New trends in physics teaching, v.4; The ... - unesdoc - Unesco

Entropy and Information
I l----i t--U-I
I 1 , I I l l 1
Figure 5. The scale height of the atmosphere.
maintaining high temperatures, not for evaporating water, which has to be avoided rather carefully,
since five times more energy is needed for evaporating than for heating water from 0 - 100°C.
This energy is required to overcome the attractive forces between water molecules and for
performing work against the air pressure. The heat of evaporation corresponds to this energy
requirement.
The higher energy of the molecules in the gaseous phase must correspond also to a higher value
of the entropy since the free enthalpies of liquid and gas have to agree [ 151.
Here A denotes the difference between gas and liquid and AH is the heat of evaporation, containing
both the work against the molecular forces and against the external air pressure.
In order to calculate AS we note that we lose ten bit of information when we go from a liquid
to a gas, since the volume of a gas at normal temperature and pressure is roughly 1000 = 21° times
the volumii of the corresponding liquid (figure 6). The entropy of each molecule increases therefore
by AS = 7 k during evaporation. According to (Eq. 15) this leads to a heat of evaporation per
molecule
The ratio of (molecular) heat of evaporation and boiling temperature T should be a universal
constant, 7 k. If the boiling temperature (at a pressure of 1 atmosphere) is not close to 300 K,
but may be approximated by T = 300 X 2n K, where y1 is a positive or negative integer, the
corresponding increase in volume during evaporation is given by 1000 X 2n x 2(10+n). This
follows from the equation of state v = kT/p, since v, the volume per molecule, is proportional to
the absolute temperature, if the pressure is kept fixed. Thus the entropy per molecule increases
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