A simple ideal Rankine cycle with water as the working fluid

A simple ideal Rankine cycle with water as the working fluid operates the boiler at 2, 500 psia and the condenser at 5 psia. What is the minimum temperature required at the turbine inlet such that the quality of the steam leaving the turbine is not below 80 percent. When operated at this temperature, what is the thermal efficiency of this cycle? T_3 = degree F n_th =

Solution

At 5 psia and 80% quality : Enthalpy h₄ = 930.615 Btu/lb and Entropy s₄ = 1.52206 Btu/lb-⁰F

In case of ideal rankine cycle, s₃ = s₄ i.e. entropy at the inlet and exit of steam turbine are equal.

At 2500 psia, saturated vapor entropy = 1.23293 Btu/lb-⁰F, but s₃ is higher than this value. So, it is superheated.

Saturation temperature = 668.17 ⁰F.

By iteration and interpolation in the superheated table, we get T₃ = 989.22 ⁰F. and h₃ = 1450.81 Btu/lb

Enthalpy of water at the inlet of feed pump, h₁ = 130.184 Btu/lb

Neglect the pump work.

Thermal Efficiency = Work done by the turbine per unit mass flow rate/ Heat addition in the boiler per unit mass flow rate

= (h₃ - h₄)/(h₃ - h₁) x 100%

= (1450.81 - 930.615)/(1450.81 - 130.184) x 100%

= 39.39% or 39.4%