Water is the working fluid in a Carnot vapor power cycle....

Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a pressure of $18 \mathrm{MPa}$, and saturated vapor enters the turbine. The condenser pressure is $6 \mathrm{kPa}$. Determine (a) the thermal efficiency. (b) the back work ratio. (c) the net work of the cycle per unit mass of water flowing, in $\mathrm{kJ} / \mathrm{kg}$. (d) the heat transfer from the working fluid passing through the condenser, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing. (e) Compare the results of parts (a)-(d) with those of Problem 8.6, respectively, and comment.

Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a pressure of $18 \mathrm{MPa}$, and saturated vapor enters the turbine. The condenser pressure is $6 \mathrm{kPa}$. Determine
(a) the thermal efficiency.
(b) the back work ratio.
(c) the net work of the cycle per unit mass of water flowing, in $\mathrm{kJ} / \mathrm{kg}$.
(d) the heat transfer from the working fluid passing through the condenser, in $\mathrm{kJ}$ per $\mathrm{kg}$ of steam flowing.
(e) Compare the results of parts (a)-(d) with those of Problem 8.6, respectively, and comment.

Key Concepts

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that defines the maximum possible efficiency for a heat engine operating between two thermal reservoirs. It involves two isothermal and two adiabatic processes and acts as a benchmark for all real cycles. Its principles are used to gauge the limits of performance in vapor power cycles using working fluids like water.

Thermal Efficiency

Thermal efficiency represents the ratio of the net work output to the heat input in a power cycle. It is a critical metric for evaluating the performance of power systems, indicating how effectively the cycle has converted supplied heat into useful work. In the context of vapor power cycles, thermal efficiency is calculated by comparing energy additions in the boiler to the net work after subtracting losses such as pump work.

Back Work Ratio

The back work ratio is the fraction of the work produced by the turbine that is consumed by the pump. It defines how much of the turbine’s output has to be reinvested in the system for the working fluid circulation. Lower back work ratios indicate more efficient cycles, as less work is required to pump the fluid compared to the net work output produced by the turbine.

Net Work

Net work in a power cycle is the difference between the work produced by the turbine and the work consumed by the pump. It is a key output measure of the cycle, representing the actual usable energy generated per unit mass of the working fluid. This value is essential for assessing the practical benefits of the cycle in power generation systems.

Heat Transfer in the Condenser

In vapor power cycles, the condenser is where the working fluid rejects unwanted heat and changes phase from vapor back to liquid. The heat transfer in the condenser is crucial as it directly affects cycle efficiency and the overall net work output. This rejected heat is quantified to understand the cycle’s thermal balance and to measure losses that limit the efficiency.

Saturation Properties

Saturation properties refer to the thermodynamic states of a substance, such as water, at which it coexists in both liquid and vapor phases. These properties help determine conditions like pressure, temperature, enthalpy, and entropy at phase boundaries, which are critical for analyzing and designing vapor power cycles. They simplify the thermodynamic analysis of processes like boiling and condensation in steam cycles.

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