Air conditioners not only cool air, but dry it as well. A...

Air conditioners not only cool air, but dry it as well. A room in a home measures $6.0 \mathrm{~m} \times 10.0 \mathrm{~m} \times 2.2 \mathrm{~m}$. If the outdoor temperature is $30^{\circ} \mathrm{C}$ and the vapor pressure of water in the air is $85 \%$ of the vapor pressure of water at this temperature, what mass of water must be removed from the air each time the volume of air in the room is cycled through the air conditioner? The vapor pressure for water at $30{ }^{\circ} \mathrm{C}$ is $31.8$ torr.

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor when it is in thermodynamic equilibrium with its condensed phases at a given temperature in a closed system. It is a critical concept for understanding the state of water in air and plays a central role in determining how much water vapor the air can hold before condensation occurs.

Relative Humidity

Relative humidity is the ratio of the current vapor pressure of water in the air to the saturation vapor pressure at the same temperature. This concept is essential for quantifying the moisture content in the air and is directly related to comfort levels, weather phenomena, and the operation of air conditioning systems in removing moisture.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is used to relate the pressure, volume, temperature, and amount of gas present. In the context of determining the mass of water vapor that must be removed from the air, it provides a framework for calculating the number of moles—and thus the mass—of water vapor in a given volume at a specified temperature and pressure.

Unit Conversion

Unit conversion is an important tool for ensuring that quantities are in compatible units when performing calculations. For example, converting pressure units such as torr to atmospheres or Pascals is necessary when applying the ideal gas law or other formulae, ensuring that calculations yield the correct physical quantities.

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