Net work_cp(T-TD)-(Ta-Ta). Heat in (7- (-0)1、(T4-1) T(T/7-1) (A3.1) To proceed further, we need to examine the relationships between the different temperatures. We know that points a and d are on a constant pressure process as are points b and c, and Pa=Pd; P=P. The other two legs of the cycle are adiabatic and reversible, so Pa P /)- y P T T Therefore -=-,or, finally,=. Using this relation in the expression for thermal T efficiency, Eq (A1.3) yields an expression for the thermal efficiency of a Brayton cycle Ideal Brayton cycle efficiency: nB=1-A (A3.2) Th pressor exit The temperature ratio across the compressor, Tb/Ta=TR. In terms of compressor temperature ratio, and using the relation for an adiabatic reversible process we can write the efficiency in terms of the compressor(and cycle) pressure ratio, which is the parameter commonly used y-1)/y (A.33) R Figure A-6 shows pressures and temperatures through a gas turbine engine(the afterburning J57 which powers the F-8 and the F-101) AFTERBURNING MILITARY TURBOJET TYPICAL SEA LEVEL STATIC INTERNAL PRESSURES AND TEMPERATURES DATA FOR PRATT WHITNEY J57"B" SERIES AXIMUM AFTERBURNERJ ITITTTT STATION 2 pt(psia)14.7 540167.0158036.0 °F)59 330660 15701013 2540 Figure A-6: Gas turbine engine pressures and temperatures1A-7 η = = [ ] ( ) − − − ( ) [ ] − Net work Heat in cTT T T cT T pc b d a pc b = − ( ) − ( ) − = − ( ) − ( ) − 1 1 1 1 T T T T TT T TT T d a c b a d a bc b / / . (A.3.1) To proceed further, we need to examine the relationships between the different temperatures. We know that points a and d are on a constant pressure process as are points b and c, and PPPP a = = d b c ; . The other two legs of the cycle are adiabatic and reversible, so P P P P T T T T d c a b d c a b = ==       =       ( ) − ( ) − > γ γ / 1 γ γ / 1 . Therefore T T T T d c a b = , or, finally, T T T T d a c b = . Using this relation in the expression for thermal efficiency, Eq. (A.1.3) yields an expression for the thermal efficiency of a Brayton cycle: Ideal Brayton cycle efficiency:η B a b T T = −1 (A.3.2) = −1 T T atmospheric compressor exit . The temperature ratio across the compressor, T T TR b a / = . In terms of compressor temperature ratio, and using the relation for an adiabatic reversible process we can write the efficiency in terms of the compressor (and cycle) pressure ratio, which is the parameter commonly used: η B γ γ TR PR =− =− ( )( ) − 1 1 1 1 1 / . (A.3.3) Figure A-6 shows pressures and temperatures through a gas turbine engine (the afterburning J57, which powers the F-8 and the F-101). Figure A-6: Gas turbine engine pressures and temperatures