Why does a watched pot always take so long to boil

Why does a watched pot always take so long to boil  

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 of energy we can put into the water per unit time was always low in the days of coal and wood fires. Accordingly, a long time was required to boil the water, hence the long wait. 

Imagine we want to convert 1 mol of water starting at a room temperature of, say, 25 °C to steam. In fact we must consider two separate thermodynamic processes we first consider the heat needed to warm the water from 25 °C to its boiling temperature of 100 °C. The water remains liquid during this heating process. Next, we convert 1 mol of the liquid water at 100°C to gaseous water (i.e. we boil it), but without altering the temperature. 

We will at the moment ignore once more the problems caused by volume changes. The change in internal energy A[/(0verall) for the overall process H20(i) at 25 °C H20(g) at 100 °C can be separated into two components  

The popular saying A watched pot never boils arose when most fires were wood or coal, neither of which generates heat as fast as, say, a modern 1 kW kettle. 

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