Thermal Equilibrium of Hot Iron & Water

AI Thread Summary
A hot iron nail at 800 K is placed in 1.0 kg of water at 25°C, and the goal is to find the final temperature at thermal equilibrium. The heat lost by the nail equals the heat gained by the water, leading to the equation 0.15*450*(800-T)=1*4138*(T-25). The initial calculation mistakenly included an incorrect temperature adjustment, resulting in a negative value for T. After correcting the equation, the final temperature is determined to be approximately 33.06°C. This solution highlights the importance of proper temperature reference points in thermal equilibrium calculations.
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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?
 
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(T+25+273) should be a difference between the final temperature and initial temp.
 
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I see thanks!
 
Is the answer 33.06 C?
 
Seems reasonable
 
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Thanks again!
 

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