Final answer:
The thermal efficiency of a Rankine cycle, mass flow rate, and change in temperature of cooling water can be determined through specific energy balance equations, while the maximum theoretical efficiency is computed using the Carnot efficiency formula. Differences between Rankine and Carnot efficiencies arise due to irreversible processes and practical operational limits, and improvements can be made by altering pressure conditions or adding reheat stages.
Step-by-step explanation:
The student has asked about the thermal efficiency of a simple ideal Rankine cycle in a steam power plant that has a net power output of 30 MW, where steam enters the turbine at 7 MPa and 500ºC and is cooled in the condenser at a pressure of 10 kPa. The question also asks to determine the mass flow rate of the system, the change in the temperature of the cooling water, and to compute the Carnot efficiency, while discussing reasons for the differences between the Rankine and Carnot efficiencies and providing suggestions to increase the efficiency of the Rankine cycle.
The calculation of the thermal efficiency (ηth) requires determining the heat added and work done in the cycle, typically through energy balance equations. To calculate the thermal efficiency of the Rankine cycle, one needs to consider the enthalpies at different points of the cycle. However, to calculate the Carnot efficiency (ηc), we use the formula ηc = 1 - (Tc/Th), where Tc is the temperature of the cooling water in Kelvin and Th is the temperature of the steam also in Kelvin.
The mass flow rate of the steam can be found by dividing the net power output by the net work per kilogram of steam. To determine the change in temperature of the cooling water, we need to perform an energy balance on the condenser. Finally, suggestions to improve the Rankine cycle efficiency could include increasing the boiler pressure, reheating the steam between turbine stages, or using a lower condenser pressure.