Water is the working fluid in an ideal Rankine cycle....

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $8 \mathrm{MPa}, 480^{\circ} \mathrm{C}$. The condenser pressure is $8 \mathrm{kPa}$. The net power output of the cycle is 100 MW. Determine for the cycle (a) the rate of heat transfer to the working fluid passing through the steam generator, in $\mathrm{kW}$. (b) the thermal efficiency. (c) the mass flow rate of condenser cooling water, in $\mathrm{kg} / \mathrm{h}$, if the cooling water enters the condenser at $15^{\circ} \mathrm{C}$ and exits at $35^{\circ} \mathrm{C}$ with negligible pressure change.

Water is the working fluid in an ideal Rankine cycle. Superheated vapor enters the turbine at $8 \mathrm{MPa}, 480^{\circ} \mathrm{C}$. The condenser pressure is $8 \mathrm{kPa}$. The net power output of the cycle is 100 MW. Determine for the cycle
(a) the rate of heat transfer to the working fluid passing through the steam generator, in $\mathrm{kW}$.
(b) the thermal efficiency.
(c) the mass flow rate of condenser cooling water, in $\mathrm{kg} / \mathrm{h}$, if the cooling water enters the condenser at $15^{\circ} \mathrm{C}$ and exits at $35^{\circ} \mathrm{C}$ with negligible pressure change.

Key Concepts

Rankine Cycle

The Rankine cycle is a thermodynamic cycle used to convert heat into mechanical work, typically through the use of a working fluid which undergoes phase change. It consists of four main processes: heat addition in the boiler (or steam generator), expansion through a turbine, heat rejection in a condenser, and compression in a pump. This cycle forms the basis for most power generation plants.

Heat Transfer in the Boiler/Steam Generator

In the Rankine cycle, heat transfer is essential in the boiler or steam generator, where the working fluid is heated from a liquid state to a vapor state. The rate of heat transferred is determined by the mass flow rate of the working fluid and the change in its enthalpy during the heating process. This concept is crucial for evaluating the performance and efficiency of the cycle.

Thermal Efficiency

Thermal efficiency in a thermodynamic cycle represents the fraction of heat input that is converted into net work output. It is calculated by taking the ratio of the net work produced by the cycle to the total heat added in the boiler. This efficiency indicator helps in comparing the performance of different power cycles and identifying potential improvements.

Mass Flow Rate Determination via Energy Balance

The calculation of mass flow rates, such as that of the condenser cooling water, is based on energy balance principles. By equating the heat removed in the condenser to the product of the mass flow rate, the specific heat capacity, and the temperature change of the cooling water, the mass flow rate necessary to achieve the desired heat rejection can be determined. This is a fundamental concept in heat exchanger analysis and condenser design.

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