Need help with basic specific heat capacity problem

[lilmul123]

Homework Statement

The specific heat of a certain metal can be determined by measuring the temperature change that occurs when a piece of the metal is heated and then placed in an insulated container that is made of the same material and contains water. Suppose the piece of metal has a mass of 86 g and is initially at 100°C. The container has a mass of 162 g and contains 504 g of water at an initial temperature of 20.0°C. The final temperature is 21.4°C. What is the specific heat of the metal?

Homework Equations

Q = mc(deltaT)
Q1 + Q2 + Q3 = 0

4.18 kJ/kg*K is the known capacity of water.

The Attempt at a Solution

I set c equal to the specific heat capacity I'm looking for. Q1 is the metal going into the bucket, Q2 is the metal of the bucket, and Q3 is the water itself. Since Q1 and Q2 are the same metal, their c's are the same.

My equation looks like this where the specific heat capacities are in kJ/kg*K:

(.086)(c)(-78.6) + (.162)(c)(1.4) + (.504)(4.18)(1.4) = 0

Solving for c gives me 2.214 kJ/kg*K which is incorrect. Have I missed a step?

 

[ideasrule]

Check your algebra. I get 0.45 kJ/kg*K using your equation.

 

[Legion81]

(.086)(c)(-78.6) + (.162)(c)(1.4) + (.504)(4.18)(1.4) = 0

Solving for c gives me 2.214 kJ/kg*K which is incorrect. Have I missed a step?

Check your algebra again when you solve for c. It looks like you may have made a mistake. I'm getting about 0.45.

 

[lilmul123]

Oh geez, I divided by the wrong side in my last step of the algebra. Thanks!