# Calorimetry Problem: Final Temp of 3.0kg Gold & 0.22kg H20

• ch3570r
In summary, the final temperature when a 3.0 kg gold bar at 99 degrees celsius is dropped into 0.22 kg of water at 25 degrees celsius is 47 degrees celsius. This is determined by using the equation CpH20 * H20M * (Tf - Ti) = -CpAu * AuM * (Tf - Ti) and solving for Tf. The negative sign on one side of the equation represents the conservation of energy, where the heat lost by the gold bar is equal to the heat gained by the water.

#### ch3570r

1. What is the final temperature when a 3.0 kg gold bar at 99 degrees celsius is dropped into 0.22 kg of water at 25 degrees celsius.

H20 Heat Capacity (CpH20)= 4186
H20M (mass) = .22 kg
H20Ti (initial temperature) = 25 degrees celsius
Au (CpAu)= 129
AuM (mass) = 3.0 kg
AuTi (initial temperature) = 99 degrees celsius

2. CpH20 * H20M * ∆TH20 = CpAu * AuM * ∆TAu
(where ∆T is change in temperature)

3. I *think* I am missing two variables, but I am not sure if I am correct. I am missing the change in temperature for H20, and the final temperature. In order to get either answer, I need another variable. However, I do know that I could get ∆TAu by (Temperature F - Temperature initial), but again, I would need the final temperature.

Im not sure what I should do in order to find the change in temperature of H20, or maybe I am just reading the problem wrong. I do know that the answer should come out to 47 degrees celsius.

The final temperature is going to be the same for both, since the system goes to equilibrium. That is the only unknown variable. You have to remember to conserve energy, so the heat lost by the gold bar will be gained by the water. This means your equation isn't quite right.

∆T= (Temperature F - Temperature initial) is useful.
Put this expression for each substance in your equation instead of just ∆T, since "Temperature F" is what you're solving for.

How about final temperature as another variable? What does your equation 2. look like in terms of that variable?

ok, I am not sure how to set up the equation if its wrong. I can change the equation to CpH20 * H20M * (Tf - Ti) = CpAu * AuM * (Tf - Ti). That would mean that energy is conserved. Is that enough to solve the problem. I could try to get Tf by itself, and get the answer that way.

Well, I plugged in the numbers, with the answer, and here is what I got;

4186 * .22 * (47 - 25) = 129 * 3 * (47 - 99)

This comes to 20260 = -20124. There seems to be a large margin of error, so I am not sure its correct.

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You are still missing one important point. The energy must be conserved, as I mentioned before. So think of it like
(heat lost by bar) + (heat gained by water) = 0.
Do you see what is wrong with your equation now?

Ive been messing around with the problem for a while, but have had no luck thus far. I'll try to figure it out tomorrow, but thanks for the help guys.

So close, yet so far...

You're almost there.

"I can change the equation to CpH20 * H20M * (Tf - Ti) = CpAu * AuM * (Tf - Ti). That would mean that energy is conserved."

This is almost correct, you are just missing a negative sign on one side of your equation.

"Heat lost by bar must be the same as heat gained by water"

Do you see where it should go? Once you have that in the right place, carefully solve your equation for Tf.