454 ENGINEERING THERMODYNAMICSdharm
\M-therm\Th10-1.pm5thermal equilibrium exists with respect to water, air and water vapour, and consequently the air
is saturated. The equilibrium temperature is called the adiabatic saturation temperature or
the thermodynamic wet bulb temperature. The make-up water is introduced at this tempera-
ture to make the water level constant. The ‘adiabatic’ cooling process is shown in Fig. 10.2 for the
vapour in the air-vapour mixture. Although the total pressure of the mixture is constant, the
partial pressure of the vapour increases, and in the saturated state corresponds to the adiabatic
saturation temperature. The vapour is initially at DBT tdb 1 and is cooled adiabatically to DBT tdb 2
which is equal to the adiabatic saturation twb 2. The adiabatic saturation temperature and wet bulb
temperatures are taken to be equal for all practical purposes. The wet bulb temperature lies
between the dry bulb temperature and dew point temperature.
Fig. 10.2. Adiabatic cooling process.
Let us now apply the first law to the entire process. Considering the process to be steady
state steady flow, neglecting changes in kinetic and potential energies, we have
h 1 + (W 2 s – W 1 )hhf 2 = 2 s ...(10.13)
The quantities W 2 s, h 2 s and hf 2 are the functions of temperature tdb 2. The term (W 2 s – W 1 )hf 2
is quite small and if this term is neglected, it can be seen that the enthalpy remains constant in
adiabatic saturation.
Equation (10.13) may be rewritten as
h 1 – Wh 1 f 2 = h 2 s – Wh 2 s f 2
The inlet term can be generalized and the expression can be written as follows :
Σ = h 2 s – Wh (^2) sf 2 = h 1 – Wh (^1) f 2 = hx – Whx f 2 ...(10.14)
This means that sigma function (Σ) as defined by the equation, is constant for any wet bulb
temperature.
Also h 1 = h 2 s – (W 2 s – W 1 ) hf 2 ...(10.15)