Page 116 - Physical chemistry understanding our chemical world

INTRODUCTION TO THERMODYNAMICS: INTERNAL ENERGY 83

Why do we still feel hot while sweating
on a humid beach?

State functions

Sometimes we feel hot even when sweating, particularly in a humid environment
like a beach by the sea on a hot day. Two processes occur in tandem on the skin:
evaporation (liquid water → gaseous water) and condensation (gaseous water →
liquid water). It is quite possible that the same water condenses on our face as
evaporated earlier. In effect, then, a cycle of ‘liquid → gas → liquid’ occurs. The
two halves of this cycle operate in opposite senses, since both exo- and endo-thermic
processes occur simultaneously. The net change in energy is, therefore, negligible,
and we feel no cooler.
These two examples of energy change involve water. The only difference between
them is the direction of change, and hence the sign of U. But these two factors are
related. If we were to condense exactly 1 mol of steam then the amount of energy
released into the skin would be 40 700 J. The change in internal energy U (ignoring
volume changes) is negative because energy is given out during the condensation
process, so U =−40 700 J.
Conversely, if we were to vaporize exactly 1 mol of water from the skin of a
sweaty body, the change in internal energy would be +40 700 J. In other words, the
magnitude of the change is identical, but the sign is different.
While the chemical substance involved dictates the magnitude of U (i.e. the
amount of it), its sign derives from the direction of the thermodynamic process. We
can go further: if the same mass of substance is converted from state A to state B,
then the change in internal energy is equal and opposite to the same process occurring
in the reverse direction, from B to A. This essential truth is depicted schematically
in Figure 3.3.
The value of U when condensing exactly 1 mol of water is termed the molar
change in internal energy. We will call it U m (condensation) , where the small ‘m’
indicates that a mole is involved in the thermodynamic process. Similarly, the molar

∆U (reaction)

A B

−∆U (reaction)

Figure 3.3 The change in internal energy when converting a material from state A to state B is
equal and opposite to the change in U obtained when performing the same process in reverse, from
BtoA