A 100 g aluminum calorimeter contains 200g of water at 15 degrees Celsius. If 100 g of lead at 50 degrees Celsius and 60 g of copper at 60 degrees Celsius are placed in the calorimeter, what is the final temperature in the calorimeter?

To find the final temperature in the calorimeter, you can use the principle of conservation of energy, specifically the principle of heat transfer. The heat lost by the lead, copper, and aluminum will be gained by the water.

First, calculate the heat gained or lost by each substance using the formula:

Q = m * c * ΔT

Where:
- Q is the heat gained or lost (in Joules)
- m is the mass of the substance (in grams)
- c is the specific heat capacity of the substance (in J/g°C)
- ΔT is the change in temperature (in °C)

For the aluminum calorimeter:
Q_calorimeter = m_calorimeter * c_aluminum * ΔT_calorimeter

Since the calorimeter and water will reach the same final temperature:
Q_water = m_water * c_water * ΔT_final

For the lead:
Q_lead = m_lead * c_lead * ΔT_lead

For the copper:
Q_copper = m_copper * c_copper * ΔT_copper

According to the principle of heat transfer, the heat lost by each substance will be equal to the heat gained by the water:

Q_water = -(Q_calorimeter + Q_lead + Q_copper)

Now, let's calculate the individual quantities:

Specific heat capacity values:
- c_aluminum = 0.897 J/g°C (specific heat capacity of aluminum)
- c_water = 4.18 J/g°C (specific heat capacity of water)
- c_lead = 0.13 J/g°C (specific heat capacity of lead)
- c_copper = 0.39 J/g°C (specific heat capacity of copper)

Given values:
- m_calorimeter = 100 g
- m_water = 200 g
- T_water_initial = 15°C
- m_lead = 100 g
- T_lead_initial = 50°C
- m_copper = 60 g
- T_copper_initial = 60°C

Now, let's calculate the initial and final heat exchange for each substance:

For the calorimeter:
Q_calorimeter = m_calorimeter * c_aluminum * (T_final - T_initial_calorimeter)

For the water:
Q_water = m_water * c_water * (T_final - T_water_initial)

For the lead:
Q_lead = m_lead * c_lead * (T_final - T_lead_initial)

For the copper:
Q_copper = m_copper * c_copper * (T_final - T_copper_initial)

Finally, substitute the values obtained into the energy exchange equation:
Q_water = -(Q_calorimeter + Q_lead + Q_copper)

By solving this equation, you will find the final temperature, denoted as T_final.