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)?
To find the final temperature inside the calorimeter, we can use the principle of conservation of energy. The heat lost by one piece of copper jewelry is equal to the heat gained by the other piece and the calorimeter.
Let's denote the mass of the first piece of jewelry as m1, its initial temperature as T1, the mass of the second piece of jewelry as m2, its initial temperature as T2, and the final temperature inside the calorimeter as Tf.
We can start by calculating the heat lost by the first piece of jewelry using the formula:
Q1 = m1 * c * (Tf - T1)
where Q1 is the heat lost, m1 is the mass of the first piece, c is the specific heat capacity of copper, and Tf is the final temperature.
Next, we can calculate the heat gained by the second piece of jewelry using the formula:
Q2 = m2 * c * (Tf - T2)
where Q2 is the heat gained, m2 is the mass of the second piece, c is the specific heat capacity of copper, and Tf is the final temperature.
Since the calorimeter has negligible heat capacity, all the heat gained by the second piece will be transferred to it, so we can write:
Q2 = Qcalorimeter
Now, since we are given that the mass of the first piece is exactly twice that of the second piece, we can write:
m1 = 2 * m2
Substituting this into the equation for Q1 and rearranging, we get:
Q1 = (2 * m2) * c * (Tf - T1)
Q1 = 2 * (m2 * c * (Tf - T1))
Q1 = 2 * Q2
Since Q1 is equal to 2 times Q2, we can equate the expressions for Q1 and Q2:
2 * (m2 * c * (Tf - T1)) = m2 * c * (Tf - T2)
Simplifying the equation, we have:
2 * (Tf - T1) = Tf - T2
2 * Tf - 2 * T1 = Tf - T2
2 * Tf - Tf = 2 * T1 - T2
Tf = T2 + 2 * T1
Plugging in the values T2 = 36.0°C and T1 = 101.0°C, we can calculate Tf:
Tf = 36.0°C + 2 * 101.0°C
Tf = 36.0°C + 202.0°C
Tf = 238.0°C
Therefore, the final temperature inside the calorimeter is 238.0°C.