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Psychrometric charts are powerful tools used in thermodynamics to understand the properties of moist air. These charts plot several air properties at different conditions. You will find axes and lines representing temperature, humidity, enthalpy, and more.

To use a psychrometric chart, locate the temperature on the horizontal axis. Then, locate the corresponding relative humidity curve. The point where these meet will give you the specific humidity and enthalpy directly.
This helps you find initial and final conditions quickly, which is essential when working on problems involving heat transfer in air.

Specific humidity represents the mass of water vapor in a unit mass of dry air. It is a useful metric because, unlike relative humidity, it doesn’t change with temperature or pressure.

Specific humidity can be calculated using: \[ \text{Specific Humidity} = \frac{\text{Mass of Water Vapor}}{\text{Mass of Dry Air}} \].

In the step-by-step solution, we recognize that the specific humidity in the duct remains constant during cooling. This simplifies our calculations, as we only need to find the initial specific humidity using the psychrometric chart.

Enthalpy is the total heat content of moist air. It includes both the sensible heat in the air and the latent heat in the water vapor. To find the enthalpy, use the formula: \[ h = c_{pa} \times T_{db} + \text{w} \times (c_{pw} \times T_{db} + L) \]
where:

• \(h\) is enthalpy,
• \(c_{pa}\) is specific heat capacity of dry air,
• \(T_{db}\) is dry bulb temperature,
• \(w\) is specific humidity,
• \(c_{pw}\) is specific heat capacity of water vapor,
• \(L\) is latent heat of vaporization.

Once you’ve determined the initial and final enthalpies from the psychrometric chart or tables, calculating the heat transfer rate becomes straightforward: \( \text{Heat Transfer Rate} = h_1 - h_2 \).

In thermodynamics, a steady-state process ensures that the properties of the system do not change over time. This is important when calculating heat transfer, as it simplifies the calculations.

In the given exercise, the moist air flows through a duct at a constant rate, and the properties of the air are steady both at the inlet and the exit. Equilibrium is maintained throughout, making it easier to track changes in enthalpy and humidity.

Relative humidity measures how close air is to being saturated with water vapor. It is expressed as a percentage and changes with temperature: when air is cooled, its capacity to hold water decreases, raising the relative humidity.

To calculate relative humidity, use the equation: \[ \text{Relative Humidity} = \frac{P_{wv}}{P_{sat}} \times 100\% \], where \(P_{wv}\) is the partial pressure of water vapor, and \(P_{sat}\) is the saturated vapor pressure at that temperature.

In the exercise, you determine the relative humidity at the exit based on the specific humidity and the saturation properties at the final temperature. This step helps confirm how the air's moisture profile changes through the duct.