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THE TEMPERATURE DEPENDENCE OF ENTROPY 139

This result of S (total) being positive helps explain how consid-
As a new criterion for
ering the entropy of a system’s surroundings can obviate the appar-
reaction spontaneity,
ent problems caused by only considering the processes occurring we say S (total) must be
within a thermodynamic system. It also explains why crystallization positive.We must con-
is energetically feasible. sider the surroundings
The concept of a thermodynamic system is essentially macro- if we are to understand
scopic, and assumes the participation of large numbers of how the overall extent
molecules. Indeed, the word ‘system’ derives from the Greek of energetic disorder
sustema, meaning to set up, to stay together. increases during a
process.

4.2 The temperature dependence of entropy

Why do dust particles move more quickly by Brownian
motion in warm water?

Entropy is a function of temperature
Brownian motion is the random movement of small, solid particles sitting on the
surface of water. They are held in position by the surface tension γ of the meniscus.
When looking at the dust under a microscope, the dust particles appear to ‘dance’
and move randomly. But when the water is warmed, the particles, be they chalk or
house dust, move faster than on cold water.
The cause of the Brownian motion is movement of water mole-
cules, several hundred of which ‘hold’ on to the underside of each ‘Brownian motion’ is a
dust particle by surface tension. These water molecules move and macroscopic observa-
jostle continually as a consequence of their own internal energy. tion of entropy.
Warming the water increases the internal energy, itself causing the
molecules to move faster than if the water was cool.
The faster molecules exhibit a greater randomness in their mo- Entropy is a function of
tion than do slower molecules, as witnessed by the dust particles, temperature.
which we see ‘dancing’ more erratically. The Brownian motion is
more extreme. The enhanced randomness is a consequence of the water molecules
having higher entropy at the higher temperature. Entropy is a function of temperature.

Why does the jam of a jam tart burn more than does
the pastry?
Relationship between entropy and heat capacity

When biting into a freshly baked jam tart, the jam burns the tongue but the pastry
(which is at the same temperature) causes relatively little harm. The reason why the
jam is more likely to burn is its higher ‘heat capacity’ C.