A large air separation plant, see Fig. P12.68, takes in...

A large air separation plant, see Fig. P12.68, takes in ambient air $(79 \%) \mathrm{N}_{2}, 21 \% \mathrm{O}_{2}$ by volume) at $14,7 \mathrm{lbf} / \mathrm{jn}_{1}^{2}, 70 \mathrm{F}$ at a rate of $2 \mathrm{lb}$ $\mathrm{mol} / \mathrm{s} .$ It discharges a stream of pure $\mathrm{O}_{2}$ gas at $30 \mathrm{lbf} / \mathrm{in.}^{2}, 200 \mathrm{F},$ and a stream of pure $\mathrm{N}_{2}$ gas at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 70 \mathrm{F}$. The plant operates on an electrical power input of $2000 \mathrm{kW}$. Calculate the net rate of entropy change for the process.

A large air separation plant, see Fig. P12.68, takes in ambient air $(79 \%) \mathrm{N}_{2}, 21 \% \mathrm{O}_{2}$ by volume) at $14,7 \mathrm{lbf} / \mathrm{jn}_{1}^{2}, 70 \mathrm{F}$ at a rate of $2 \mathrm{lb}$ $\mathrm{mol} / \mathrm{s} .$ It discharges a stream of pure $\mathrm{O}_{2}$ gas at $30 \mathrm{lbf} / \mathrm{in.}^{2}, 200 \mathrm{F},$ and a stream of pure $\mathrm{N}_{2}$ gas
at $14.7 \mathrm{lbf} / \mathrm{in.}^{2}, 70 \mathrm{F}$. The plant operates on an electrical power input of $2000 \mathrm{kW}$. Calculate the net rate of entropy change for the process.

Key Concepts

Irreversibility and Entropy Generation

Irreversibility in a process leads to the generation of additional entropy beyond that which is carried by material flows. This entropy generation is a measure of the inefficiencies and losses that occur during a process. By quantifying the entropy generation, engineers can assess the performance of a system and identify ways to reduce energy dissipation and improve efficiency.

Second Law of Thermodynamics

The second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time, provides the theoretical underpinning for entropy analysis. It implies that any process occurring in nature is accompanied by an increase in entropy, reflecting the irreversibility of real processes. This principle is crucial when analyzing systems to ensure compliance with thermodynamic limitations.

Thermodynamic Property Analysis

Thermodynamic property analysis involves the use of state variables such as temperature, pressure, and composition to characterize the state of a system. These properties are used to calculate the entropy of each process stream and, in combination with the entropy balance, determine the overall performance of processes like separations. Accurate property data is crucial for performing energy and entropy analyses in any thermodynamic system.

Entropy

Entropy is a thermodynamic state function that quantifies the disorder or randomness of a system. It plays a central role in determining the direction of natural processes and is fundamental to the analysis of energy transformations. In engineering systems, entropy changes help in assessing performance, efficiency, and the irreversibility inherent in any real process.

Entropy Balance in Control Volumes

The entropy balance in a control volume is the application of the second law of thermodynamics to a system with mass and energy flows. It accounts for the entropy carried in and out by the mass streams and any entropy generated within the system due to irreversibilities. This balance is essential in evaluating the net rate of entropy change in processes such as separations, mixing, and heat transfer.

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