Air enters the compressor of a gas-turbine engine at 300 k and 100 kpa, where it is compressed to 700 kpa and 580 k. heat is transferredto air in the amount of 950 kj/kgbefore it enters the turbine. for a turbine efficiency of 86 percent, determine (a) the fraction of the turbine work output used to drive the compressor and (b) the thermal efficiency. assume variable specific heats for air.

- the fraction of the turbine work output used to drive the compressor is 50%

- the thermal efficiency is 29.6%

Explanation:

given information:

= 300 k

= 700 kPa

= 580 K

Qin = 950 kj/kg

efficiency, η = 86%  = 0.86

Assume, Ideal gas specific heat capacities of air, = 1.005

k = 1.4

(a) the fraction of the turbine work output used to drive the compressor

Qin = ( - )

- = Qin /

= Qin / +

thus,

= = 1525 K

= \

 =

so,

= \

= \

                        = 1525 K  

                        = 875 K

= ( - )

                          = 1.005 kj/kgK  (580 K - 300 K)

                          = 281.4 kJ/kg

= η ( - )

                            = 0.86 (1.005 kj/kgK) (1525 k - 875 K)

                            = 562.2 kJ/kg

therefore,

the fraction of turbine =

                                     =

                                     = 50%

(b) the thermal efficiency

η = ΔW/

  = ( - )/

  = /950

  = 29.6%

this means that the temperature of both substances will be equal

true tan speed = ang vel x radius