You have just washed your hair and you now blow dry it in a...

You have just washed your hair and you now blow dry it in a room with $23^{\circ} \mathrm{C}, \phi=60 \%,(1) .$ The dryer, $500 \mathrm{~W}$, heats the air to $49^{\circ} \mathrm{C},$ (2), blows it through your hair, where the air becomes saturated (3), and then flows on to hit a window, where it cools to $15^{\circ} \mathrm{C}$ (4). Find the relative humidity at state $2,$ the heat transfer per kilogram of dry air in the dryer, the air flow rate, and the amount of water condensed on the window, if any.

You have just washed your hair and you now blow dry it in a room with $23^{\circ} \mathrm{C}, \phi=60 \%,(1) .$ The dryer, $500 \mathrm{~W}$, heats the air to $49^{\circ} \mathrm{C},$ (2), blows it through your hair, where the air becomes saturated
(3), and then flows on to hit a window, where it cools to $15^{\circ} \mathrm{C}$ (4). Find the relative humidity at state $2,$ the heat transfer per kilogram of dry air in the dryer, the air flow rate, and the amount of water condensed on the window, if any.

Key Concepts

Psychrometrics

Psychrometrics is the study of the thermodynamic properties of moist air and the processes involving heat and mass transfer associated with water vapor. It involves understanding how temperature, water content, and pressure interact in air, and is vital for evaluating processes such as heating, cooling, humidification, dehumidification, and condensation in air-conditioning and drying applications.

Relative Humidity

Relative humidity is the ratio of the partial pressure of water vapor present in the air to the saturation vapor pressure at the same temperature, expressed as a percentage. It quantifies how close the air is to being saturated with moisture, and is essential in determining the potential for condensation or evaporation during heating or cooling processes.

Sensible and Latent Heat Transfer

Sensible heat transfer refers to the energy exchange that results in a temperature change of a substance, while latent heat transfer involves energy exchange during phase changes such as evaporation or condensation without a temperature change. Understanding both is critical in processes like blow drying, where air is heated (sensible heating) and moisture may condense or evaporate (latent heating) when the air’s temperature or water content changes.

Air Flow Rate Determination

Determining the air flow rate involves relating the power input from a heat source to the energy required to raise the temperature of a given mass of air. This typically requires knowledge of the specific heat capacity of air and the mass flow rate needed to achieve a desired temperature change, linking mechanical power with thermodynamic properties.

Condensation and Saturation

Condensation occurs when air, particularly when saturated, is cooled to a temperature at which its water vapor content exceeds the saturation limit. This results in the phase change of water vapor to liquid water. In drying and air-cooling applications, analysis of saturation conditions helps predict whether any water will condense when the temperature decreases below the dew point.

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