An air-conditioning system consists of a spray section...

An air-conditioning system consists of a spray section followed by a reheater. Moist air at $32^{\circ} \mathrm{C}$ and $\phi=77 \%$ enters the system and passes through a water spray, leaving the spray section cooled and saturated with water. The moist air is then heated to $25^{\circ} \mathrm{C}$ and $\phi=45 \%$ with no change in the amount of water vapor present. For operation at steady state, determine (a) the temperature of the moist air leaving the spray section, in ${ }^{\circ} \mathrm{C}$. (b) the change the amount of water vapor contained in the moist air passing through the system, in $\mathrm{kg}$ per $\mathrm{kg}$ of dry air. Locate the principal states on a psychrometric chart.

An air-conditioning system consists of a spray section followed by a reheater. Moist air at $32^{\circ} \mathrm{C}$ and $\phi=77 \%$ enters the system and passes through a water spray, leaving the spray section cooled and saturated with water. The moist air is then heated to $25^{\circ} \mathrm{C}$ and $\phi=45 \%$ with no change in the amount of water vapor present. For operation at steady state, determine
(a) the temperature of the moist air leaving the spray section, in ${ }^{\circ} \mathrm{C}$.
(b) the change the amount of water vapor contained in the moist air passing through the system, in $\mathrm{kg}$ per $\mathrm{kg}$ of dry air.
Locate the principal states on a psychrometric chart.

Key Concepts

Sensible Heating Process

Sensible heating refers to the process of changing the temperature of air without altering its moisture content or humidity ratio. In the reheater section of the system, air is heated from its cooled, saturated state to a higher dry-bulb temperature while the water vapor content remains constant. This concept is fundamental in designing air-conditioning systems where temperature adjustment is required without affecting the moisture balance.

Steady-State Operation

Steady-state operation implies that the operating conditions of the system do not change with time; the input equals the output and mass and energy balances are maintained over time. Analyzing steady-state conditions is crucial for ensuring that the system design properly accounts for all process changes, including the cooling, condensation, and reheating stages, to achieve the desired overall performance.

Moist Air Properties

Moist air is a mixture of dry air and water vapor, and its properties are characterized by parameters such as dry?bulb temperature, humidity ratio (or specific humidity), relative humidity, and enthalpy. Understanding these properties is essential in evaluating the state of air before and after processes, as well as in calculating changes in water content, as demonstrated in the system described.

Psychrometric Chart

The psychrometric chart is a graphical representation of the thermodynamic properties of moist air, showing relationships among dry?bulb temperature, wet?bulb temperature, humidity ratio, relative humidity, and enthalpy. In problems like the one described, it is used to locate the various states of air as it undergoes processes such as cooling, humidification, or dehumidification, and to visualize process paths like constant water vapor content or saturated conditions.

Saturation Condition and Relative Humidity

The saturation condition occurs when the air contains the maximum possible amount of water vapor at a given temperature, corresponding to a relative humidity of 100%. Relative humidity is the ratio of the actual water vapor pressure to the saturation vapor pressure at a given temperature. In this system, reaching the saturated state after the spray section means that the air is cooled to its dew point, which is a key concept for understanding condensation and moisture removal in air-conditioning systems.

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