Final answer:
Relative humidity increases as temperature drops if the water vapor density stays constant because the air can hold less moisture at lower temperatures. To find the exact relative humidity at different temperatures, one would need saturation vapor densities at those temperatures, often found in a psychrometric chart.
Step-by-step explanation:
To calculate the relative humidity on an autumn day when the temperature drops from 20.0°C to 10.0°C with constant water vapor density, we use the concept that relative humidity is the ratio of the current vapor density to the saturation vapor density at that temperature. The saturation vapor density is the maximum amount of water vapor that the air can hold at a certain temperature.
Given that the relative humidity is 45.0% at 20.0°C, we know that the air's actual vapor density is 45.0% of the saturation density at 20.0°C. When the temperature drops to 10.0°C, the saturation vapor density decreases; however, if the actual vapor density remains constant, the relative humidity will increase because it will constitute a larger percentage of the new, lower saturation density.
To find the new relative humidity, we would need to know the exact saturation vapor densities at 20.0°C and 10.0°C, which are typically found in a psychrometric chart or related reference material. In general, as temperature decreases, the relative humidity will increase if the actual vapor density does not change.
In a separate example, if the air temperature is 25 °C with a dew point of 15 °C, we look up the saturation vapor density for 25 °C and compare it to the actual vapor density represented by the dew point of 15 °C to compute the relative humidity.