Step-by-step explanation:
To determine the absolute humidity of a parcel of air when it is saturated, we need to calculate its maximum water vapor capacity at 40°C, also known as its saturation specific humidity.
The maximum water vapor capacity of air increases with temperature, so we need to use a formula that takes into account both temperature and pressure. One such formula is the Magnus-Tetens equation:
e = 6.112 × exp[(17.67 × T)/(T + 243.5)]
where e is the vapor pressure in hPa and T is the temperature in degrees Celsius.
Using this equation, we can calculate that at 40°C, the vapor pressure of saturated air is:
e = 6.112 × exp[(17.67 × 40)/(40 + 243.5)] = 7.958 kPa
Next, we need to convert this vapor pressure into absolute humidity using the following formula:
AH = (0.622 × e)/(P - 0.378 × e)
where AH is the absolute humidity in g/m3, P is the atmospheric pressure in kPa, and 0.622 and 0.378 are constants representing the molar mass ratio of water vapor to dry air and the ratio of the gas constants for water vapor and dry air, respectively.
Assuming a standard atmospheric pressure of 101.325 kPa, we can calculate that at 40°C and saturation, the absolute humidity of air would be:
AH = (0.622 × 7.958)/(101.325 - 0.378 × 7.958) = 51 g/m3
Therefore, if the initial parcel of air had an absolute humidity of 35 g/m3 and was heated to its saturation point at 40°C, its absolute humidity would increase to approximately 51 g/m3.