Why do digital watches lose time in the winter

A digital watch keeps time by applying a tiny potential (voltage) across a crystal of quartz, causing it to vibrate at a precise frequency of v cycles per second. The watch keeps time by counting off 1 s each time the quartz vibrates v times, explaining why the majority of the components within the watch comprise a counting mechanism. 

Unfortunately, the number of vibrations of the crystal per second is dictated by the potential applied to the quartz, so a larger voltage makes the frequency v increase, and a smaller voltage causes v to slow. For this reason, the potential of the watch battery must be constant. 

In Section 4.6, we saw how the value of AG is never independent of temperature, except in those rare cases when A.S iccii, = 0. Accordingly, the value of AG(cen) for a battery depends on whether someone is wearing the watch while playing outside in the cold snow or is sunbathing in the blistering heat of a tropical summer. 

And the emf of the watch battery is itself a function of the change in Gibbs function, AG(ceu) according to 

So we understand that as the emf changes with temperature, so the quartz crystal vibrates at a different frequency - all because 

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