A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 100 and 1600 kPa. The working fluid is air, which enters the compressor at 40°C at a rate of 850 m^3/min and leaves the turbine at 650°C. Using variable specific heats for air and assuming a compressor isentropic efficiency of 85 percent and a turbine isentropic efficiency of 88 percent, determine:
(a) the net power output, (b) the back work ratio, and (c) the thermal efficiency.

(a) The net power output is 6081 kW

(b) The back work ratio is 0.536

(c) The thermal efficiency is 37.4%

Explanation:

Process 1-2 is compression

Obtain the properties from EES software.

Enthalpy is function of Temperature for an ideal gas whereas the entropy is a function of both temperature and pressure.

T₁ = 40°C, P₁ = 100 KPa

Enthalpy, h₁ = 313.6 kJ/kg

Enthropy, S₁ = 5.749 kJ/kg.k

Entropy at state 2, s₂ = s₁ = 5.749 kJ/kg.k

P₂ = 1600 kPa and Entropy s₂ = 5.749 kJ/kg.k

Saturated Enthalpy, = 691.9 kJ/kg

The Compressor efficiency is,

h₂ = 758.6 kJ/kg

Process 3 - 4 is expansion

T₄ = 650°C, specific enthalpy, h₄ = 959.2 kJ/kg

The turbine efficiency is,

Enthalpy cannot be found directly at state 3.

Using the EES software together with isentropic efficiency relation, we find

Temperature, T₃ = 1353°C

Enthalpy, h₃ = 1790 kJ/kg

Entropy, s₃ = 6.75 kJ/kg.k

Note that: h₃ = enthalpy(Air, T=T₃)

                 s₃ = entropy(Air, T=T₃, P=P₂)

                  = enthalpy(Air, P=P₁, s=s₃)

The mass flow rate is determined from

m = P₁V₁ ÷ RT₁

   = (100 kPa) (850 m³/min) ÷ (0.287) (40 + 273)

   = 15.77 kg/s

The work input to the compressor is:

    = (15.77 kg/s) (758.6 kJ/kg - 313.6 kJ/kg)

    = 7017 kW

The work output from the turbine is:

    = (15.77 kg/s) ( 1790 kJ/kg - 959.2 kJ/kg)

    = 13098 kW

(A)  the net power output,

              = 13098 kW - 7017 kW

              = 6081 kW

(B) The back work ratio is

      = 7017 kW / 13098 kW

      = 0.536

(C) The thermal efficiency is

     = 6081 kW ÷ [m(h₃ - h₂)]

     = 6081 kW ÷ [15.77 kg/s (1790 kJ/kg - 758.6 kJ/kg)]

     = 37.4%