Problems and Solutions on Thermodynamics and Statistical Mechanics

132 Problems tY Solutions on Thermcdynamica El Statbticd Mechanics

1134
The latent heat of vaporization of water is about 2.44~10~ J/kg and
the vapor density is 0,598 kg/m3 at 100OC. Find the rate of change of the
boiling temperature with altitude near sea level in "C per km. Assume the
temperature of the air is 300 K.
(Density of air at O°C and 1 atm is 1.29 kg/m3).
( wis co nsin)

Solution:

The Boltzmann distribution gives the pressure change with height:

where p(0) is the pressure at sea level z = 0, m is the molecular weight of
air, and To = 300 K is the temperature of the atmosphere. The Clausius-
Clapeyron equation can be written as

dv L L (Y

with p1 = 1000 kg/m3, p2 = 0.598 kg/m3 and L/M = 2.44 x 106 J/kg, we

have

(Y= Lp1p2 = 1.40 x lo6 J/m3.

WPl - P2)

So the rate of change of the boiling point with height is

Using the equation of state for ideal gas p = pkTo/rn, we have near

the sea level

where p = 1.29 kg/m3 is the density of air, g = 9.8 m/s2 and T(0) = 100OC.

dT

dz

Thus - = -0.87OC/km.