What Is the Final Temperature After Dropping Hot Coins into Cooler Water?

[jcwhitts]

Homework Statement

In a physics lab experiment a student immersed 191 one-cent coins (each having a mass of 3.00 g) in boiling water, at a temperature of 100 degrees C. After they reached thermal equilibrium, she fished them out and dropped them into an amount of water of mass 0.275 kg at a temperature of 17.0 degrees C in an insulated container of negligible mass.

What was the final temperature of the coins? (One-cent coins are made of a metal alloy - mostly zinc - with a specific heat capacity of 390 J/(kg * K).)

Use 4190 J/(kg* K) for the heat capacity of the water.

Homework Equations

Q=mc(deltaT)

Q1 + Q2=0

The Attempt at a Solution

I'm not sure where you can get a workable system of equations from this problem. I tried finding the Q of the coins, which I found to be Q=(191*.003kg)(390)(T-100) where T=the final temperature of the coins. And the Q of Water: Q=(.275)(4190)(T-17).

You also know that the Q of water and the Q of the coins must be equal to 0 because they are in an insulated container.

Because the water is heated and the coins are cooled, you know that the Q for water is positive and that Qwater=Qcoins, However, they have different final temperatures and I'm not sure how to find one in terms of the other so I can solve the equation I've come up with. Please help!

 

[CompuChip]

I don't know if you did it on purpose or by accident, but you used the same letter T in both equations. Is it really the same? If not, use a different letter. But if you can argue they are, you can set Qwater = Qcoins which gives you: 191*0.003*390*(T - 100) = 0.275*4190*(T - 100) and solve for T (one equation, one unknown).

 

[jcwhitts]

You can't assume the final temperatures are the same, sorry. So Qcoins=Qwater but
(191*.003)(390)(R-100)=.275(4190)(T-17)

 

[jcwhitts]

I guess you can assume the final temperatures are equal. I think it was a problem with my signs in that I overcompensated for the fact that the coins lose heat, so they have a negative value for Q. The final temperature will obviously be less than 100 so I suppose that accounts for the sign change.