For a simple ideal Rankine cycle, which uses water as the working fluid, the work produced by the turbine is 962.37 kJ/kg and heat supplied in the boiler is 2,568.32 kJ/kg . The condenser operates at 8 kPa and its boiler operates at 8,614 kPa. Use v1 = 0.001008 m3/kg in your calculations.Note: v-specific volumeAssumptions:Steady operating conditionKinetic and potential energy changes are negligible.Determine the thermal efficiency in % of this Rankine cycle when steam enters the turbine without any super-heating.
Question
For a simple ideal Rankine cycle, which uses water as the working fluid, the work produced by the turbine is 962.37 kJ/kg and heat supplied in the boiler is 2,568.32 kJ/kg . The condenser operates at 8 kPa and its boiler operates at 8,614 kPa. Use v1 = 0.001008 m3/kg in your calculations.Note: v-specific volumeAssumptions:Steady operating conditionKinetic and potential energy changes are negligible.Determine the thermal efficiency in % of this Rankine cycle when steam enters the turbine without any super-heating.
Solution
The thermal efficiency of a Rankine cycle can be calculated using the formula:
η = W_net/Q_in
Where: W_net = net work output Q_in = heat input
In this case, the work produced by the turbine (W_turbine) is given as 962.37 kJ/kg, and the heat supplied in the boiler (Q_in) is given as 2,568.32 kJ/kg.
However, to find the net work output (W_net), we need to subtract the work done by the pump (W_pump) from the work produced by the turbine.
The work done by the pump can be calculated using the formula:
W_pump = v1 * (P2 - P1)
Where: v1 = specific volume at the inlet of the pump = 0.001008 m3/kg P2 = pressure at the boiler = 8,614 kPa P1 = pressure at the condenser = 8 kPa
Substituting the given values:
W_pump = 0.001008 m3/kg * (8,614 kPa - 8 kPa) W_pump = 0.001008 m3/kg * 8,606 kPa W_pump = 8.67 kJ/kg
Now, we can calculate the net work output:
W_net = W_turbine - W_pump W_net = 962.37 kJ/kg - 8.67 kJ/kg W_net = 953.7 kJ/kg
Finally, we can calculate the thermal efficiency:
η = W_net/Q_in η = 953.7 kJ/kg / 2,568.32 kJ/kg η = 0.371 or 37.1%
So, the thermal efficiency of this Rankine cycle when steam enters the turbine without any super-heating is approximately 37.1%.
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