If the relative humidity is 66% and the vapor pressure is 16 mb, what is the approximate air temperature? Answer: _________ °C. (Round to one decimal place, do not include units.)
To determine the approximate air temperature given the relative humidity and vapor pressure, we can use the concept of saturated vapor pressure. The saturated vapor pressure is the maximum amount of water vapor that can exist in the air at a particular temperature.
First, we need to find the saturation vapor pressure at the given air temperature. This can be done using meteorological equations or tables. However, since we don't have the air temperature, we can't directly calculate the saturation vapor pressure.
But we can make use of the fact that relative humidity is defined as the ratio of the actual vapor pressure to the saturation vapor pressure, multiplied by 100%. Mathematically, it can be written as:
Relative humidity = (Actual vapor pressure / Saturation vapor pressure) * 100%
Given that the relative humidity is 66% and the vapor pressure is 16 mb, we can rearrange the equation to solve for the saturation vapor pressure:
Saturation vapor pressure = (Actual vapor pressure / Relative humidity) * 100%
Substituting the given values:
Saturation vapor pressure = (16 mb / 66%) * 100%
Calculating that value using the given numbers:
Saturation vapor pressure = (16 mb / 0.66) * 100% = 24.24 mb
Now, we need to find the air temperature corresponding to this saturation vapor pressure. Again, this can be done using meteorological equations or tables. However, since we don't have access to those, we can make use of the approximate relationship between saturation vapor pressure and air temperature.
As a rough approximation, the saturation vapor pressure increases exponentially with air temperature. So, we can estimate the air temperature by finding the temperature at which the saturation vapor pressure is equal to the given value of 24.24 mb.
This estimation can be done using trial and error or iterative methods. For simplicity, let's assume a starting temperature and iterate until we find the closest value to 24.24 mb.
Let's start with an initial air temperature of 20°C and calculate the corresponding saturation vapor pressure.
Using meteorological equations or tables, let's say the saturation vapor pressure at 20°C is approximately 23 mb. Since 24.24 mb is greater than 23 mb, we need to slightly increase the air temperature and recalculate the saturation vapor pressure.
Again, let's assume a new air temperature of 22°C and calculate the saturation vapor pressure.
Using meteorological equations or tables, let's say the saturation vapor pressure at 22°C is approximately 26 mb. Since 24.24 mb is less than 26 mb, we need to slightly decrease the air temperature and recalculate the saturation vapor pressure.
Let's assume a new air temperature of 21°C and calculate the saturation vapor pressure.
Using meteorological equations or tables, let's say the saturation vapor pressure at 21°C is approximately 24 mb. Since 24.24 mb is very close to 24 mb, we can consider this as our approximate air temperature.
Therefore, the approximate air temperature corresponding to a relative humidity of 66% and vapor pressure of 16 mb is approximately 21°C.
Answer: 21 °C.