a piece of copper at 120 degrees celsius has exactly twice the mass of another piece of copper at 40 degrees celsius. The two pieces are brought together and allowed to reach equilibrium. What is the final temperature.
heat lost by 120 C Cu + heat gained by 40 C Cu = 0
I would choose some convenient number like 10 g for one of the pieces and 20 g for the other; substitute into the
[mass x specific heat x (Tfinal-Tinitial)] + [mass x specific heat x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
I obtained an answer approximately 90 C.
To find the final temperature when two objects of different temperatures reach equilibrium, we can use the principle of thermal equilibrium.
In this case, we have two pieces of copper, one at 120 degrees Celsius and the other at 40 degrees Celsius. We are given that the mass of the first piece is twice the mass of the second piece.
Let's denote the mass of the second piece as m, so the mass of the first piece is 2m.
In thermal equilibrium, the heat lost by one object is equal to the heat gained by the other object.
The amount of heat gained or lost by an object can be calculated using the formula: Q = mcΔT, where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
Since both objects are made of copper, we can assume that they have the same specific heat capacity, denoted as c.
Therefore, the heat gained by the 40 degrees Celsius copper piece can be calculated as: Q1 = mcΔT1 = m * c * (final temperature - 40)
Similarly, the heat lost by the 120 degrees Celsius copper piece can be calculated as: Q2 = (2m) * c * (120 - final temperature)
Since the heat gained and the heat lost are equal at thermal equilibrium, we can set up the equation:
m * c * (final temperature - 40) = (2m) * c * (120 - final temperature)
Now, we can solve this equation to find the final temperature.
m * (final temperature - 40) = 2m * (120 - final temperature)
m * final temperature - 40m = 240m - 2m * final temperature
Adding 2m * final temperature to both sides:
3m * final temperature - 40m = 240m
Subtracting 240m from both sides:
3m * final temperature - 40m - 240m = 0
3m * final temperature - 280m = 0
Dividing both sides by m:
3 * final temperature - 280 = 0
3 * final temperature = 280
final temperature = 280 / 3
final temperature ≈ 93.33 degrees Celsius
Therefore, the final temperature when the two pieces of copper reach equilibrium is approximately 93.33 degrees Celsius.