If the relative humidity is 66.8% in the middle of a spring day in auckland when the temperature is 15 degrees celsius, What will the relative humidity be in the evening when the temperature falls to 10 degrees celius (Assume the partial pressure of water in atmosphere remain as constant as possible) The saturated vapour pressure of water has values as follows:
Temp 5∘C 10∘C 15∘C 20∘C 25∘C
P(kPa) 0.87 1.19 1.69 2.33 3.17
At 66.8% humidity on a 15C day, the air partial pressure is 66.8% of 1.69 kPa, or 1.13 kPa. That is 94.9% of the saturation pressure at 10 C.
Therefore the relative humidity becomes 94.9% when the temperature drops to 10C
To determine the relative humidity in the evening when the temperature falls to 10 degrees Celsius, we need to use the concept of saturation vapor pressure.
Saturation vapor pressure is the pressure exerted by the water vapor when the air is saturated at a given temperature. It can be obtained from the table you provided:
At 10 degrees Celsius, the saturation vapor pressure is 1.19 kPa.
The relative humidity (RH) is the ratio of the actual vapor pressure to the saturation vapor pressure, expressed as a percentage. We can calculate the actual vapor pressure using the given relative humidity and temperature:
Actual vapor pressure = RH × saturation vapor pressure
Given that the relative humidity is 66.8% and the temperature is 15 degrees Celsius, we can calculate the actual vapor pressure at that time:
Actual vapor pressure = 0.668 × 1.69 kPa
Actual vapor pressure = 1.127 kPa
Now, we can use this actual vapor pressure to calculate the relative humidity in the evening when the temperature falls to 10 degrees Celsius:
Relative humidity in the evening = Actual vapor pressure / Saturation vapor pressure
Relative humidity in the evening = 1.127 kPa / 1.19 kPa
Relative humidity in the evening ≈ 0.946
So, the relative humidity in the evening when the temperature falls to 10 degrees Celsius will be approximately 94.6%.