a) What is the density (in kilograms per cubic meter) of moist air at 25oC, a pr

Question

a) What is the density (in kilograms per cubic meter) of moist air at 25oC, a pressure of 1000 mb and vapor pressure of 25 mb? b) What is the saturated vapor pressure (in Pa) at a temperature of 25oC? Explain the physical meaning of saturated vapor pressure. Be precise. How does it change as the temperature increases? How does it change as the actual humidity level of air changes? c) What is the specific humidity (in g/kg) of air with a vapor pressure of 25 mb at a pressure of 1000mb? d) What is the relative humidity of the air in part c)? e) What is the dewpoint temperature (in oC) of the air in part c)? f) What is the specific humidity (in kg/kg) of air at 1000mb with a dewpoint temperature of 15oC?

Explanation / Answer

(a) The density of humid air can be calculated as the sum of the densities of the two gases, dry air and water vapor in proportion with their partial pressures.

humid air = Pd/Rd.T + Pv/Rd.T

               = 1000x100/287.05x298 + 25x100/461.5x298        [science, 1 mb = 100 Pa]

                = 100000/85540.9 + 2500/137527

                = 1.169 + 0.018178

                = 1.187 kg/m3

Where,

humid air = density of humid air (kg/m3)

Pd = partial pressure of dry air (Pa), Rd = specific gas constant of dry air, 287.05 J/kg.K

Pv = partial pressure of water vapor (Pa), Rd = specific gas constant for water vapor, 461.495 J/kg.K

(b) We know saturation vapor pressure (pws) can be given by

pws = e(77.3450 + 0.0057 T - 7235 / T) / T8.2  

       = e(77.3450 + 0.0057x298 - 7235 / 298) / 2988.2  Pa      

Where, pws = water vapor saturation pressure (Pa)

e = the constant 2.718.......

T = temperature of the moist air (K)

Saturated vapor pressure: The process of evaporation of a solvent in a closed container will proceed until there are as many molecules returning to the liquid as there are escaping (that is at its equilibrium point). At this point the vapor is said to be saturated, and the pressure of that vapor is called the saturated vapor pressure.

According to Le Chatelier principle, increasing the temperature of a system in a dynamic equilibrium favours the endothermic change. That means that increasing the temperature increases the amount of vapor present, and so increases the saturated vapor pressure.

As the humidity (amount of water vapor in air) increases the vapour content in the air increases and hence the vapour pressure.

We know,

Specific humidity = (0.622 x Pv)/Pd

      = (0.622x1000 x 2500)/100000 [science, 1 mb = 100 Pa And 1000 is the conversion factor from kg to g]

   = 15.55 g/kg

(d) Relative humidity = partial pressure of water vapor/ saturation vapor pressure of water

                              = 2500 x 2988.2/e(77.3450 + 0.0057x298 - 7235 / 298) [using solution (b)]

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