinder has a heat of combustion of 1000 J.

a) What are p, V, and T at each corner of the cycle?

b) What is the net work done by the cylinder during one full

cycle?

c) What is the thermal efficiency of this engine?

d) What is the power output in kW and horsepower (1 hp = 746 W) of

an eight cylinder diesel engine running at 2400 rpm?

Please give detailed explanations, showing each step. Thank you...

Explanation / Answer

V1-V2=100 V1/V2=21 V1=1050 V2=50 STATE 1 V1=1050 P1=1 atm T1=298 K STATE 2 v2=50 P1V1^1.4=P2V2^1.4 P2=70.97 atm (T1/T2)^1.4/1-1.4)=P2/P1 T2=1007.43 K STATE 3 Q=Cp(T3-T2) 1000*10^3=1005(T3-T2) T3=2002.45K P3=P2=70.97 atm V2/T2=V3/T3 V3=99.38 STATE 4 V4=V1=1050 V4/V3=10.56 P3V3^1.4=P4V4^1.4 P4=2.61atm P1/T1=P4/T4 1/298=2.61/T4 T4=779.83 b)W(net)=Q1-Q2=1000-Cp(T4-T1)=1000-1005(779.83-298)=515.75 KJ/Kg c)effeciency=Q1-Q2/Q1=610.96/1000=51.57% D)power o/p=610.96*8=4126.06 KW=5530.91 hp

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