Answer to Question #226543 in Physics for Mike

Question

An electric immersion heater has a power rating of 1500 W. If the heater is placed in a liter of water at 20

Answer 1

Here's what I believe the complete condition of the problem is:

An electric immersion heater has a power rating of 1500 W. If the heater is placed in a liter of water at 20°C, how many minutes will it take to bring the water to a boil? (Assume that there is no heat loss except to the water itself.)

So, the energy required to increase the temperature is

$$Q=cm\Delta \tau.$$

The electrical energy required for this is equivalent to power times time:

$$E=Pt,\\ Q=E,\\ cm\Delta\tau=Pt,\\\space\\ t=\frac{cm\Delta\tau}{P}=\frac{4200·1·(100-20)}{1500}=224\text{ s},$$

or 3 min 44 s.