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Crazylegs008 · Jul 15, 2008, 11:25 AM

A 11.5 kg piece of zinc at 71.0°C is placed in a container of water. The water has a mass of 18.5 kg and has a temperature of 10.0°C before the zinc is added. What is the final temperature of the water and zinc?

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ebaines · Jul 16, 2008, 05:42 AM

This involves using the initial temp heat capacity of the two materials (zinc and water) to determine the total energy of the system, then finding what the temp would have to be for both materials to be at that temp and have the same total energy. This assumes that no energy is lost as the system comes to equilibrium. Heat capacity is measured in Joules/Gram-degree K (or equivalent units). I assume you have a table of values, so you know what these values are for zinc and water. If we are given:

$ C_z = \text {heat capacity of zinc} \\ C_w = \text {hear capacity of water} \\ $

then:

$ Energy = C_z * 11500g * (273.15+71 K) + C_w * 18500g * (273.15+10 K) = (C_z * 11500 + C_w*18500) * T $

Now solve for T, which is in Kelvins, and convert back to Celsius.