Air at 35^∘ C, 1 atm, and 50 % relative humidity enters a...

Air at $35^{\circ} \mathrm{C}, 1 \mathrm{~atm}$, and $50 \%$ relative humidity enters a dehumidifier operating at steady state. Saturated moist air and condensate exit in separate streams, each at $15^{\circ} \mathrm{C}$. Neglecting kinetic and potential energy effects, determine (a) the heat transfer from the moist air, in $\mathrm{kJ}$ per $\mathrm{kg}$ of dry air. (b) the amount of water condensed, in $\mathrm{kg}$ per $\mathrm{kg}$ of dry air. (c) Check your answers using data from the psychrometric chart. (d) Check your answers using Interactive Thermodynamics: $I T$.

Air at $35^{\circ} \mathrm{C}, 1 \mathrm{~atm}$, and $50 \%$ relative humidity enters a dehumidifier operating at steady state. Saturated moist air and condensate exit in separate streams, each at $15^{\circ} \mathrm{C}$. Neglecting kinetic and potential energy effects, determine
(a) the heat transfer from the moist air, in $\mathrm{kJ}$ per $\mathrm{kg}$ of dry air.
(b) the amount of water condensed, in $\mathrm{kg}$ per $\mathrm{kg}$ of dry air.
(c) Check your answers using data from the psychrometric chart.
(d) Check your answers using Interactive Thermodynamics: $I T$.

Key Concepts

Moist Air Properties

This concept deals with the thermodynamic characteristics of air when it contains water vapor. It involves parameters such as temperature, pressure, relative humidity, and the humidity ratio, which describes the mass of water vapor per mass of dry air. An understanding of these properties is essential for analyzing systems that involve humid air, such as dehumidifiers or air-conditioning systems.

Mass Balance in Moist Air Systems

Mass balance is the principle of conservation of mass applied to processes involving moist air, ensuring that the mass of dry air and water (in both vapor and liquid forms) is accounted for at all points of the system. In dehumidification problems, the mass balance is used to determine the amount of moisture removed from the air during the process while tracking the constant mass flow of dry air.

Energy Balance in Thermodynamic Processes

The energy balance involves applying the first law of thermodynamics, which states that energy is conserved in a system. In systems handling moist air, the energy balance is used to calculate the heat transfer associated with both the sensible heating or cooling of the air and the latent heat involved in phase changes, such as condensation. This allows for determining how much heat is extracted or added as the air transitions between different states.

Psychrometric Analysis

Psychrometric analysis involves using the graphical representation, or psychrometric chart, to examine and analyze the state of moist air. This tool depicts properties such as dry-bulb temperature, wet-bulb temperature, relative humidity, humidity ratio, and enthalpy. It provides a way to visually assess changes and transitions in these properties during processes like dehumidification, and is essential for validating thermodynamic calculations in practical applications.

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