Page 164 - Physical chemistry understanding our chemical world

THE DIRECTION OF PHYSICOCHEMICAL CHANGE: ENTROPY 131

Why, when one end of the bath is hot and the other
cold, do the temperatures equalize?

Entropy and the second law of thermodynamics

Quite often, when running a bath, the water is initially quite cold. After the hot
water from the tank has had time to travel through the pipes, the water from the tap
is hot. As a result, one end of the bath is hotter than the other. But a short time
later, the temperature of the water is the same throughout the bath, with the hot
end cooler and the cold end warmer. Temperature equilibration occurs even without
stirring. Why?
We saw in Chapter 1 how the simplest way to gauge how much energy a molecule
possesses is to look at its temperature. We deduce through a reasoning process such as
this that molecules of water at the cold end of the bath have less energy than molecules
at the hot end. Next, by combining the minus-oneth and zeroth laws of thermody-
namics, we say that energy (in the form of heat) is transferred from molecules of
water at the hot end of the bath to molecules at the cold end. Energy transfers until
equilibrium is reached. All energy changes are adiabatic if the bath
is lagged (to prevent energy loss), in accordance with the first law The word ‘entropy’
of thermodynamics. comes from the Greek
As no chemical reactions occur, we note how these thermo- en tropa, meaning
‘in change’ or ‘during
dynamic changes are purely physical. But since no bonds form or
transformation’.
break, what is the impetus – the cause – of the transfer of energy?
We have already seen the way processes occur with an attendant
increase in disorder. We now introduce the concept of entropy.The
extent of energetic disorder is given the name entropy (and has the
The ‘second law of ther-
symbol S). A bigger value of S corresponds to a greater extent of modynamics’ says a
energetic disorder. process occurs sponta-
We now introduce the second law of thermodynamics: a physic- neously only when the
ochemical process only occurs spontaneously if accompanied by concomitant energetic
an increase in the entropy S. By corollary, a non-spontaneous disorder increases. We
process – one that we can force to occur by externally adding can usually approxi-
energy – would proceed concurrently with a decrease in the ener- mate, and talk in terms
getic disorder. of ‘disorder’ alone.
We can often think of entropy merely in terms of spatial disorder,
like the example of the sugar grains above; but the entropy of a
substance is properly the extent of energetic disorder. Molecules of The energy is trans-
hot and cold water in a bath exchange energy in order to maximize ferred via random,
inelastic collisions bet-
the randomness of their energies.
ween the molecules of
Figure 4.1 depicts a graph of the number of water molecules
water. Such molecular
having the energy E (as y) against the energy of the water mole-
movement is some-
cules E (as x). Trace (a) in Figure 4.1 shows the distribution of times called Brownian
energies in a bath where half the molecules have one energy while
motion; see p. 139.
the other half has a different energy, which explains why the graph
contains two peaks. A distribution of energies soon forms as energy