In a foundtry operation, molten lead of mass 90 g at 327.3 C is poured into an i

Question

In a foundtry operation, molten lead of mass 90 g at 327.3 C is poured into an iron casting block tht has a mass of 300 g and is initially at 20 C. What is the equilibrium temperature of the system? Assume no heat losses to the surroundings.

Heat loss = heat gain.
(0.09 kg)(2.45X10^4 J/kg) + (0.09kg)(128 J/kg*C)(327.3-Tf) = (0.3 kg)(448 J/kg*C)(Tf-20C)
solved Tf = 59.4 C
MY QUESTION: is what is the first part (the 0.09 x 2.45X10^4 J/kg) for and why do I need it. I would have just set the two equal to each other, but would have had the wrong answer. Thanks for the help!

Explanation / Answer

That part, in question, is part of the heat lost. The formula for that part is Q = mHf where Hf is the latent heat of fusion of the lead. This initial lead is molten, meaning it is in liquid form. When it reaches the equilibrium temperature, it is now a solid, so it changed phase. Remember that during a phase change the temperature does not change, so Q = mH. Whereas a temp change does occur as the substance heats up while in the same phase by the formula Q = mcT. What you basically have, for your equation, is...

mHf(lead) + mcT(lead) = mcT(iron)

Hope that helps.

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