Final temperature when 10 kg zinc at 68°C is added to 32 kg water at 14°C

[DrMcDreamy]

Homework Statement

A 10 kg piece of zinc at 68◦C is placed in a container of water. The water had a mass of 32 kg and a temperature of 14◦C before the zinc was added. The specific heat of zinc and water are 388 J/kg ·◦C and 4180 J/kg ·◦C. What is the final temperature of water and zinc? Answer in units of ◦ C.

Homework Equations

How do you do this? What formula do I use? TIA

 

[danago]

Think about the law of energy conservation. If you assume that the system is insulated from the surroundings, then any heat transferred from the water will be absorbed by the zinc. i.e.:

Energy gained by water = energy lost by zinc

You also know that two objects in contact will eventually reach thermal equilibrium, so that their final temperatures are the same. What final temperature, T, will make the energy transferred by the water and zinc equal?

 

[DrMcDreamy]

So is it 41 C?

 

[DrMcDreamy]

m_ZnC_Zn(T_f-T_{Zn i}) + m_H2OC_H2O(T_f-T_{H2O i})=0

When I plug in my numbers:

(10 kg)(388 J/kg C)(T_f-68 C) + (32 kg)(4180 J/kg C)(T_f- 14 C) = 0
3880 J/C (T_f-68 C) + 133760 J/C (T_f- 14 C) = 0

Than?!