One should always cover a pan while heating (Slideshow version)
Stage 5/5 :
The result is shown more clearly in the diagram: the temperature of the uncovered pan in red and that of the covered pan in green.
Remarks
False: The time difference is too small to be significant. It really doesn't matter whether the pan is covered or not.
And to drink?
We are going to heat 1 litre of water in an uncovered pan and measure the time it takes to boil , then another litre in a covered pan, heated and measured in the same way.
Comparing these times will tell us if it is really necessary to cover the pan.