Air at 25^∘ C and 1 atm that contains water vapor at a...

Air at $25^{\circ} \mathrm{C}$ and 1 atm that contains water vapor at a partial pressure that is $50 \%$ of the vapor pressure at $25^{\circ} \mathrm{C}$ ( $50 \%$ relative humidity) is required for a process. This air is generated by saturating room air by passing through water sprays, compressing this saturated air to a certain pressure, $\mathrm{P}$, and cooling the compressed air to $25^{\circ} \mathrm{C}$. The partial pressure of water in the cooled saturated air that leaves the compressor is the vapor pressure of water at $25^{\circ} \mathrm{C}$. This air is allowed to expand to $1 \mathrm{~atm}$ pressure isothermally. Calculate $\mathrm{P}$ such that after expansion, the air will have $50 \%$ relative humidity.

Key Concepts

Compression and Expansion Effects on Gas Mixtures

Gas mixtures undergo changes in pressure and volume during compression and expansion, which affect the concentration and partial pressures of individual components. Understanding these effects is important for processes that require control over moisture content and saturation levels, as the relationships between pressure, volume, and temperature determine the final state of the gas mixture.

Ideal Gas Law and Partial Pressures

The ideal gas law relates the pressure, volume, temperature, and moles of a gas, forming the basis for understanding gas behavior under various conditions. Partial pressures, representing the fraction of the total pressure contributed by each gas in a mixture, enable the analysis of gas mixtures and are critical in calculating changes due to processes like compression and expansion.

Relative Humidity

Relative humidity is a measure of the current amount of water vapor present in air expressed as a percentage of the amount needed for saturation at the same temperature. It plays a fundamental role in heat and mass transfer processes and affects atmospheric behavior and process conditions in engineering applications.

Isothermal Process

An isothermal process occurs when a gas expands or is compressed at a constant temperature. During such processes, while the volume and pressure change, the internal energy of the gas remains constant, making it essential for analyzing thermodynamic cycles and calculating work and heat transfer using the ideal gas law.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases at a given temperature. It represents the tendency of molecules to escape from the liquid phase to the gaseous phase and is a crucial parameter in determining phase transitions and saturation levels in mixtures.

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