The total volume of a new house is 800 m^3 . Before the heat...

The total volume of a new house is $800 \mathrm{m}^{3} .$ Before the heat is turned on, the air temperature inside is $10^{\circ} \mathrm{C},$ and the relative humidity is 50 percent. After the air is warmed to $20^{\circ} \mathrm{C}$, how much water vapor must be added to the air to make the relative humidity 50 percent?

Key Concepts

Psychrometrics

Psychrometrics is the study of the physical and thermodynamic properties of mixed air and water vapor. It involves understanding various parameters, including dry-bulb temperature, wet-bulb temperature, relative humidity, and saturation conditions, which are all essential when evaluating how changes in temperature affect air moisture content.

Temperature Dependence of Air Moisture Capacity

The moisture capacity of air refers to the maximum amount of water vapor that air can hold, which is highly dependent on its temperature. As the temperature rises, the saturation vapor pressure increases, requiring more water vapor to maintain the same relative humidity level, a concept critical to understanding why heating indoor air can lower its relative humidity if moisture is not added.

Relative Humidity

Relative humidity is the ratio, expressed as a percentage, of the current water vapor content of the air to the maximum amount it can hold at a given temperature. It is a crucial measure in assessing how saturated the air is with moisture and determines how close the air is to forming condensation.

Saturation Vapor Pressure

Saturation vapor pressure is the pressure exerted by water vapor in equilibrium with liquid water at a given temperature. It represents the maximum possible partial pressure of water vapor in the air and increases exponentially with temperature, meaning warmer air can accommodate more moisture.

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