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98 ENERGY AND THE FIRST LAW OF THERMODYNAMICS

Why does a watched pot always take so long to boil?

Introduction to Hess’s law

We sometimes say, ‘A watched pot never boils’. This empirical observation – that
we get bored waiting a long time for the pot to boil – follows because we need to put
a lot of energy (heat) in order for the water to boil. The amount
The popular saying of energy we can put into the water per unit time was always low
‘A watched pot never in the days of coal and wood fires. Accordingly, a long time was
boils’ arose when most required to boil the water, hence the long wait.
fires were wood or Imagine we want to convert 1 mol of water starting at a room
coal, neither of which temperature of, say, 25 C to steam. In fact we must consider
◦
generatesheat asfast
two separate thermodynamic processes: we first consider the heat
as, say, a modern 1 kW needed to warm the water from 25 C to its boiling temperature
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kettle. ◦
of 100 C. The water remains liquid during this heating process.
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Next, we convert 1 mol of the liquid water at 100 C to gaseous
This argument relies water (i.e. we boil it), but without altering the temperature.
only on words. In real- We will at the moment ignore once more the problems caused
ity, the situation is by volume changes. The change in internal energy U (overall) for
somewhat more com- the overall process H 2 O (l) at 25 C → H 2 O (g) at 100 C can be
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◦
plicated because water separated into two components:
expands slightly on
heating, and greatly on Energy U 1 relates to the process
boiling.
◦
◦
H 2 O (l) at 25 C −−→ H 2 O (l) at 100 C
Energy U 2 relates to the process
◦
◦
H 2 O (l) at 100 C −−→ H 2 O (g) at 100 C
so U 1 relates to warming the water until it reaches the boiling temperature, and
U 2 relates to the actual boiling process itself.
We can obtain U (overall) algebraically, according to

(3.11)
U (overall) = U 1 + U 2
We canobtainthe
answer in several dif- In practice, we could have measured U (overall) directly in the
ferent ways because laboratory. Alternatively, we could have measured U 1 or U 2
internal energy is a in the laboratory and found the U values we did not know in a
‘state function’. book of tables. Either way, we will get the same answer from these
two calculation routes.
Equation (3.11) follows directly from U being a state function,
Hess’s law states that and is an expression of Hess’s law. The great German thermody-
the value of an energy
namicist Hess observed in 1840 that, ‘If a reaction is performed in
obtained is indepen- more than one stage, the overall enthalpy change is a sum of the
dent of the number of
enthalpy changes involved in the separate stages’.
intermediate reaction
steps taken. We shall see shortly how the addition of energies in this way
provides the physical chemist with an extremely powerful tool.