Saturated (cloudy) air at a temperature of 20 °C (68 °F) has a vapor pressure of __________ mb and a relative humidity of _________%.
To determine the vapor pressure and relative humidity of saturated air at a given temperature, we can use the concept of saturation vapor pressure.
Saturation vapor pressure (es) is the maximum amount of water vapor that can exist in the air at a specific temperature. It is directly related to the temperature: as the temperature increases, the saturation vapor pressure also increases.
To find the saturation vapor pressure at 20 °C (68 °F), you can use various empirical formulas or refer to tables specifically designed to provide saturation vapor pressure values.
One commonly used formula is the Magnus-Tetens formula:
es = 6.112 × e^(17.67 × T / (T + 243.5))
Where:
es = saturation vapor pressure in hectopascals (hPa) or millibars (mb)
T = temperature in degrees Celsius (°C)
For T = 20 °C:
es = 6.112 × e^(17.67 × 20 / (20 + 243.5))
Using a scientific calculator or programming language, calculate the value of es.
Once you have the saturation vapor pressure (es), you can calculate the relative humidity (RH) using the equation:
RH = (actual vapor pressure / saturation vapor pressure) × 100
Given that the air is saturated, the actual vapor pressure (ea) is equal to the saturation vapor pressure (es).
So, the relative humidity is:
RH = (es / es) × 100
Compute the value of RH to get the relative humidity in percentage (%).
Remember to use the obtained values for temperature and es correctly, as rounding errors or using different units could affect the accuracy of the result.