Posted by **y912f** on Wednesday, February 18, 2009 at 10:13am.

A 0.10 kg piece of copper at an initial temperature of 95degC is dropped into 0.20 kg of water contained in a 0.28 kg aluminum calorimeter. The water and calorimeter are initially at 15degC. What is the final temperature of the system when it reaches equilibrium?

(Cp of Copper=387J/kg * degC; Cpof Aluminum=899J/kg * degC; Cp of Water=4186J/kg * degC)

someone gave me a very long and complicated formula for this. does anyone know a simple way to solve this problem? thanks for any help

- physics -
**drwls**, Wednesday, February 18, 2009 at 10:35am
At thermal equilibrium, the heat lost by the hot copper will equal the heat gained by the water and calorimeter. By the time you have turned that fact into an equation for the final temperature, with symbols for the different masses and Cp's, you will have a lot of terms in a rather cumbersome equation. There is no other way to do it.

0.10*387*(95 - T) = 0.28*899*(T-15) + 0.20*4186*(T-15)

38.7 (95-T) = 1088.9(T-15)

188.9 T + 38.7 T = 16344 + 3676

227.6 T = 20020.

T = 88.0 C

No gurantees on the math.

- physics -
**y912f**, Wednesday, February 18, 2009 at 10:56am
this is what i got:

0.10*387*(95-T)=0.28*899*(T-15)+0.20*4186*(T-15)

38.7(95-T)=1088.92(T-15)

1088.92T+39.7T=16333+3676

1127.62T=20009.5

and i''m confused from here

- physics -
**drwls**, Wednesday, February 18, 2009 at 12:13pm
You're right. I left out a zero in the 1088.9 T term. You changed 38.7 to 39.7, but that is not a big change.

1088.92T +38.7T = 16333+3676

1127.5 T = 20,009

T = 17.7 C. Not much of an increase. That is because the heat capacity of the small piece of copper is much less than that of the calorimeter and water.

- physics -
**aD**, Wednesday, May 8, 2013 at 9:08pm
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