Calculating Humidity and Dew Point

(a) Percent relative humidity is defined as the ratio of vapor density to saturation vapor density.

The first is given to be $9\text{.}{\text{40 g/m}}^3$, and the second is found in Table 13.5 to be $\text{23}\text{.}{\text{0 g/m}}^3$. Thus,

(b) The air contains $9\text{.}{\text{40 g/m}}^3$ of water vapor. The relative humidity will be 100% at a temperature where $9\text{.}{\text{40 g/m}}^3$ is the saturation density. Inspection of Table 13.5 reveals this to be the case at $\text{10}\text{.}0\text{º}\text{C}$, where the relative humidity will be 100%. That temperature is called the dew point for air with this concentration of water vapor.

(c) Here, the dew point temperature is given to be $–\text{10}\text{.}0\text{º}\text{C}$. Using Table 13.5, we see that the vapor density is $2\text{.}{\text{36 g/m}}^3$, because this value is the saturation vapor density at $–\text{10}\text{.}0\text{º}\text{C}$. The saturation vapor density at $\text{25}\text{.}0\text{º}\text{C}$ is seen to be $\text{23}\text{.}{\text{0 g/m}}^3$. Thus, the relative humidity at $\text{25}\text{.}0\text{º}\text{C}$ is

The importance of dew point is that air temperature cannot drop below $\text{10}\text{.}0\text{º}\text{C}$ in part (b), or $–\text{10}\text{.}0\text{º}\text{C}$ in part (c), without water vapor condensing out of the air. If condensation occurs, considerable transfer of heat occurs (discussed in Heat and Heat Transfer Methods), which prevents the temperature from further dropping. When dew points are below $0\text{ºC}$, freezing temperatures are a greater possibility, which explains why farmers keep track of the dew point. Low humidity in deserts means low dew-point temperatures. Thus condensation is unlikely. If the temperature drops, vapor does not condense in liquid drops. Because no heat is released into the air, the air temperature drops more rapidly compared to air with higher humidity. Likewise, at high temperatures, liquid droplets do not evaporate, so that no heat is removed from the gas to the liquid phase. This explains the large range of temperature in arid regions.