Q1 Steam turbine cycles A steam turbine operates on a basic

Q.1 Steam turbine cycles A steam turbine operates on a basic Rankine cycle with a maximum pressure of 20 bar and a condenser pressure of 0.5 bar. Evaluate the thermal efficiency of the plant. Calculate the maximum net work available from the cycle, and evaluate the rational efficiency of the cycle. Solution The T-s diagram for the Rankine cycle is shown in Fig 4.4. The parameters for the state points on cycle 1-2-3-4-6-1 will now be evaluated. Conditions at 4 20 bar, x-1 t, 212.4°Cs h,- 2799 J/kg; s,-6.340 kl/kg K Conditions at 6 pe 0.5 bar, so 6.340 kJ/kg K t, -81.3 C h,-2645 /kg; hr-340 kl/kg s,-7.593 J/kg K; sr-1.091 kJ/kg K Thus 6.340-1.091 0.8073 7.593-1.091 he-xh,+(i-x) hr -0.8073x2645 (i -0.8073 x340-2200.8 kl/kg 72 Rational efficiency of a powerplant Ta-20 Entropy S Fig. 4.4 Temperature-entropy diagram for a basic Rankine cycle Conditions at pi -0.5 bar, s 1.091 k/kg K: hi -340 J/kg vi vy 0.001029 m\'/kg Conditions at 2 v2-0001157+0.2 x (-0.0009x 10-2) 0.001155 m\'/kg Hence feed pump work, v dp dh (0.001029 +0.001155)/2 x 19.5 x 100- 2.11 kl/kg 340+2.11 342.1 kl/kg Work done by turbine, wT 2799- 2200.8 598.2 k/kg K Thermal efficiency of the cycle is

Solution

The specific volume at an entropy of 1.091 kJ/kgK is obtained from

the compressed water table at 20 bar by interpolation

The equation is just an outcome of an interpolation formula where the specific volume is found out by interpolating between two entropy range of values