Question

A parcel of air moves adiabatically and without phase changes of water from 900 hPa (Point A) to 700 hPa (Point B) and then to 800 hPa (Point C).

(a) At which of these three points is the relative humidity the largest, and at which point is it the smallest? Justify your answer

(b) At which of these three points is the specific humidity the largest, and at which point is it the smallest? Justify your answer

Answer 1

relative humidity is the ratio of partial pressure of water vapor to the equilibrium vapor pressure of water at that temperature.

in adiabatic process pressure and temperature are related by the equation, P^{(1-(C_P/C_V))}T^(C_P/C_V) = constant

C_P >C_V therefore,C_p/C_V>1

therefore, in adiabatic process as P increases , T increases.

as the temperature increases relative humidity decreases,because equilibrium vapor pressure of water increases.

but as the pressure increases relative humidity increases because partial pressure of water vapor increases .

generally, (1-(C_P/C_V))<(C_P/C_V)

so, change in temperature will be dominant,as it change by the power of (C_P/C_V) whereas P changes by the power of (1-(C_P/C_V)).

so, the relative humidity decreases with increase in pressure.

largest relative humidity will be largest at point B and smallest will be at point A.

specific humidity is the ratio of mass of the water vapor to the mass of the moist air parcel.

mass of the water vapor and air parcel does not depend on the pressure or temperature. so, it will be same at point A,B and C.