Question 6.12: Problem: Air enters an adiabatic turbine at 6 MPa and 500 °C...
Problem: Air enters an adiabatic turbine at 6 MPa and 500 °C and leaves at 100 kPa with a flow rate of 2 kg / s. Determine the maximum possible power output from the turbine.
Find: Maximum power output \dot{W} .
Known: Mass flow rate m = 2 kg / s, inlet pressure P_1 = 6 MPa, inlet temperature T_1 = 500 °C = 773.15 K, outlet pressure P_2 = 100 kPa.
Assumptions: Air is an ideal gas with constant specific heats, the turbine is isentropic, changes in kinetic and potential energy are negligible.
Governing Equations:
Work output from a turbine \dot{W} _{shaft} = \dot{m} (h_2 – h_1)=\dot{m} c_p (T_2 – T_1)
Isentropic process (ideal gas, \frac{T_2}{T_1} =\left\lgroup\frac{P_2}{P_1} \right\rgroup ^{(\gamma -1) / \gamma }
constant specific heats)
Properties: Air at 773.15 K (interpolation) has specific heat c_p = 1.093 (Appendix 4), specific heat ratio of air at 773.15 K (interpolation) \gamma =1.357 (Appendix 4).
T_2=T_1\left\lgroup\frac{P_2}{P_1} \right\rgroup ^{(\gamma -1)/\gamma } = 773.15 \ K\left\lgroup\frac{100 \times 10^3 \ Pa}{6 \times 10^6 Pa} \right\rgroup ^{\frac{1.357-1}{1.357} }=263.3 \ K
\dot{W} _{shaft}=\dot{m} c_p(T_2 – T_1)=2 \ kg/s \times 1.093 \ kJ/kgK (263.3 \ K – 773.15 \ K)=-1115 \ kW
Answer: The maximum power output is 1.1 MW.