Problems and Solutions on Thermodynamics and Statistical Mechanics

128 Problema €4 Solutions on Thermcdynam’ca d Statistical Mechanics

I mm

critical

ice point

vapor

T

27216

(K)

Fig. 1.35.

(b) The Clausius-Clapeyron equation gives

= -2.4 cal/cm3. K.

• 
  
  
  
  • L
    ice-water T(Vwater - Vice)
  
  
  
  

>O

(‘) water-vapor

When the pressure, which is slowly reduced, reaches the solid-liquid
phase line, heat is released by the water while the pressure remains un-
changed until all the water is changed into ice. Then at the vapor-solid
line, the ice absorbs heat until it is completely changed into vapor. After-
wards the pressure begins to decrease while the vapor phase is maintained.
The pressure at which water is converted to ice is given by

T - To

.~ = 6.3 x 103cmHg

L

Pwater-ice = PO +

Vwater - he TO

where we have used the values T = 272.15 K, TO = 273.16 K and po =

4.6 mmHg. As Vvapor = - > Kce, we have

kT

Pm

---- dP L - mLp

dT TVvapor T2k a

The pressure at which ice is converted to vapor is

Pice-vapor FJ PO exP [ - :L ( - io - - k)] = 4.4 mmHg

where rn is the molecular mass of water.