Solving for Final Equilibrium Temperature of Water-Copper System

AI Thread Summary
The discussion revolves around calculating the final equilibrium temperature of a water-copper system after adding hot water to a cooler water-copper mixture. The relevant equation used is Q = mcΔT, which accounts for the heat transfer between the water and the copper container. Participants confirm that the method applied is correct but suggest rechecking algebraic calculations to find the accurate final temperature. The original poster acknowledges the guidance and successfully identifies the error in their approach. The conversation emphasizes the importance of careful algebraic manipulation in solving thermal equilibrium problems.
Sam Vermeulen
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Homework Statement


173 g of water at 20°C is contained in a copper container of mass 327 g. An additional 129 g of water at 100°C is added. What is the final equilibrium temperature (in degrees C) if we treat the system's water and container as isolated?

Homework Equations


Q = mcΔT

The Attempt at a Solution



0 = mwater1c(Tf - Ti) + mwater2cwater(Tf - Ti) + mcopperccopper(Tf - Ti)
0 = (.173kg)(4.186kJ/kg°C)(Tf - 20°C) + (0.129kg)(4.186kJ/kg°C)(Tf - 100°C) + (.327kg)(.387kJ/kg°C)(Tf - 20°C)

I attempted to solve for Tf but the answer was not correct.
 
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Hi Sam Vermeulen and welcome to PF.

The method is correct. Recheck your algebra.
 
kuruman said:
Hi Sam Vermeulen and welcome to PF.

The method is correct. Recheck your algebra.
Thank you! I figured out where I was going wrong. Much appreciated.
 
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