A well-insulated rigid tank contains 6 lbm of a saturated...

A well-insulated rigid tank contains 6 lbm of a saturated liquid-vapor mixture of water at 35 psia. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is turned on and kept on until all the liquid in the tank is vaporized. Assuming the surroundings to be at $75^{\circ} \mathrm{F}$ and 14.7 psia, determine $(a)$ the exergy destruction and $(b)$ the second-law efficiency for this process.

Key Concepts

Phase Change in Saturated Mixtures

Phase change in a saturated liquid-vapor mixture involves transformation between liquid and vapor phases at equilibrium conditions. The quality, or the mass fraction of vapor in the mixture, directly affects the thermodynamic properties and energy content of the system. Understanding phase change is essential for the analysis of processes involving heating or cooling where latent heats and equilibrium conditions determine the energy exchange.

Constant Volume Process

A constant volume process refers to a thermodynamic process occurring in a system with fixed volume, such as a rigid tank. In these processes, no work is done by expansion or compression, and energy changes manifest primarily as changes in internal energy and heat transfer. This condition critically influences the system's state evolution and the distribution of energy and exergy.

Irreversibility

Irreversibility in a thermodynamic process refers to the inherent losses that prevent a system from achieving the ideal reversible behavior. It is associated with entropy production due to factors such as friction, heat transfer across finite temperature differences, and unrestrained expansion. Quantifying irreversibility is crucial in exergy analysis because it determines the extent of exergy destroyed during a process, impacting overall system efficiency.

Exergy Analysis

Exergy analysis is a thermodynamic approach that quantifies the maximum useful work obtainable from a system as it comes into equilibrium with its environment. It highlights the effects of irreversibilities during a process by identifying where and how much potential work is destroyed. This concept is used in evaluating the performance of systems where energy quality is as important as energy quantity.

Second-Law Efficiency

Second-law efficiency is a metric that compares the actual performance of a process to its maximum possible performance as dictated by the second law of thermodynamics. It is defined as the ratio of the useful exergy output to the exergy input, providing insight into how efficiently a system converts available energy into work, taking into account the losses due to irreversibilities.

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