Solutions 237The density pv of vapour at a temperature T =
293 K can be found from the equation of state for
an ideal gas:
PsaatPv (^) RT
Thus, the height h of vapour column satisfies the
quadratic equation
,0.05c 2 RT 2h 1
//—
Kg h - 1
Substituting the numerical values and solving the
quadratic equation, we obtain
h 16.4 cm.
It is interesting to note that, as follows from
the problem considered above, if two identical
vessels containing solutions of different concen-
trations are placed under the bell, the liquid will
evaporate from the solution of a lower concentra-
tion. Conversely, water vapour will condense to
the solution of a higher concentration. Thus, the
concentrations tend to level out. This phenomenon
explains the wetting of sugar and salt in an atmo-
sphere with a high moisture content.
2.34. Since the lower end of the duct is maintained
at a temperature Ti which is higher than the melting
point of cast iron, the cast iron at the bottom will
be molten. The temperature at the interface be-
tween the molten and solid cast iron is naturally
equal to the melting point Tin it.
Since the temperatures of the upper and lower
ends of the duct are maintained constant, the
amount of heat transferred per unit time through
the duct cross section must be the same in any
region. In other words, the heat flux through the
molten and solid cast iron must be the same (the
brick duct is a poor heat conductor so that heat
transfer through its walls can be neglected).
The heat flux is proportional to the thermal
conductivity, the cross-sectional area, and the
temperature difference per unit length. Let