Suppose the relative humidity is 80 % on a day when the...

Suppose the relative humidity is $80 \%$ on a day when the temperature is $30.0^{\circ} \mathrm{C}$. (a) What will the relative humidity be if the air cools to $25.0^{\circ} \mathrm{C}$ and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?

Key Concepts

Relative Humidity

Relative humidity is the ratio of the current water vapor pressure in the air to the saturation vapor pressure at a given temperature, expressed as a percentage. It provides a measure of how close the air is to being saturated with water vapor, and thus indicates the potential for condensation and the formation of dew or clouds.

Saturation Vapor Pressure

Saturation vapor pressure is the maximum pressure exerted by water vapor in the air at a given temperature; it increases with higher temperatures. This concept is pivotal in understanding relative humidity because it defines the upper limit of water vapor that air can hold before condensation occurs.

Effect of Temperature on Water Vapor Capacity

The water vapor capacity of the air changes with temperature; warmer air can hold more water vapor before reaching saturation compared to cooler air. When the temperature drops while the actual amount of water vapor remains constant, the saturation vapor pressure decreases, which in turn increases the relative humidity and can lead to condensation if it exceeds 100%.

Condensation and Supersaturation

Condensation occurs when the relative humidity exceeds 100%, meaning the air cannot hold all the water vapor present. The concept of supersaturation refers to the unphysical or transient state where water vapor exceeds the saturation limit; in realistic scenarios, condensation would take place to bring the relative humidity back to 100%. This highlights the unrealistic nature of assuming a constant vapor density when cooling the air below its dew point.

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