⦁ A gas-turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 300 K at the compressor inlet and 1400 K at the turbine inlet. Utilizing the air-standard assumptions, determine (a) the gas temperature at the exits of the compressor and the turbine, (b) the back work ratio, and (c) the thermal efficiency.

The value of temperature at compressor outlet = 543.43 K

The temperature at turbine outlet = 773.04 K

Back work ratio = 0.388

The value of efficiency of the Ideal Brayton cycle =0.448

Explanation:

Pressure ratio ()= 8 And specific heat ratio () = 1.4

Compressor inlet temperature () = 300 K

Turbine inlet temperature () = 1400 K

(a). Temperature ratio inside the compressor is given by

                  =

Where & represents the compressor inlet and outlet temperature.

Put all the values in the given formula  we get

⇒ =

⇒ = 1.811

⇒ = 543.43 K

This is the value of temperature at compressor outlet.

The temperature ratio inside the turbine is given by

        =

Where & represents the turbine inlet & outlet temperatures.

Put all the values in the given formula we get

⇒ =

⇒ = 773.05 K

This is the temperature at turbine outlet.

(b). The work done by the turbine is given by the formula () = ( - )

Put all the values in the above formula we get = 1.005 × (1400 - 773.05)

                                                                            = 630.08

And work done inside the pump is given by = ( - )

Put all the values in the above formula we get = 1.005 × (543.43 - 300)

                                                                            = 244.65

Back work ratio is given by =

Put the values of & in above formula we get

⇒ =

⇒ = 0.388

This is the value of back work ratio.

(C). Thermal Efficiency is given by  E = 1 -

⇒ E = 1 -

⇒ E = 0.448

This is the value of efficiency of the Ideal Brayton cycle.