One piece of copper jewelry at 101°C has exactly twice the mass of another piece, which is at 36.0°C. Both pieces are placed inside a calorimeter whose heat capacity is negligible. What is the final temperature inside the calorimeter (c of copper = 0.387 J/gK)?

Thanks Bob, this helped!

heat lost by piece 1 + heat gained by piece 2 = 0

[mass jewl 1 x specific heat x (Tfinal-Tinitial)]+[mass jew2 x specific heat x (Tfinial-Tinitial)] = 0

I don't understand it still.

heat lost by one object + heat gained by another object ALWAYS will reach equilibrium at some intermediate temperature. For example, if you have a 2g piece of iron at 20C and another 2 g piece of iron at 30C, you put them together so they can exchange heat, the final temperature will be 25C. Ergo, the 30 C piece of iron lost 5C and the 20 C piece of iron gained 5C.

Your jewelry problem isn't QUITE that simple because they don't weigh the same AND they are at uneven temperatures (not a simple 20 and 30C).
So heat lost or gained is
mass x specific heat metal x (Tfinal-Tinitial).
The mass isn't given, so make up a mass for the first one that is convenient, say 20 g; that makes the second piece of jewelry 10 g. What is the specific heat Cu. That's 0.387 in the problem.
[20 x 0.387 x (Tfinal-101)] + [10 g x 0.387 x (Tfinal-36)]= 0
The ONLY unknown is Tfinal. Solve for that.

To find the final temperature inside the calorimeter, we can use the principle of conservation of energy. The heat lost by the hotter copper piece is equal to the heat gained by the cooler copper piece.

First, let's determine the heat lost by the hotter copper piece. We can use the formula:

Q1 = m1 * c * ΔT1

where Q1 is the heat lost, m1 is the mass of the hotter copper piece, c is the specific heat capacity of copper, and ΔT1 is the change in temperature.

In this case, the hotter copper piece is at 101°C, and we want to find the final temperature inside the calorimeter, so ΔT1 = 101°C - final temperature.

Now, let's determine the heat gained by the cooler copper piece. We can use the same formula:

Q2 = m2 * c * ΔT2

where Q2 is the heat gained, m2 is the mass of the cooler copper piece, and ΔT2 is the change in temperature.

In this case, the cooler copper piece is at 36.0°C, and the final temperature inside the calorimeter is the same as the final temperature of the copper pieces, so ΔT2 = final temperature - 36.0°C.

Since the heat lost by the hotter copper piece is equal to the heat gained by the cooler copper piece, we can set Q1 = Q2:

m1 * c * ΔT1 = m2 * c * ΔT2

Now let's substitute the given values into the equation:

(2 * m2) * 0.387 J/gK * (101 - final temperature) = m2 * 0.387 J/gK * (final temperature - 36.0)

Simplifying the equation:

2 * (101 - final temperature) = final temperature - 36.0

2 * 101 - 2 * final temperature = final temperature - 36.0

202 - 2 * final temperature = final temperature - 36.0

Adding 2 * final temperature to both sides:

202 = 3 * final temperature - 36.0

Adding 36.0 to both sides:

238 = 3 * final temperature

Dividing both sides by 3:

final temperature = 238 / 3 ≈ 79.33°C

Therefore, the final temperature inside the calorimeter is approximately 79.33°C.