In a gas turbine, the working substance can usually be approximated to behave like an ideal gas. The pressure and temperature at the inlet of the turbine are p1 and T1, and at the outlet, the pressure has dropped to p2.

 

a) Find the expression for the final temperature of the gas, T2, at the turbine outlet when the isentropic efficiency is assumed to be ηT. The expression for the final temperature should depend on the initial temperature, T1, the isentropic efficiency ηT, and the ratio of initial and final pressures, p2/p1.

 

b) Let the pressure ratio of the gas turbine be p1/p2 = 15 and the inlet temperature be 1200°C. The working substance is air with a molar mass of M = 29 g/mol, and its isobaric specific heat capacity can be assumed to be cp = 1.15 kJ/kg/K. If the isentropic efficiency of the turbine is ηT = 0.8, at what temperature does the gas exit the turbine? 

 

Utilize the fundamental relation dh = T ds + vdp, the ideal gas state equation pV = nRT, and the definition of isobaric specific heat capacity. Remember that the enthalpy of an ideal gas is directly proportional to temperature. 

 

From part b), it is known that 600°C ≤ T2 ≤ 650°C.