26 HANDBOOK OF ELECTRICAL ENGINEERING
Where,Cp is the specific heat of the air at constant pressure, kcal/kg K 1. 005
Cv is the specific heat of the air at constant volume, kcal/kg K 0. 718
R is the particular gas constant for air, kJ/kg K 0. 287
γ is the ratio of specific heats 1. 4
From (2.3) and (2.7),
γ
γ− 1
=
Cp
R( 2. 8 )
Substitute (2.4, 2.5 and 2.8) into (2.1),
Uc=Cp(T 2 −T 1 )kJ/kg ( 2. 9 )The air leaving the compressor at pressureP 2 passes into the combustion chamber where its
temperature is raised toT 3 , at constant pressure.
The hot air–fuel mixture burns and the gaseous products of combustion pass into the turbine
where the pressure falls to the atmospheric pressureP 4 =P 1 (in practice slightly higher due to the
resistance or ‘back pressure’ of the exhaust silencer and ducting). The exhaust gas temperature is
T 4 and is lower than the combustion temperatureT 3. (The ducting systems should be arranged so
that the exhaust gas is discharged at a point far enough away from the inlet ducting entrance that no
interaction occurs i.e.T 4 does not influenceT 1 .)
The turbine expansion process can be described by similar equations to (2.1) through (2.7),
withT 3 replacingT 2 andT 4 replacingT 1. Hence the work done by the turbine (Ut)is,
Ut=Cp(T 3 −T 4 )kJ/kg ( 2. 10 )The heat supplied by the fuel isCp(T 3 −T 2 ).
In a conventional gas turbine the turbine supplies power to drive its compressor and so the
power available to drive a generator is the net power available from the turbine. Neglecting ineffi-
ciencies in the compressor and the turbine, the work done on the generator at the coupling of the gas
turbine isUout,
Uout=Ut−Uc=Cp(T 3 −T 4 −T 2 +T 1 )kJ/kg ( 2. 11 )The ideal cycle efficiencyηiof the gas turbine is:
ηi=Cp(T 3 −T 4 −T 2 +T 1 )
Cp(T 3 −T 2 )= 1 −
(
T 4 −T 1
T 3 −T 2
)
= 1 −
Rejection temperature difference
Combustion temperature difference(2.12)
From (2.1), raise to the powerγ, (
P 2 V 2
T 2
)γ
=(
P 1 V 1
T 1
)γ
( 2. 13 )