An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and 27 degree Celsius. (a) Determine the temperature after the heat-addition process.
(b) Determine the thermal efficiency.
(c) Determine the mean effective pressure. Solve the problem in the constant heat supposition.

a) T₃ = 1818.8 K

b) η = 0.614 = 61.4%

c) MEP = 660.4 kPa

Explanation:

a) According to Table A-2 of The ideal gas specific heat of gases, the properties of air are as following:

At 300K

The specific heat capacity at constant pressure = = 1.005 kJ/kg.K,

The specific heat capacity at constant volume = = 0.718 kJ/kg.K

Gas constant R for air = 0.2870 kJ/kg·K

Ratio of specific heat  k = 1.4

Isentropic Compression :

=    

   = 300K ()

   = 909.4K

P = Constant heat Addition:

2 = 2(909.4K)

      = 1818.8 K

b) =

         =   ( - )

         = (1.005 kJ/kg.K)(1818.8 - 909.4)K

         = 913.9 kJ/kg

Isentropic Expansion:

=    

    =  

    = 1818.8 K (2 / 16

    = 791.7K

v = Constant heat rejection

= μ₄ - μ₁

      =

      = 0.718 kJ/kg.K (791.7 - 300)K

      = 353 kJ/kg

 η = 1 - /

       = 1 - 353 kJ/kg / 913.9 kJ/kg

       = 1 - 0.38625670

       = 0.6137

       = 0.614

      = 61.4%

c) = -

                = 913.9 kJ/kg - 353 kJ/kg

                = 560.9 kJ/kg

   = (0.287 kPa.m³/kg/K)*(300 K) / 95 kPa

   =  86.1 / 95

   = 0.9063 m³/kg = v

Mean Effective Pressure = MEP =  

                                                    =

                                                    = 560.9 kJ/kg / (0.9063 m³/kg)*(1-1)/16

                                                    = (560.9 kJ / 0.8493m³) (kPa.m³/kJ)

                                                    = 660.426 kPa

Mean Effective Pressure = MEP = 660.4 kPa

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