Question

A blacksmith heats a 1.4 kg iron horseshoe to 500?C , then plunges it into a bucket containing 20 kg of water at 15?C

What is the equilibrium temperature?

Express your answer using two significant figures.

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Answer 1

Solution Key Number One: We start by calling the final, ending temperature 'x.' Keep in mind that BOTH the iron and the water will wind up at the temperature we are calling 'x.' Also, make sure you understand that the 'x' we are using IS NOT the ?t, but the FINAL temperature. This is what we are solving for.

The warmer iron goes down from to 500 to x, so this means its ?t equals500 minus x. The colder water goes up in temperature, so its ?t equals x minus 15.

To compute the absolute distance, it's the larger value minus the smaller value, so 500 to x is 500 minus x and the distance from x to 15 is x minus 15

Solution Key Number Two: the energy amount going out of the warm water is equal to the energy amount going into the cool water. This means:

q_lost = q_gain

So, by substitution, we then have:

(1.4) (500 - x)(0.45) = (20) (x - 15) (4.184)

.63(500-x)=83.68*(x-15)

(500-x)=132.82*(x-15)

Solve for x

x= 18.62 degree ANSWER

Please note the use of the specific heat value for iron. It is 0.45 J per gram degree Celsius.