# Time to Heat Water

1. Apr 11, 2014

### GoodOldLimbo

1. The problem statement, all variables and given/known data

A tank contains 125 litres of water. If it's temperature is 20C, how long would it take for a 2kW immersion heater to raise its temperature to 60C if the average rate of heat loss is 150W?

2. Relevant equations

I am using the specific heat capacity equation:

ΔQ = mcΔT

3. The attempt at a solution

ΔQ = 125 x 4200 x 40 = 21, 000, 000 J

2kW = 2kJ per second.

Concerning Heat Loss:
2000W - 150 W = 1850 W = 1.85kW

21,000KJ = 11, 351 seconds.

11, 351 / 60 = Approximately 190 minutes.

I kind of get the feeling I'm not right. Any tips? Would be appreciated.

2. Apr 11, 2014

### Simon Bridge

Unless your course includes thermal mixing and nonlinear differential equations, that seems to be fine.
The way you could check this sort of thing is relate it to common experience ...

Your figure works out to 1.5mins to heat 1L of water by 40deg, or 3mins to start it boiling.
A good-sized cup would be about 1/3L ... or 1min to start boiling.
Does that seem reasonable?

An electric kettle is usually 2-3kW ... does it normally take about a minute or so to boil a cup of water?

3. Apr 11, 2014

### dauto

Your answer seems fine. I'd just take marks down for the statement "21,000KJ = 11, 351 seconds." which is obviously wrong.

4. Apr 11, 2014

### Simon Bridge

dauto is correct - someone marking what you wrote will expect you to be articulate.
It is easy to see what you mean, but it is sloppy notation.