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

You have just washed your hair and 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 airflow rate, and the amount of water condensed on the window, if any.

Key Concepts

Energy Balance and Air Flow Rate Calculation

The energy balance approach involves equating the energy input from a device (like a hair dryer) to the energy required to heat air based on its mass flow rate and specific heat capacity. This concept is used to determine parameters such as the airflow rate and the heat transfer per unit mass of air, which are essential for understanding the overall energy efficiency and moisture transport in the system.

Psychrometrics

Psychrometrics is the study of the thermodynamic properties of moist air and the relationships between temperature, humidity, and energy. This field is essential for understanding how air can hold different amounts of water vapor at various temperatures and pressures, and it provides the tools for calculating key parameters such as relative humidity, dew point, and humidity ratio.

Relative Humidity

Relative humidity is the ratio of the current water vapor content of air to the maximum amount it can hold at a given temperature, expressed as a percentage. It is a critical concept in assessing air moisture conditions, influencing comfort, evaporation, condensation processes, and the potential for moisture-related phenomena in air systems.

Saturated Air and Dew Point

When air is saturated, it contains the maximum possible water vapor – any further cooling below the dew point will lead to condensation. The dew point, the temperature at which air becomes saturated, is pivotal in predicting when and where condensation might occur, such as on surfaces that are cooled below the dew point temperature.

Sensible and Latent Heat Transfer

Heat transfer in systems involving moist air is divided into sensible heat and latent heat. Sensible heat refers to energy exchanged that causes a change in temperature, while latent heat is associated with phase changes, such as water vapor condensing into liquid water. Both aspects are important in analyzing how energy inputs from devices like hair dryers affect air temperature and moisture content.

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