Finding equilibrium temperature when hot iron is placed in water

[TT0]

Homework Statement

A hot (800 K) iron nail of mass 150 g is placed into a 1.0 kg of water at 25°C. What is the common temperature of the 2 objects once they have reached thermal equilibrium? Assume no change of state of the water.

Heat capacity of iron nail is 450 J/kg/K
Heat capacity of water is 4138 J/kg/K

Homework Equations

Q=mc∆T

The Attempt at a Solution

Q lost in nail=Q gained in water

let T = final temperature

0.15*450*(800-T)=1*4138*(T+25+273)
T=-280.38 K

I don't know why it is negative. Can someone explain what I did wrong?

 

[rpthomps]

(T+25+273) should be a difference between the final temperature and initial temp.

 

[TT0]

I see thanks!

 

[TT0]

Is the answer 33.06 C?

 

[rpthomps]

Seems reasonable

 

[TT0]

Thanks again!