I can't seem to get the right answe

[Em_And_Chem]

I can't seem to get the right answer, any help is appreciated!
I have a question under the topic "First law of thermodynamics", I've also been told that I should use the complete Energy (or perhaps entropy?) balances.
The question goes as follows; A body of iron with constant heat capacity 460 J/(kg K) and mass 3 kg is heated with a heating effect of 500 W. How long does it take to heat the body from 250C to 1000C if the heat loss to the surroundings can be estimated at 15 W?

so far Ive (perhaps incorrectly) assumed:

The answer is apparently 213 seconds

 

[Latexman]

Which temperatures are right? 250 C ---> 1000 C or 25 C ---> 100 C.

Spoiler

213 seconds aligns with 25 C ---> 100 C.
Q = MCp[Δ]T = 3 x 460 x 75 = 103500 J
500 W - 15 W = 485 W = 485 J/s
103500 J / 485 J/s = 213 s

Good Luck,
Latexman

 

[lucky-guesser]

I agree with latexman, you are making this way too complicated. This can be done with one simple equation.

Also, as he pointed out, your answer corresponds with 25-100, not 250-1000, although all you need to do to correct for that is move the decimal over one spot in your answer.

 

[BridgeSmith]

I think the last zero in the ext of the post was supposed to be degree symbol, but it didn't come through as a superscript.

 

[rb1957]

he had the right "Q", but didn't figure the nett heat input (500W-15W), and so the time to gain the required "Q".

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[Em_And_Chem]

Thank you so much! It was 100, youre right, I had done a handwriting to text feature and didnt proofread properly! It really does work to think it through logically I suppose, I was stuck in the mindset that I had to use the energy balance equation, but I much prefer your suggestion. Thanks again!