Steam enters the turbine of a vapor power plant at 100 bar, 520^∘ C and expands adiabatically, e

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Steam enters the turbine of a vapor power plant at 100 bar,...

Steam enters the turbine of a vapor power plant at 100 bar, $520^{\circ} \mathrm{C}$ and expands adiabatically, exiting at $0.08$ bar with a quality of $90 \%$. Condensate leaves the condenser as saturated liquid at $0.08$ bar. Liquid exits the pump at 100 bar, $43^{\circ} \mathrm{C}$. The specific exergy of the fuel entering the combustor unit of the steam generator is estimated to be $14,700 \mathrm{~kJ} / \mathrm{kg}$. No exergy is carried in by the combustion air. The exergy of the stack gases leaving the steam generator is estimated to be $150 \mathrm{~kJ}$ per $\mathrm{kg}$ of fuel. The mass flow rate of the steam is $3.92 \mathrm{~kg}$ per $\mathrm{kg}$ of fuel. Cooling water enters the condenser at $T_{0}=20^{\circ} \mathrm{C}, p_{0}=$ $1 \mathrm{~atm}$ and exits at $35^{\circ} \mathrm{C}, 1 \mathrm{~atm}$. Develop a full accounting of the exergy entering the plant with the fuel.

Key Concepts

Thermodynamic Cycle Exergy Accounting

In systems like vapor power plants operating on cycles such as the Rankine cycle, exergy accounting involves evaluating the exergy of streams (like high-pressure steam, expanded vapor, condensate, and pumped liquid) at different stages of the cycle. This process helps identify the contributions and losses of exergy in each component, providing insight into the overall performance and efficiency of the cycle.

Exergy Losses and Destruction

Exergy losses and destruction represent the degradation of work potential due to irreversibilities in real processes. In a power cycle, losses occur in components such as the turbine, condenser, and in the form of exhaust or stack gases. Quantifying these losses helps in understanding where improvements can be made to enhance overall system efficiency.

Fuel Exergy

Fuel exergy refers to the high-quality energy content of a fuel that is available for conversion into work. It is typically higher than the fuel's calorific value because it accounts for the potential work obtainable under ideal, reversible conditions. This concept is critical when assessing the performance of combustion processes in power plants.

Exergy Analysis

Exergy analysis involves tracking the flow of available work potential throughout a system. In the context of a power plant, it is used to quantify how much exergy is input (via fuel, for example), how much is converted into useful work, and how much is lost or destroyed due to irreversibilities. This provides a clearer picture of system efficiency compared to simple energy balances.

Exergy

Exergy is the measure of the maximum useful work that can be extracted from a system as it comes into equilibrium with its environment. It takes into account not only the quantity of energy but also its quality, acknowledging that some forms of energy are more capable of doing work than others due to the second law of thermodynamics.

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