Answer:
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.