Thread: What was the temperature of the water after the iron and the water came to thermal equilibrium?

A 375 g piece of iron was heated to 975 degress Celsius and then quenched in a bucket containing one gallon of water at 20 degress Celsius. What was the temperature of the water after the iron and the water came to thermal equilibrium? The answer is 30.1 degrees Celsius. How do you solve this. It would be helpful if you show this step by step. Thank you.

To solve this, you use the principle that Heat In = Heat Out. The heat comes out of the hot iron and goes into the cool water. The equation for heat is Q = mC?T where Q = heat, m = mass, C = specific heat of the substance and ?T = difference in temperature. Now set this up so that the heat out of the iron is equal to the heat into the water. One gallon of water is 3.785 L or 3785 ml and at 1g/ml, this is 3785g.

(375 g)(0.44 J/g deg C)(975-x) = (3785 g)(4.184 J/g deg C)(x - 20)
160875 - 165x = 15836.44x - 316728.8
477603.8 = 16001.44x
29.8 deg C = x

Rounding error? C for iron might have been used as 0.45

I would give credit for this.