Late on an autumn day, the relative humidity is 45.0% and...

Late on an autumn day, the relative humidity is 45.0\% and the temperature is $20.0^{\circ} \mathrm{C}$. What will the relative humidity be that evening when the temperature has dropped to $10.0^{\circ} \mathrm{C}$ assuming constant water vapor density?

Key Concepts

Constant Water Vapor Density

Constant water vapor density, or constant absolute humidity, means that the total amount of water vapor in the air remains unchanged. When temperature changes under this condition, the relative humidity will vary because the saturation vapor pressure, which depends on temperature, changes even though the absolute amount of water vapor is constant.

Temperature Dependence

Temperature dependence refers to the strong relationship between temperature and the amount of water vapor air can hold; warmer air has a higher saturation vapor pressure compared to cooler air. This relationship means that if the air’s water vapor content remains constant, cooling will lead to a higher relative humidity, potentially reaching saturation and causing dew or fog formation.

Relative Humidity

Relative humidity is the ratio of the actual water vapor pressure in the air to the saturation vapor pressure at a given temperature, expressed as a percentage. It indicates how close the air is to being saturated with water vapor, and is a key measure of atmospheric moisture affecting weather and comfort.

Saturation Vapor Pressure

Saturation vapor pressure is the maximum pressure exerted by water vapor in the air at a specific temperature. It increases with temperature; as the temperature rises, air can hold more water vapor before reaching saturation, which is essential for understanding processes like condensation and precipitation.

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