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INTRODUCTION TO CELLS: TERMINOLOGY AND BACKGROUND 293

Finally, we join the two half-cells via a salt bridge, as
As an extra check,
we note how the salt
Pt (s) |H 2(g) |H (aq) ||Br 2 , Br (aq) |Pt (s) ⊕ .
−
+
bridge dips into the
proton solution, so the
From now on, we will omit both the symbols and ⊕,and merely
term for H + needs to
assume that the right-hand side is the positive pole and the left-hand
be written adjacent to
side the negative.
the symbol ‘||’.
Why do digital watches lose time in the winter?

The temperature dependence of emf

A digital watch keeps time by applying a tiny potential (voltage)
Frequency ν has the SI
across a crystal of quartz, causing it to vibrate at a precise fre-
unit of hertz (Hz). 1 Hz
quency of ν cycles per second. The watch keeps time by counting
represents 1 cycle or
off 1 s each time the quartz vibrates ν times, explaining why the
vibration per second,
majority of the components within the watch comprise a count- so a frequency of ν
ing mechanism. Hz means ν cycles per
Unfortunately, the number of vibrations of the crystal per second second.
is dictated by the potential applied to the quartz, so a larger voltage
makes the frequency ν increase, and a smaller voltage causes ν
to slow. For this reason, the potential of the watch battery must
The voltage from the
be constant.
battery induces a minute
In Section 4.6, we saw how the value of G is never indepen-
mechanical strain in
dent of temperature, except in those rare cases when S (cell) = 0. the crystal, causing it
Accordingly, the value of G (cell) for a battery depends on whether to vibrate – a property
someone is wearing the watch while playing outside in the cold known as the piezo-
snow or is sunbathing in the blistering heat of a tropical summer. electric effect.
And the emf of the watch battery is itself a function of the
change in Gibbs function, G (cell) according to

G (cell) =−nF × emf (7.15)

where F is the Faraday constant and n is the number of moles of
Care: The output volt-
electrons transferred per mole of reaction. The value of G (cell) is age of a battery is only
negative if the reaction proceeds reversibly (see Section 4.3), so the an emf when mea-
emf is defined as positive to ensure that G (cell) is always negative. sured at zero current,
In other words, the value of G (cell) relates to the spontaneous i.e. when not operating
cell reaction. the watch.
So we understand that as the emf changes with temperature, so
the quartz crystal vibrates at a different frequency – all because