The amount of heat required to vaporize a certain amount of water is given by:
Q = ml
where Q is the amount of heat, m is the mass of water, and l is the specific latent heat of vaporization.
In this case, the heat energy supplied to the water is:
Q = Pt
where P is the power supplied and t is the time taken.
Since the water is at its boiling point, its temperature remains constant while it is vaporizing. Therefore, the energy supplied to the water is solely used for vaporization.
Equating the two expressions for Q, we have:
Pt = ml
Solving for t, we get:
t = ml / P
where m = 250 g and l = 2260 J/g.
Substituting the values, we get:
t = (250 g) x (2260 J/g) / (3000 W) = 0.1883 hours
Converting to minutes, we have:
t = 0.1883 hours x (60 minutes/hour) = 11.3 minutes (approx.)
Therefore, it will take approximately 11.3 minutes for 250 g of water to vaporize.