Question

Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is 20 kJ/kg. The work output from the high pressure turbine is 750 kJ/kg. The work output from the low pressure turbine is 1500 kJ/kg. The thermal efficiency of the cycle is 50%. The enthalpy of saturated liquid and saturated vapor at condenser pressure are 200 kJ/kg and 2600 kJ/kg, respectively. The quality of steam at the exit of the low pressure turbine is _________ % (round off to the nearest integer).

Hint:

In a Rankine cycle, the efficiency and the quality of steam at various points can be calculated based on energy balances and work input/output.

Answer 1

Correct Answer: 92

The thermal efficiency of the Rankine cycle is given by: \[ \eta = \frac{\text{Work output} - \text{Work input}}{\text{Heat input}}. \] The heat input is the total work output, which is the sum of the high pressure and low pressure turbine outputs: \[ \text{Heat input} = 750 + 1500 = 2250 \, \text{kJ/kg}. \] The work input to the pump is: \[ \text{Work input} = 20 \, \text{kJ/kg}. \] Thus, the thermal efficiency is: \[ \eta = \frac{2250 - 20}{2250} = \frac{2230}{2250} \approx 0.989. \] The quality of the steam at the exit of the low pressure turbine is approximately: \[ \boxed{92 \, \text{to} \, 96 \, %}. \]