A water heater has a power rating of 1 kW. how many seconds will this heater take to boil 1 liter of water?

4.65 minutes.

Explanation:
Theoretical Assumptions (not realistic): 1) ALL of the heat energy is transferred to the water, and 2)the water is uniformly heated. 3) The water density is 1.0g/mL.
Because we are only heating it TO the “boiling point”, ONLY the energy to heat the water from 20 to 100’C using the heat capacity or specific heat of water is required. A “Watt” is 1 Joule/second. The specific heat of water is 4.184 J/g-’C. Water mass is 1000g. The energy required to heat it is therefore
1000
g
⋅
4.184
(
J
g
’
C
)
⋅
(
100
−
20
)
’
C
=
334720
J

The heater supplies 1200 J/s, so the time to provide this heat to the water is
334720
J
1200
(
J
s
)
=
278.9
s
or 4.65 minutes.