A geothermal power plant uses geothermal liquid water at 150^∘ C at a rate of 210 kg / s as the

step 1 High friends, the exergy of water entering the plant, x1. Mass flow rate into H1 minus H0, minus

A geothermal power plant uses geothermal liquid water at...

A geothermal power plant uses geothermal liquid water at $150^{\circ} \mathrm{C}$ at a rate of $210 \mathrm{~kg} / \mathrm{s}$ as the heat source, and it produces $5.1 \mathrm{MW}$ of net power in an environment at $25^{\circ} \mathrm{C}$. If $7.5 \mathrm{MW}$ of exergy entering the plant with the geothermal water is destroyed within the plant, determine $(a)$ the exergy of the geothermal water entering the plant, $(b)$ the second-law efficiency, and $(c)$ the exergy of the heat rejected from the plant.

Key Concepts

Exergy

Exergy is the measure of the maximum useful work obtainable from a system as it reaches thermodynamic equilibrium with its environment. It considers not just the quantity of energy but also its quality, meaning the ability of energy to perform work, which is a central concept in the analysis of systems governed by the second law of thermodynamics.

Exergy Analysis

Exergy analysis involves performing an energy audit that tracks how much of the available work potential (exergy) is converted into useful output versus how much is destroyed due to irreversibilities. This method is crucial for diagnosing inefficiencies in thermal systems, such as heat engines or power plants, and it helps engineers identify areas where improvements can be made.

Second-Law Efficiency

Second-law efficiency is a performance metric that compares the actual useful work output of a system to the maximum work that could be theoretically obtained from the available exergy. It provides insight into how effectively a system utilizes its energy resources while accounting for the inherent losses dictated by the second law of thermodynamics.

Exergy Destruction

Exergy destruction quantifies the irreversibilities present in a process by measuring the amount of exergy that is lost or rendered unavailable for work due to factors such as friction, heat transfer across finite temperature differences, and other entropy-generating processes. It is a critical concept for understanding and minimizing inefficiencies in energy conversion systems.

Exergy Balance

The exergy balance is an accounting tool that tracks the input, output, accumulation, and destruction of exergy in a system. It parallels the energy balance but incorporates the quality of energy, allowing for a more detailed assessment of where and how energy degradation occurs within a system's operation.

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