The pressure and temperature at the beginning of compression of an air-standard Diesel cycle are 95 kPa and 300 K, respectively. At the end of the heat addition, the pressure is 7.2 MPa and the temperature is 2150 K. Determine (a) the compression ratio (b) the cutoff ratio (c) the thermal efficiency of the cycle (d) the mean effective pressure in kPa Assume perfect gas, use u=cv*T, h=Cp*T, isentropic equations, ideal gas equations where required. CV = 0.7 kJ/kg/K, Cp = 1 kJ/kg/K, k = 1.4 for air.

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Answer 1

a) the compression ratio ( r )=23.19

b) the cutoff ratio ( rc )=2.19

c) the thermal efficiency of the cycle ( nth )=0.597 ( 59.7%)

d) the mean effective pressure, mep=975 KPa

What is the explanation?

We shall ascertain the working fluid's (Air) characteristics at each state value.

To assist us, we will consult the air standard property tables (A-22) and note the following:

State 1:

P1 equals 95 KPa, and T1 is 300 K.

vr1 = 621.2, Pr1 = 1.386, and u1 = 214.07 KJ/kg.

- We calculate the lowered pressure value at state 2 using relations for isentropic compression:

State 2:

P2 = P3 = 7200 KPa

h2 = 1022.82 KJ/kg, vr2 = 26.793, and T2 = 979.6 K.

State3

- Using isentropic expansion relations, we calculate the decreased volume.

P3 = 7200 KPa , T3 = 2150 K

h3 = 2440.3 KJ/kg , vr3 = 2.175 , Pr1 = 1.386

state 4:

T4 = 1031 K ,  u4 = 785.75 KJ/kg

a) the compression ratio ( r )=23.19

b) the cutoff ratio ( rc )=2.19

c) the thermal efficiency of the cycle ( nth )=0.597 ( 59.7%)

d) the mean effective pressure, mep=975 KPa

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