A semipermeable membrane is used for the partial removal of...

A semipermeable membrane is used for the partial removal of oxygen from air that is blown through a grain elevator storage facility. Ambient air $(79 \%$ nitrogen, $21 \%$ oxygen on a mole basis) is compressed to an appropriate pressure, cooled to ambient temperature $25^{\circ} \mathrm{C}$, and then fed through a bundle of hollow polymer fibers that selectively absorb oxygen, so the mixture leaving at $120 \mathrm{kPa}, 25^{\circ} \mathrm{C}$ contains only $5 \%$ oxygen. The absorbed oxygen is bled off through the fiber walls at $40 \mathrm{kPa}, 25^{\circ} \mathrm{C}$ to a vacuum pump. Assume the process is reversible and adiabatic, and determine the minimum inlet air pressure to the fiber bundle.

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is transferred into or out of the system, meaning that any change in the system's internal energy is solely due to work performed on or by the system. This concept is vital in analyzing rapid processes or insulated systems, where adiabatic assumptions simplify the energy balance and help in calculating changes in temperature, pressure, and volume during the process.

Semipermeable Membrane

A semipermeable membrane is a barrier that allows certain molecules or ions to pass through it by diffusion and sometimes by facilitated transport, while blocking others. This selective passage is based on differences in size, solubility, or specific interactions, making them key components in separation and purification processes across various applications such as gas separation or desalination.

Selective Permeation

Selective permeation refers to the process by which a membrane or barrier preferentially allows one component of a mixture to pass through more readily than others. This selectivity is often based on inherent physical or chemical properties such as molecular size, solubility, or affinity for the membrane material, and is critical for achieving the desired separation of components in a mixture.

Reversible Process in Thermodynamics

A reversible process is an idealized thermodynamic process that occurs infinitely slowly, ensuring that the system remains in thermodynamic equilibrium at each stage. Reversible processes are characterized by the absence of dissipative effects like friction or unrestrained expansion, making them important benchmarks for calculating the maximum work obtainable or the minimum work required in various thermodynamic operations.

Partial Pressure in Gas Mixtures

Partial pressure is the pressure that each gas in a mixture would exert if it occupied the entire volume by itself at the same temperature. Understanding partial pressures is crucial when dealing with gas mixtures, as it directly relates to the mole fractions of the components and influences the driving forces for processes like diffusion, selective permeation in membranes, and chemical reactions involving gases.

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