How Long Does a 2.02 kW Heater Take to Match the Heat from Solar-Heated Water?

[rlc]

Homework Statement

To help keep his barn warm on cold days, a farmer stores 859 kg of solar-heated water (Lf = 3.35E+5 J/kg) in barrels. For how many hours would a 2.02 kW electric space heater have to operate to provide the same amount of heat as the water does, when it cools from 11.3 to 0 °C and completely freezes?

Homework Equations

Q=mc(deltaTdegC)+mL

The Attempt at a Solution

Q=(859)(4187)(11.3)+(859)(335000)
Q=328406952 J
1kW=1000W=1000J/sec
1000t=328406952 J
t=328406 secs*1min/60secs*1hour/60mins=91 hours

But this is wrong. What am I missing?

 

[NascentOxygen]

You have calculated for a 1000w heater.

 

[collinsmark]

You're correct that 1 kW = 1000 J/sec. But the heater is a 2.02 kW heater, not a 1 kW heater.

[Edit: like NascentOxygen said.]