A steam turbine receives steam at 15 bar, 350°C [h = 3147.5 kJ/kg, s = 7.100 kJ/kg-K] and exhaust to the condenser at 0.06 bar. [ $h_{f}$ = 151.5 kJ/kg, $h_{f g}$ = 2416.0 kJ/kg, $s_{f}$ = 0.520 kJ/kg-K, $s_{f g}$ = 7.800 kJ/kg-K] What will be the approximate thermal efficiency of ideal Rankine cycle operating between these two limits? [Neglect the pump work

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SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

For an ideal Rankine cycle (neglecting pump work), thermal efficiency is given by:

$ \eta = \frac{h_1 - h_2}{h_1 - h_f} $

Given:

Step 1: Find dryness fraction at turbine exit

$ s_2 = s_1 = s_f + x \cdot s_{fg} \Rightarrow x = \frac{7.1 - 0.520}{7.8} = 0.8436 $

Step 2: Find $ h_2 $

$ h_2 = h_f + x \cdot h_{fg} = 151.5 + 0.8436 \cdot 2416.0 = 2190.1~\text{kJ/kg} $

Step 3: Thermal efficiency

$ \eta = \frac{3147.5 - 2190.1}{3147.5 - 151.5} = \frac{957.4}{2996} = 0.3197 = {31.97\%} $